Quantum Physics Paper Analysis

Quantum teleportation (QT) over satellite-based free-space optical (FSO) channels is a promising approach for long-distance quantum communication. However, its performance is significantly degraded by atmospheric loss and turbulence. In this paper, we investigate continuous-variable (CV) QT in a dual-downlink scenario, where a satellite distributes entangled states to two ground stations. To mitigate channel-induced degradation, we employ a non-Gaussian entanglement distillation protocol based on the sequential application of photon addition and photon subtraction (PA-PS) on the weaker channel. The results show that the proposed scheme improves teleportation fidelity by up to 7.7% and enhances entanglement negativity by approximately 105% in the low-to-moderate (below 600 km) loss regime. In addition, we identify an optimal squeezing parameter that balances entanglement strength and noise sensitivity. Taken together, these results demonstrate the effectiveness of PA-PS distillation for improving CV quantum communication in realistic satellite networks. We further characterize the trade-off between fidelity gain and the heralded success probability of the protocol.

Efficiently solving nonlinear ordinary and partial differential equations using a quantum computer is a major challenge due its inherent linearity. To circumvent this challenge, the Carleman linearization method has been proposed to transform a nonlinear ordinary differential equation into a linear system of equations, the primary advantage being that existing quantum linear systems algorithms may then be applied to obtain a solution. However, this methodology also brings forth several major challenges that must be addressed to attain a quantum advantage. Herein, we address several of these challenges enabling us to solve the Carleman linearized one-dimensional Burgers' equation on real and simulated quantum hardware. All simulations were performed on BlueQubit's platform allowing for quantum circuits to be run on GPU or QPU's seamlessly. We first demonstrate that the Carleman linearized Burgers' equation can be efficiently loaded onto a quantum computer using the linear combination of non-unitaries method, an alternative to the linear combintaiton of unitaries approach. Once loaded, the linear system is then solved using the variational quantum linear solver. Since a naive implementation of this solver is hindered by the barren plateau phenomenon, we introduce a multigridding method to solve the problem in a series of stages with the solution of the previous stage acting as a warm start for the next stage. This approach is found to significantly improve the accuracy of the solution compared with a naive cold start. Finally, circuits with a combined number of spatial and temporal discretization points totaling up to $2^{80} \approx 10^{24}$ are transpiled onto real quantum hardware demonstrating that the proposed methodology could feasibly produce a quantum advantage on future hardware.

Quantum phase transitions in many-body systems give rise to highly entangled states, and understanding their quantum correlations is crucial for characterizing quantum materials. However, traditional entanglement measures such as entanglement entropy are difficult to interpret for noisy or mixed states and require complex circuits to evaluate. Therefore, we explore the Positive Partial Transpose (PPT) criterion, coupled with overlapping state tomography, as an efficient and scalable spin-spin entanglement witness. It detects pairwise entanglement from reduced density matrices, distinguishes quantum from classical correlations, and applies to both pure and mixed states. It is ideal for studying condensed matter systems prepared on noisy quantum devices as well as future extensions to finite temperatures. We demonstrate the approach on quantum hardware, using variational circuits to prepare quantum critical states with up to 20 qubits and completely map their two-spin entanglement across various quantum phase transitions.

Spontaneous collapse models provide a possible solution to the measurement problem by modifying standard quantum dynamics. The modification consists of adding non-linear and stochastic terms inducing wavefunction collapse in space. Non-Markovian versions of these models are motivated by physical reasons, phenomenological consistency, and potential for relativistic extensions. Here, we investigate a non-Markovian version of the Poissonian Spontaneous Localization (PSL) model, i.e., a model characterized by instantaneous and localized collapse events. We assume that our model is characterized by a typical time scale $τ_C$ so that, given an initial state $ρ_0$ of standard quantum matter at time $t=0$, we derive an effective long-time ($t\gg τ_C$) statistical dynamics in terms of a CPTP map $Φ_t$. We then show how $Φ_t$ can be made equal to that obtained by non-Markovian CSL models. Moreover, given $Φ_t$, we obtain the associated time-convolutionless master equation by means of a supercumulant expansion. Finally, we characterize the collapse events process (for events with $t \gg τ_C$) given an initial quantum state $ρ_0$ at $t=0$.

Hardware teams building fault-tolerant quantum computers (FTQCs) must decide which imperfections to suppress, and that decision requires the logical performance of the architecture under the device's actual noise. Hardware noise often departs from the stochastic Pauli models used by scalable stabilizer simulators: superconducting transmons leak out of the computational subspace, neutral atoms scatter through intermediate states, trapped ions heat as their motional modes absorb phonons, and miscalibrated controls over-rotate coherently. We present Plaquette, a theoretical framework and software suite that computes the logical performance of fault-tolerant architectures directly from the physics of such imperfections. In Plaquette, a hardware error model is specified once, as Kraus operators, Hamiltonian-Lindblad dynamics, or an experimentally reconstructed quantum channel, and is compiled automatically into the exact or approximate representation required by each of four sampler classes: stabilizer sampling for Pauli noise, the new XPauli sampler for leakage and environment sectors, near-Clifford samplers for coherent errors, and full-state simulation for exact reference calculations. We validate the XPauli and near-Clifford samplers against full-state simulation, which they can match within statistical uncertainty while Pauli twirling can fall short depending on the error model. We demonstrate the framework on three error models: leakage in superconducting qubits, intermediate-state scattering in neutral atoms, and heating in trapped ions. The size of the discrepancy between Plaquette and Clifford-only simulations varies with platform and noise process, so reliable thresholds, error budgets, and overhead estimates require the most accurate simulation available. Plaquette provides a direct path from the open-system physics of a device to the logical performance of the FTQC built on it.

Phenomena that slip beyond the grasp of our classical intuition reveal uniquely quantum effects that deepen our understanding of the physical world and enable advances in information processing, particularly in quantum communication and computation. One such phenomenon is quantum steering, whereby measurements performed by one party influence the conditional states of another when the two share an entangled quantum system. If the observed correlations cannot be explained by a local hidden state model, the state is said to be steerable. In this work, we investigate the typicality of this behavior: given a generic two-qubit state and $m$ Haar-random projective measurements, what is the probability of observing steering? We derive analytical expressions for the steering probability $\mathcal{P}_S$ of Werner states in two- and three-setting scenarios, the latter restricted to coplanar projective measurements on the Bloch sphere. For larger numbers of settings and various random states ensembles, we perform numerical analyses showing that $\mathcal{P}_S$ increases systematically with the number of measurements and substantially exceeds the corresponding probabilities associated with Bell nonlocality. Our results demonstrate that random states with minimal environmental coupling exhibit a high probability of steering for finite $m$ and approach genuine typicality, $\mathcal{P}_S=100\%$, as the number of settings increases. We provide a detailed characterization of $\mathcal{P}_S$ across different state ensembles and specific families, including Bell-diagonal and Werner states, identifying those with the greatest non-classical potential and highlighting their relevance for protocols in which steering serves as a key resource.

Programmable quantum simulators are beginning to access correlators of increasing complexity, ranging from four-point out-of-time-ordered correlators to even higher-order many-body correlators. The theoretical framework for interpreting such data, however, remains comparatively underdeveloped. Although a variety of higher-order correlators can be constructed straightforwardly, their physical meaning is often difficult to infer. A further complication is that different correlators are generally not independent: some may be mutually redundant, while others may encode genuinely distinct information. These features make it necessary to analyze correlators not as isolated quantities, but as a structured family. In this work, we develop a geometric framework for the collective analysis of higher-order correlator families. By representing correlators as inner products between operator words, we recast each family as a geometry in operator space. The key idea is to introduce conditioning subspaces that separate this geometry into reducible information, already explained by a chosen resolved sector, and irreducible information, encoded in the residual correlator geometry. Focusing on the latter component, we define irreducible volume profiles that quantify how broadly the unexplained part of a correlator family spreads over independent geometric directions. This perspective leads to several complementary forms of conditioning. Canonical conditioning optimally explains a correlator family. Targeted conditioning fixes the resolved sector to isolate a chosen physical feature. Krylov and cross conditioning extend the framework from a single correlator family to comparisons among correlator geometries. Our framework reveals irreducible structures hidden at the level of individual correlator values and establishes correlator geometry as a higher-level description of quantum many-body dynamics.

In this paper we give a systematic and unified treatment and extensions of various results on a new notion of quantum $f$-divergences defined from quantum hockey stick divergences, the theory of which has been developed recently in \cite{BHT_fdiv,HircheTomamichel_integral,LiuHircheCheng2025}. In particular, we consider non-normalized states and hockey stick $f$-divergences defined from more general notions of quantum hockey stick divergences, as well as a somewhat more general form of the integral representation defined in terms of an additional real parameter. We also consider the extension of the theory to general von Neumann algebras, and extend various results from \cite{HircheTomamichel_integral,LiuHircheCheng2025} to this setting. Our main results here are the representation of the hockey stick $f$-divergences in terms of Neyman-Pearson error probabilities, which was given in the finite-dimensional case in \cite{LiuHircheCheng2025}, an extension of Jen\v cová's result \cite{Jencova2023} on the detection of reversibility of a quantum channel on a pair of states in terms of the hockey stick divergences, and an extension of a result in \cite{HircheTomamichel_integral} showing that the regularized hockey stick Rényi $α$-divergences coincide with the Petz-type Rényi divergences for $α\in(0,1)$ and with the sandwiched Rényi divergences for $α>1$. Moreover, we give some partial results on the characterization of when different notions of quantum $f$-divergences give the same value on a pair of quantum states.

Whether a heat engine can approach Carnot efficiency while maintaining finite power is a fundamental question in finite-time thermodynamics. For classical Markovian heat engines with local interactions, the power-efficiency trade-off forbids an asymptotic approach to Carnot efficiency at finite power. In quantum systems, by contrast, degeneracy, symmetry, and collective jumps have been theoretically predicted to enable such an asymptotic attainment by enhancing activity. It has remained open, however, whether this mechanism can be realized in an experimentally implementable heat engine. In this Letter, we propose a superconducting-circuit heat engine that emulates the collective enhancement, thereby enabling an asymptotic approach to Carnot efficiency at finite power. This result demonstrates that, in an implementable model, such an enhanced dissipative mechanism circumvents the power-efficiency trade-off of classical Markovian engines. Our work connects abstract bounds in finite-time thermodynamics to a concrete circuit-QED platform and suggests a route toward quantum-device design based on collectively enhanced dissipative processes.

Quantum key distribution (QKD) brings the promise of communication with information-theoretic security but is limited in practice due to its susceptibility to noise, losses, and device imperfections. To address these challenges, we propose a robust high-dimensional (HD) one-sided device-independent QKD (1sDI-QKD) protocol and present a proof-of-principle experimental implementation using photons entangled in the transverse-spatial degree-of-freedom. We develop a systematic security analysis of HD 1sDI-QKD protocols, leveraging quantum steering to certify security, and evaluate achievable secret key rates for different measurement configurations and system dimensions using reverse reconciliation. Our analysis shows that increasing the dimension enhances robustness against both noise and loss. We then demonstrate the key experimental building blocks required for implementing the protocol: (a) a high-quality source of high-dimensional photonic entanglement, and (b) a fully programmable, high-dimensional multi-outcome measurement device operating in up to dimension 11. Using these components, we obtain positive key rates for all investigated dimensions under the fair-sampling assumption, with the highest key rates achieved for dimension d=7. Finally, we discuss the steps required for a practical, loophole-free implementation of 1sDI-QKD in realistic regimes of loss and noise.

We perform a semiclassical, large-spin S, analysis of the quantum approximate optimization algorithm (QAOA) on the Sherrington-Kirkpatrick (SK) model, using the truncated Wigner approximation. Fixing the QAOA angles to their previously determined optimal S=1/2 values, we observe a non-monotonic dependence of the final energy on the spin. At small S the semiclassics is dominated by noise, while the large-S limit is constrained by the exponential growth of the initial fluctuations. For a depth-p QAOA one achieves the optimal balance at S of order p, resulting in a convergence of the final energy to the Parisi value like log(p)/p. We find that the semiclassics slightly outperforms the true spin-1/2 QAOA, and thus suggest they both converge to the Parisi value in the same way. Finally, removing all the initial noise, and re-optimizing the parameters to account for that change, results in superior performance with 1/p convergence.

We present a trade-off between the amount of observed measurement incompatibility and the capabilities of a classical Eavesdropper in a prepare-and-measure scenario. The result is based on a qualitative connection between measurement incompatibility and randomness generation together with the utilization of incompatibility witnesses as randomness certificates. This allows one to use a geometric measure of incompatibility, the generalised robustness, to bound Eve's strategies through a semi-definite program, while providing an explicit protocol for generating randomness from any set of incompatible measurements. By translating the result to quantum steering, we find a tight connection between steerability and randomness generation in a setting using any finite number of measurement inputs. We further show how our techniques can be generalised to scenarios where Eve has a quantum memory by using a dimensional generalisation of joint measurability.

The scalability of neutral atom quantum computing demands integrated electronic control systems with low latency, modular architecture, and real-time feedback capability. Here, we present an FPGA-based electronic control system that eliminates the PC from the feedback loop, integrating photon counting, real-time decision-making, and waveform generation within a unified PXIe architecture. The system achieves a total feedback latency of $282\,\mathrm{μs}$ and is validated in practical experiments by assembling defect-free atom arrays from 24 stochastically loaded optical tweezers. A single-round rearrangement achieves a filling fraction of $\sim96\%$, while feedback-controlled iterative rearrangement over five rounds boosts the success probability for generating a 10-atom defect-free array from $65.7\%$ to $95.4\%$. This system establishes the electronic infrastructure necessary for mid-circuit measurement and real-time quantum error correction on neutral-atom platforms.

The problem of determining the existence of a spectral gap in a lattice quantum spin system was previously shown to be undecidable for one [J. Bausch et al., "Undecidability of the spectral gap in one dimension", Physical Review X 10 (2020)] or more dimensions [T. S. Cubitt et al., "Undecidability of the spectral gap", Nature 528 (2015) and Forum of Mathematics Pi, 10 (2022)]. In this work, we focus on the 1-dimensional result, showing that the constructed family with undecidable behavior is extremely sensitive to perturbations. In particular, for any $\varepsilon > 0$, there exists a 1-local, rank 1, perturbation with norm $O(\varepsilon)$, such that the spectral gap problem for the family in [J. Bausch et al., "Undecidability of the spectral gap in one dimension", Physical Review X 10 (2020)] now becomes decidable.

Bulk reconstruction is a central problem in AdS/CFT, and entanglement wedge reconstruction is its subregion version. We argue that this subregion statement should be separated from the stronger holographic quantum error correction interpretation, in which one region-independent logical bulk operator has code-preserving representatives in several boundary regions. A simple locality argument shows that such a common reconstruction must commute with the code-preserving local algebras in the complementary regions. This is the mechanism realized in HaPPY-type codes: the erased regions are blind to a protected logical algebra. An ordinary finite $N$ holographic CFT does not have such a protected invisible sector for supergravity fields. Its low-energy local observables, in particular, suitably smeared stress tensors, detect the physical support and gravitational dressing of ordinary bulk operators, up to possible center or superselection data. Thus, there is no such holographic quantum error correction and the $N=\infty$ agreement of global and subregion HKLL formulae is a free-theory statement. What remains is entanglement wedge reconstruction without holographic quantum error correction, or subregion complementarity: each boundary region has its own code-preserving low-energy algebra and its own region-adapted bulk interpretation, rather than a shared logical operator.

Temperature is one of the central concepts of thermodynamics, yet its meaning away from equilibrium remains elusive. This problem is particularly acute in isolated quantum many-body systems: their states evolve unitarily, need not be close to equilibrium, and can retain energy coherence, a feature with no classical thermodynamic analogue. A non-stationary quantum state contains two kinds of energy fluctuations. One is associated with energy populations and has the usual thermodynamic interpretation; the other arises from coherence between energy sectors and drives time dependence. We propose that temperature, also out of equilibrium, locates the state within the family of regular states compatible with its energy-coherence structure. This leads to a natural definition of temperature for regular nonequilibrium states. The resulting inverse temperature is not generally the derivative of thermodynamic entropy with respect to energy. Indeed the principle of maximum entropy does not extend in its usual form; it is replaced by a principle of minimum discrimination information. We also develop the corresponding theory for subsystems, where temperature cannot in general be inferred from the reduced state alone. Instead, it is determined by the induced local thermodynamic structure, with boundary ambiguities removed in the thermodynamic limit.

Conformal field theory provides universal predictions for Loschmidt amplitudes following quenches from product states to critical Hamiltonians. Building on this observation, we develop a route to extracting conformal data from real-time dynamics without preparing critical low-energy states. After analytic continuation, the Loschmidt amplitude is described by a boundary-CFT partition function on a strip, whose transverse transfer matrix encodes both the boundary operator spectrum and the central charge. Local space-time perturbations of the amplitude are governed by equilibrium correlation functions, and therefore provide access to critical exponents. In parallel, generalized temporal entropies exhibit scaling with time analogous to the equilibrium scaling of spatial entanglement entropy. We show that the low-lying boundary spectrum can be reconstructed from the system-size dependence of finite-chain Loschmidt echoes, whose damped oscillations encode differences of boundary scaling dimensions. Finally, we propose a finite-size scaling protocol that can extract these quantities from simulations or experiments on state-of-the-art quantum platforms.

The bosonic Kitaev chain (BKC) model is a deceptively simple looking quadratic pairing Hamiltonian. Despite being purely Hermitian, it exhibits a number of striking non-Hermitian topological phenomena, including skin effects. We show here how symmetries play a key role in this model, and how identifying these allows one to develop generalized BKC-like models. We emphasize the surprising fact that any quadratic bosonic pairing Hamiltonian with a sublattice (chiral) symmetry necessarily has a dynamical matrix with an effective time reversal symmetry. This symmetry is unrelated to physical time-reversal, but enables non-trivial topological invariants. We also discuss how this symmetry is unrelated to another key property of the BKC, the decoupling of quadrature dynamics. This feature can instead be connected to a distinct symmetry, namely an effective particle-hole symmetry of the dynamical matrix. We discuss non-trivial generalized BKC models that only keep one of these two effective symmetries intact. We also provide a classification of all translationally-invariant 1D pairing Hamiltonians, and show connections between the BKC and a well-studied non-Hermitian fermionic system, the symplectic Hatano-Nelson model.

The Noisy Intermediate-Scale Quantum (NISQ) era poses a challenge for developers: hardware providers expose capabilities through heterogeneous interfaces with proprietary metrics varying widely across providers, hindering informed backend selection. Static characterization metrics - coherence times T1/T2, gate error rates - exhibit limitations: they fail to capture dynamic variability across successive executions, overlook the impact of transpilation, and lack architectural comparability across physically distinct technologies. We propose a Figure of Merit (FoM) based on Grover's algorithm as an algorithmic stress test evaluating quantum backend performance holistically. The metric combines success probability on target states with penalties for non-uniform amplification and leakage to non-marked states, yielding a unified score across hardware architectures. Implemented via the Qonscious framework - a conditional execution platform using polymorphic adapters, it executes agnostically on IBM, IonQ backends, and simulators. Main contributions: (1) proposal and validation of GroverFigureOfMerit, incorporating uniformity and leakage penalties (adapted from GRADE) with emphasis on noise, transpilation, and topological constraints; (2) systematic analysis of heterogeneity across nine quantum providers motivating agnostic metrics; and (3) experimental demonstration via ideal simulators and real-processor noise models, confirming sensitivity to noise, topology, and transpilation overhead. Results confirm the metric distinguishes backend performance under a unified score, capturing intrinsic algorithmic limits. Validation on physical QPUs is identified as a natural next step.

The identification of molecules that combine long spin coherence times and efficient spin-optical interfaces, ideally at room temperature, is pivotal towards the development of molecular quantum technology. By means of advanced first-principles methods, we here unravel the electronic structure for triangulene (1), its aza-cation derivative (2), and the crystal of 2,6,10-tri-tert-butyl-4,8,12-trimesityl-triangulene (3), and show that these organic diradicals possess a triplet ground state well separated from the first singlet excited state approaching 0.5 eV, closely resembling solid-state defects like nitrogen vacancy centers. In addition, we compute spin decoherence times due to the interaction with phonons and surrounding nuclear spins, showing that a deuterated molecule of 3 in a nuclear spin-free environment would support $T_2 = 0.21$ ms at 10 K. Importantly, we show that the engineering of specific low-energy vibrations could significantly improve $T_2$ toward the limit imposed by the molecular core spin relaxation, here estimated to be as long as $T_1=27$ ms at 300 K for 2. Finally, we compute two-phonon contributions to inter-system crossing at 300 K for2 as a luminescent prototype, and find that it is highly spin-selective, supporting the possibility to engineer optical read out and spin initialization. These results advance a unified first-principles theoretical foundation of spin decoherence and spin-selective excited-state processes and point to novel chemical design strategies for optically addressable, highly coherent molecular qubits.

Quantum state purification aims to recover higher-fidelity quantum states from multiple noisy copies and is a fundamental primitive for quantum information processing. Magic resources enable operations beyond classically simulable dynamics and are central to universal fault-tolerant quantum computation. Recent no-go results show that classically simulable operations cannot achieve a nontrivial universal fidelity gain. This motivates a quantitative theory of the magic required for purification at prescribed success probability and target fidelity. For universal purification with two input copies, we prove an exact linear mana law in odd dimensions and a two-sided linear robustness law for multi-qubit systems, which becomes exact for a single qubit. We also identify an explicit successful purification map that makes the tradeoff transparent. These results establish universal purification as a task obeying a quantitative magic-fidelity law and link magic resources to error mitigation and fault-tolerant quantum information processing.

We investigate how irreducible multipartite entanglement, a long-range correlation by nature, can emerge from short-range dynamics far from equilibrium. Focusing on the Markov gap as a probe of irreducible tripartite entanglement (IrTE) in free-fermion chains, we uncover qualitatively distinct dynamical behaviors: the Markov gap grows either quasi-linearly or in staircase-like jumps depending on the initial state. We also propose attainable upper and lower bounds for the onset time of IrTE based on the Lieb-Robinson bound. Strikingly, the Markov gap saturates to a volume-law value on a timescale $t\sim\! L^2$, much slower than the ballistic spreading of bipartite correlations. To understand what information about the wavefunctions is revealed by the Markov gap calculation, we introduce the concept of essential tripartite fermion (ETF) and an associated tripartite null matrix. The value of Markov gap closely tracks the number of small singular values of this tripartite null matrix, yielding a transparent, operational physical interpretation of the measure. We further demonstrate that several dynamical signatures persist in the interacting XXZ chain.

Entanglement is monogamous: if it is shared among more than two parties, the entanglement between any pair cannot be very strong. For an integer $k\geq 2$, $k$-extendibility of a state $ρ_{AB}$ quantifies this as the number of copies of $B$ that can be simulated by the state's environment. We introduce fractional extendibility, which gives a finer characterization of the quantum correlation that is leaked to the environment, and prove that it is invariant under tensor products and monotonic under local processing. We also establish the distributed monogamy of entanglement: for any state on $AB_1B_2\dots B_n$, the maximum average probability of extracting an EPR pair from a random subset of $k \leq n/2$ systems among the $B_i$'s is the fraction $k/n$. With these tools we show that any quantum erasure channel with erasure probability more than a half cannot simulate a less noisy erasure channel, even with asymptotically many uses of the more noisy channel.

We study the critical properties of random quantum circuits with a $U(1)$ symmetry subject to local projective measurements that explicitly break this symmetry. We find that, at the measurement-induced phase transition, symmetry-breaking measurements act as a relevant perturbation at large scales, leading to the same universal critical properties as the corresponding monitored random circuit with non-symmetric unitary dynamics. In particular, we consider monitored $U(1)$-symmetric Haar-random circuits in the limit of large local Hilbert-space dimension, where the trajectory-averaged entanglement entropy can be exactly obtained in terms of a classical statistical mechanics model. In this model, the charge associated with the conservation law follows a symmetric simple exclusion process, in which symmetry-breaking measurements correspond to disordered defects that create and destroy charges. We prove that the charge correlation length remains finite for any measurement rate, ruling out a charge-sharpening transition, in contrast to the case of symmetry-preserving measurements. We further support our predictions at finite local Hilbert-space dimension through numerical finite-size scaling analyses of the entanglement transition in monitored $U(1)$-symmetric Haar and stabilizer random circuits.

We develop a general framework for the statistics of mixed-dimensional excitations subject to intertwined conservation laws, extending the familiar Fermi statistics with conserved particle number. We define statistics microscopically through a \emph{hopping-operator algebra}: a local operator subalgebra (LOsA) generated by operators that locally move or deform excitations while preserving the conservation law. Nontrivial statistics arise when this subalgebra is nontrivial. We first focus on LOsAs that encode \emph{pointed} conservation laws. These give rise to invertible excitations, whose fusion rules are exactly those of the symmetry defects of a higher group $\cG$. For such $\cG$-conserved excitations in $d$-dimensional space, we show that the corresponding LOsA -- and hence the statistics it defines -- is classified by a cohomology class $[ω] \in H^{d+2}(B\cG;\R/\Z)$, where changing $[ω]$ by a coboundary corresponds merely to a rephasing of the local operators. We further provide a holographic realization: excitations with this prescribed conservation law and statistics live on the boundary of a $\cG$ higher-group gauge theory in $(d+1)$-dimensional space, twisted by $[ω]$. More generally, non-pointed conservation laws and the associated statistics of non-invertible excitations are defined by a pair: a LOsA together with its excitation-complex representation. This is equivalent to the pair consisting of a LOsA and its Hilbert-space representation, which is the data defining a generalized symmetry. Consequently, non-pointed conservation laws and their statistics in $d$-dimensional space are classified by fusion $d$-categories, just as generalized symmetries are. The higher-group results above are the fully-pointed special cases of this more general classification.

Renormalization provides a framework for relating microscopic models of physical systems to effective descriptions at larger length scales. This procedure is studied for the boundary states of non-chiral two-dimensional topologically ordered models. The initial data consist of renormalization fixed points built from representations of finite-dimensional $C^*$-Hopf algebras, which are then perturbed by uniform on-site noise quantum channels and repeatedly coarse-grained. The resulting flows admit an intrinsic algebraic description in terms of completely positive maps on the $C^*$-Hopf algebra or, equivalently, positive linear functionals on its enveloping $C^*$-Hopf algebra. Their iteration is governed by convolution powers, and convergent trajectories yield new matrix product density operator fixed points, described by finite $*$-quantum hypergroups. This provides a concrete physical interpretation of such structures. For finite group algebras and their duals, we provide explicit classifications via Goursat's lemma for groups. Finally, we formulate and prove a quantum generalization of Goursat's lemma for finite-dimensional $C^*$-Hopf algebras, a result of independent interest, which gives an explicit structural description of all convergent renormalization trajectories.

The Quantum Scientific Computing Open User Testbed (QSCOUT) has developed a qubit-boson gate set for hybrid continuous-discrete variable (CV-DV) quantum computing. This document outlines how to utilize these gates on QSCOUT using Just Another Quantum Assembly Language, Jaqal\textsuperscript{TM}.

While quantum hardware remains limited, hybrid quantum-classical algorithms with complex control structures, including unbounded loops, are emerging, posing new challenges for quantum program analysis, including the accurate estimation of the resource consumption of a given program. Meanwhile, precise analysis techniques such as symbolic execution have largely left out hybridization and unbounded recursion. On the other hand, current quantum Hoare logics that generally support them are lacking in expressiveness and miss out on efficient computational equational reasoning that could be implemented in a semi-automated tool. This leaves a gap awaiting to be filled. In this work, we answer this challenge with the first semi-automated static analysis solution combining effective functional verification and resource (termination or cost) estimation for hybrid quantum programs with unbounded loops. Towards that end, we introduce integer hybrid path-sums (IHPS), extending path-sums to handle unbounded while loops, as a representation of possible executions of a program. A generic strategy for determining termination and expected resource consumption via loop invariants is also proposed and illustrated on several examples. Finally, the solution is implemented as a semi-automatic Haskell program. This work is the first step toward the design of a complete static resource analysis tool for hybrid quantum programs, essential for the development of real-world quantum computing.

The description of the optomechanical system is commonly based on the quantum Langevin equation formalism. This framework is introduced phenomenologically or based on a model Hamiltonian. However, once dealing with the optomechanical Fabry-Perot cavity or the modified Michelson-Sagnac interferometer with a semitransparent mechanically active membrane inside, a model-free consideration is also possible by using an alternative approach. Such an approach, which is based on the classical wave equations in the systems, is popular in the gravitational-wave community where it is termed as input-output relations approach. In this work, using the aforementioned approach, we derived the equations for the ladder operator of the intracavity field, stochastic back-action force, and the relation between the fields at the input mirror. Then we simplified the obtained results down to the range of applicability of the Langevin equation formalism and compared these with the corresponding predictions of the latter formalism. This enabled us to critically assess the validity of the Langevin equation formalism and rectify its range of applicability. In the case where the dissipative optomechanical coupling is involved we identified appreciable problems with this formalism. We found that, disregarding the fact that decay rate of the optomechanical Fabry-Perot cavity depends on its length, no dissipative optomechanical coupling is generated. This is in contrast with the prediction of the standard Langevin-equation based treatment. We found that, staying inside the range of applicability of the Langevin equation formalism, the relation between the fields at the input mirror may not be correct. We found that the Langevin equation formalism misses a phase factor at the input field, this factor turns out to be important for the situation involving the dissipative optomechanical coupling.

We study one-way quantum communication lower bounds for search problems. Unlike decision problems, search problems can have many valid outputs, which pose a fundamental barrier to standard quantum lower-bound techniques. We overcome this by developing a novel method based on matrix discrepancy, which allows us to bound the output measurements of a quantum protocol jointly. As applications of our method, we establish the first tight quantum lower bounds for two fundamental search problems in some natural parameter regimes: collision finding and triangle finding. For collision finding, we prove a tight $Ω(N^{1/4})$ one-way quantum communication lower bound. Previously, the best-known quantum communication lower bound for collision finding was $Ω(N^{1/12})$ due to Göös and Jain (RANDOM 2022), and no stronger bound was known even under the one-way restriction. For triangle finding in graph streams, we prove a one-pass quantum streaming space lower bound of $Ω\left(\sqrt{Δ_V}\right)$ for graphs with $m$ edges, $Θ(m)$ triangles, and constant $Δ_E$, where $Δ_V$ and $Δ_E$ denote the maximum number of triangles sharing a common vertex and edge, respectively, under the condition that $1\le Δ_V\le m^{2/3}$. This constitutes the first nontrivial quantum space lower bound in this regime, matching the classical upper bound of Jayaram and Kallaugher (RANDOM 2021) up to logarithmic factors. Notably, our method also recovers the classical lower bound of Kallaugher and Price (SODA 2017) through an entirely different argument, avoiding their Boolean-Hidden-Matching reduction that breaks down for quantum protocols.

Entanglement distribution is the overarching purpose of quantum networks. While communication over long distances can use deployed fiber infrastructure, it requires photons in the telecom band. However, advanced quantum network nodes do not operate at such wavelengths. Here we overcome this limitation with two tailor-made low-noise quantum-frequency converters to distribute entanglement between a single atom and a resonant photon over 14km line-of-sight via 24km of a deployed commercial fiber. The photon at wavelength 780nm is first entangled with the atom, then converted to the telecom S-band, and finally back-converted after propagation through the fiber. This link enables a photon transfer efficiency of 1.7% while affecting the atom-photon entanglement fidelity by less than 1%. This brings integration of atomic quantum nodes with existing long-distance fiber networks into reach, enabling novel applications in quantum information processing.

Quantum gate teleportation is a key technique in fault-tolerant quantum computation that uses resource states to implement logical gates. Here, we develop a theory of quantum gate teleportation protocols that implement non-Clifford gates on arbitrary input states without revealing any information about them; we refer to these protocols as magic gate teleportation (MGT). We uncover a hidden structure within MGT -- after backpropagating the Pauli measurements, MGT protocols can be viewed as encoding the input state into a stabilizer code heralded by the measurement outcomes, followed by a logical non-Clifford gate. Using this structure, we construct MGT protocols for any resource state obtained by applying commuting Pauli rotations to a stabilizer state, and provide an efficient algorithm for synthesizing their circuit implementations. Conversely, we prove that useful resource states for MGT, i.e., states that can be used for non-Clifford gates through MGT protocols, are necessarily Clifford-equivalent to diagonal states; in particular, the output state distilled from the $[\![5, 1, 3]\!]$ protocol is not useful for MGT. Finally, we identify conditions under which the feedforward operators can be implemented by Pauli operators, shedding light on the paradigm of algorithmic fault tolerance and simplifying the feedforward operations needed for quantum computing.

An identity term in the Hamiltonian is conventionally regarded as spectrally inert-it shifts energies but does not alter eigenstate topology. We show that under non-Hermitian skin pumping, this paradigm fails: a momentum-dependent identity term actively deforms the generalized Brillouin zone, thereby challenging established topological criteria that rely on fixed complex contours. Here, by introducing spin-orbit coupling into a Hatano-Nelson chain, we present an exact analytical solution for the entire non-Hermitian eigensystem under open boundary conditions. Our solution reveals how inter-cell spin-orbit coupling, synergizing with this non-trivial identity term, induces topological edge states and robust zero modes in the complete absence of chiral symmetry. This work establishes an exactly solvable paradigm for non-Hermitian topology beyond symmetry protection, and provides a rigorous benchmark for testing topological invariants in systems with momentum-dependent identity terms.

Multipartite Bell nonlocality provides a device-independent probe of many-body quantum correlations, but its characterization is limited by the rapid growth of the underlying classical and quantum optimization problems. We develop a scalable method for constructing and certifying permutationally invariant Bell inequalities using only one- and two-body correlators. The construction gives families of inequalities with robust quantum violations for general $m$ measurements as the number of parties $N$ becomes large. To improve robustness against noise, we optimize the ratio of the quantum value to the classical bound for these families in the large-$N$ limit. We then certify the resulting quantum violation using semidefinite programming. For the broad class of Bell inequalities studied here, the infinite-$N$ ratios take simple rational values for finite $m$ and converge to $\coth(1)$ as $m\to\infty$. The optimized inequalities efficiently detect many-body Bell nonlocality with collective measurements, with more measurement settings leading to stronger violations.

We present the analytical, exact, explicit, and assumption free formulas for the evolution operators corresponding to four instances of time-dependent Hamiltonians relevant to quantum spin batteries including two stochastic cases. We demonstrate how to recover and go beyond existing expansions and approximations directly from the exact solutions giving, for example, an explicit exact formula for Floquet Hamiltonians at all orders. The exact solutions are obtained through a completely novel combination of three mathematical techniques, the $\star$-algebra, path-sums and Omega calculus, which we briefly overview. These are widely applicable to other non-autonomous differential systems.

By leveraging a GPU-accelerated Schrödinger-Poisson (SP) solver, we characterize exchange coupling in a hole spin double-qubit device involving a double quantum dot (DQD) system formed inside a 5-gate silicon fin field-effect transistor (FinFET) similar to real experimental structures. The self-consistent SP simulations rely on a finite difference discretization of the 3D volume and on a Luttinger-Kohn 6x6 kp Hamiltonian accounting for magnetic fields and strain distribution. They return the gate-induced confined electronic states and the corresponding electrostatic potential hosting the DQD. These quantities serve as inputs to a two-particle Hamiltonian that is constructed from single-particle Slater determinants through the configuration interaction (CI) method. By diagonalizing this two-particle Hamiltonian, the eigenstates and eigenenergies of the DQD system are obtained, together with their exchange coupling. We show that our simulation framework, using a reduced number of basis states, is capable of reproducing the magneto-electrostatic behavior of the devices of interest, as predicted from theory and observed experimentally. We finally leverage our approach to determine the optimal operating conditions of a two-qubit quantum logic gate implemented in a Si FinFET structure.

Critical quantum metrology with equilibrium states predicts quantum-enhanced sensitivity only in the vicinity of criticality, where large prior information about the parameter is required. By employing quantum Ziv-Zakai bounds, we derive a limit on the mean-square error in critical quantum metrology. For second-order quantum phase transitions, we show that the precision predicted by the Cramér-Rao bound offers no substantial improvement over the prior standard deviation. Thus, the critical quantum sensor's precision can only achieve a constant gain compared to the prior standard deviation, even without performing any measurement. We elucidate the fundamental limitation on the achievable precision in critical quantum metrology in the context of local sensing, even without considering state-preparation costs or noise. Thus, the super-Heisenberg-limited sensitivity at criticality arises from precise prior knowledge rather than a genuine gain due to criticality. Our work provides a practical framework for assessing critical quantum metrology and a routine for studying quantum sensing with many-body systems.

The emergence of equilibrium universality from intrinsically nonequilibrium dynamics is a fundamental open problem. Bose-Hubbard lattices realized in photonic and circuit-QED platforms provide a versatile setting to engineer nonlinear interactions, dissipation, and multiphoton processes. Here we investigate a Bose-Hubbard lattice subject to three-photon parametric driving, whose nonequilibrium steady state spontaneously breaks a $\mathbb Z_3$ symmetry and realizes the criticality of the three-state Potts model, a three-state generalization of the Ising model. Using a variational phase-space approach with systematically controllable accuracy based on a Variational Multi-Gaussian ansatz, we perform finite-size scaling analyses in one and two spatial dimensions. We find that, in two-dimensional lattices with single-photon losses, the nonequilibrium steady-state transition belongs to the universality class of the 2D classical three-state Potts model. In contrast, in one-dimensional lattices with three-photon losses, the transition is governed by the one-dimensional quantum three-state Potts universality class. These results establish driven-dissipative bosonic lattices as a platform for emergent Potts criticality and identify multiphoton dissipation as a mechanism that promotes nonequilibrium critical behavior from classical to quantum universality classes.

We measure the spatial pattern associated with the superradiant emission from a cloud of cold 87Rb atoms using Fourier imaging. We observe a highly directional, ring-shaped emission structure, which corresponds to a single collective jump operator associated to the most superradiant mode of the ensemble. Using spatial filtering, we isolate this channel and find the typical superradiant burst with superlinear scaling of the intensity with atom number. We compare our results to two models that describe the competition between the various decay channels, finding good agreement. Our work shows that the collective jump operators introduced by Carmichael et al. [Optics Communications 179, 417 (2000)] can be measured and manipulated.

Rydberg atoms are highly sensitive to external electric fields due to their exaggerated electronic properties. This unique feature lays the foundation for many of their applications in quantum science. However, an uncontrolled stray electric field can be detrimental, severely degrading their quantum control. In this work, we demonstrate a universal scheme that relies on the efficient creation of an in-vacuum plasma source by photo-ionizing laser-cooled atoms to eliminate detrimental electric fields in a Rydberg-atom tweezer array platform, requiring only readily available resources. With this method, we began with a Stark-ionized Rydberg continuum spectrum caused by a large, unknown stray electric field and ultimately recovered stable, coherent excitation of an individual Rydberg state after fully eliminating the field. Our method is directly applicable to existing Rydberg-atom platforms and can also be useful in other experiments sensitive to stray electric fields.

We extend Nielsen's geometric approach for quantum complexity from closed to open quantum systems, whose dynamics is governed by Lindbladian evolution. In this framework, complexity is defined through an optimal-control problem on the space of mixed states, with a cost assigned to both unitary and non-unitary generators. We show that the resulting geometric structure differs fundamentally from the Riemannian geometry that emerges in the case of unitary evolution. In the open-system setting, the natural geometry is typically sub-Finslerian. Dissipation makes the geodesics non-reversible, while the admissible tangent directions are restricted by the physically allowed controls. We analyze several physically motivated examples, including a single qubit subject to depolarizing and amplitude-damping channels, as well as the damped harmonic oscillator. We show that, similarly to the unitary case, varying the penalty factors in the cost functional modifies the geometric properties through changes in the flag curvature, the Finslerian analog of sectional curvature. Our results provide a geometric framework for quantifying the abstract notion of complexity in dissipative quantum systems, with potential connections to experimentally realizable setups.

We introduce a family of quantum circuits that possess standard indicators of classical simulation hardness including high entanglement entropy, magic, and non-Gaussianity, yet admit efficient classical simulation via matrix product states (MPS). Our construction uses logical circuits of high-rate Calderbank-Shor-Steane (CSS) codes with enhanced symmetries. Using code automorphisms and transversal diagonal gates from higher levels of the Clifford hierarchy, we realize nonlocal logical Clifford and non-Clifford gates, showing how error-correcting codes can compile complex logical circuits into simple physical operations. Simulation efficiency rests on two properties: (i) diagonal transversal gates do not increase bond dimension, and (ii) permutations are tracked classically via on-the-fly relabeling, avoiding costly SWAP networks. Unlike Clifford or matchgate simulation, our method accepts a broad class of initial states, including dense entangled, magic, and non-Gaussian inputs, provided the encoded state retains an efficient MPS representation. We also release an exact phase-polynomial backend for monomial subfamilies, whose cost is set by higher-degree phase terms rather than entanglement growth. We demonstrate the method on an infinite polar CSS code family, showing bond dimension stays bounded by the encoding cost regardless of circuit depth. These results show that for some circuit families, standard resource measures are individually insufficient to indicate simulation hardness. As a near-term application, we use the compiled MPS as a classical reference for direct fidelity estimation of a quantum device running nontrivial logical circuits. Pauli sampling on the encoded reference, with a Clifford pushback through the known encoder, provides the ideal expectation values, so the logical output fidelity can be estimated from local Pauli readout alone, without costly state tomography.

A novel parallel approach is proposed for QEC decoding based on Belief Propagation with Ordered Statistics Decoding. The main idea is to pre-process the error vectors obtained from Belief Propagation by applying Singular Value Decomposition locally to sub-regions of the lattice. The proposed approach is applied to distributed quantum computers and evaluated in terms of complexity, accuracy, and scalability.

Dissipatively stabilized cat qubits provide a promising route toward fault-tolerant quantum computation, exhibiting exponential suppression of bit-flip errors with increasing phase-space separation of the logical states, while incurring only a linear increase in phase-flip errors. Existing implementations rely on engineered two-photon dissipation via nonlinear coupling to a lossy environment, an approach largely confined to superconducting platforms and limited by spurious decay channels and finite dissipation rates. Here, we propose a fundamentally different stabilization paradigm based on repeated interactions with an auxiliary two-level system mediated by a quadratic Hamiltonian, enabling dissipative stabilization without reservoir engineering. Our approach overcomes key limitations of existing schemes and is compatible with a wider class of experimental platforms. Furthermore, it preserves the noise bias and extends to squeezed cat qubits, rendering single-photon loss errors partially correctable.

Grokking, the delayed transition from memorization to generalization, is a fundamental phenomenon in gradient-based learning, yet its dynamics within variational quantum machine learning (QML) remain largely unexamined. In this work, we report the empirical observation of both the grokking transition and epoch-wise double descent in a two-qubit quantum neural network (QNN) under a complete parameterization of the SU(4) manifold. We demonstrate that overparameterization via increased circuit depth improves the probability of successful generalization. Notably, these architectures frequently exhibit an epoch-wise double descent in test error, degrading at a critical epoch before recovering into a generalizing state. Crucially, we identify a generalization decay in late-stage training, where the test error increases significantly despite a stagnant training loss. Bridging this behavior with algorithmic stability theory, our analysis reveals that this decay correlates with an unconstrained increase of the weight-norm, drifting away from sparse, phase-aligned harmonic solutions toward overfitted solutions in the Hilbert space. We analyze the underlying temporal dynamics of this transition, demonstrating how the onset of generalization is linked to optimization hyperparameters such as learning rate and weight decay. Finally, to mitigate late-stage decay, we introduce a weak explicit weight-norm regularization into the loss function. We demonstrate that this structural anchor stabilizes the post-grokking phase and permanently preserves generalization gains, providing a robust framework for training overparameterized quantum circuits.

Quantum computing research increasingly depends on complex software stacks, yet the reproducibility of published results does not receive the priority and longevity mandated by recommendations of large international scientific bodies and best practices in software-centric systems research. In this paper, we present a combined manual and automated large-scale analysis of the reproducibility landscape in quantum computing research, quantify shortcomings, and derive actionable steps forward. We manually evaluate a curated sample of 127 papers using a five-question framework that covers code availability, environment specification, documentation, hardware description, and executability. To place these findings in a broader context, we conduct an automated large-scale screening of nearly 5000 quantum computing papers for the same reproducibility indicators. Our manual analysis reveals that only 24.4% of the sampled papers provide code artefacts, and among those, 64.5% fail to execute successfully in a clean environment. This assessment is corroborated by a large-scale automated analysis that yields a consistent code availability rate of 26.8%. Further, it shows that approximately one-third of the papers with accessible code lack machine-readable environment specifications. The results in this paper indicate that reproducibility is not yet consistently achieved in quantum computing research. In response, we outline a set of practical recommendations that address the observed failure modes and illustrate how reproducibility can be improved in practice.

In this paper, we consider Hamiltonians for aperiodic crystals of the form \begin{align*} H_\varepsilon:=T(-i\nabla_x+{\mathbf A}(x,\varepsilon x))+V(x,\varepsilon x),\qquad x\in {\mathbb R}^d \end{align*} where $T$ represents either a Dirac operators or a Schrödinger operator, and $x\mapsto {\mathbf A}(x,X)$ and $x\mapsto V(x,X)$ are $\mathbb L$-periodic with respect to some lattice $\mathbb L\subset{\mathbb R}^d$. Let \begin{align*} (k,X)\ni {\mathbb R}^d\times {\mathbb R}^d\mapsto h(k,X):=T(-i\nabla_x+k+{\mathbf A}(x,X))+V(x,X) \end{align*} be a family of operators acting on $L^2_{\rm per}(\mathbb{R}^d/\mathbb{L})$ with periodic boundary conditions. We show that, under some suitable assumptions on the family of operators $ (h(k,X))_{k,X}$ around an energy level $e_0\in {\mathbb R}$ and some points $(k_0,X_0)\in {\mathbb R}^d\times {\mathbb R}^d$, one can construct localized approximate eigenfunctions $Φ_\varepsilon\in L^2({\mathbb R}^d)$ of the operator $H_\varepsilon$ such that for $\varepsilon$ small enough and for some $m\in \{1,2\}$ and $μ\in {\mathbb R}$, \begin{align}\label{eq:abstract} \|(H_\varepsilon-e_0-\varepsilon^{\frac{m}{2}}μ)Φ_\varepsilon\|_{L^2({\mathbb R}^d)}={\mathcal O}(\varepsilon^{\frac{m}{2}+\frac{1}{4}}). \end{align} with \begin{align*} \|Φ_\varepsilon\|_{L^2({\mathbb R}^d)}=\frac{1}{|{\mathbb R}^d/\mathbb L|^{1/2}}+{\mathcal O}(\sqrt{\varepsilon}). \end{align*}

We study the influence of an external magnetic field on the Goos-Hänchen (GH) shift and the group delay time (GDT) in monolayer WSe$_2$ in the presence of a magnetic barrier. The transport properties of Dirac-like carriers are obtained by solving the effective low-energy Hamiltonian and evaluating the corresponding transmission amplitudes. The GH shift and the GDT are subsequently extracted from the phase of the transmission coefficient. We systematically analyze their dependence on the magnetic field strength, incident energy, angle of incidence, and barrier width, with particular emphasis on the spin and valley degrees of freedom associated with the $K$ and $K'$ valleys. Our results show that the magnetic barrier strongly modulates both the GH shift and the GDT, leading to oscillatory behavior and pronounced spin-valley-dependent transport characteristics. Remarkably, the magnetic field enables selective control of the lateral shift and traversal time of carriers for each spin and valley channel, allowing for tunable spatial and temporal separation of electronic wave packets. This provides a mechanism for manipulating fermionic trajectories after transmission through the barrier in a highly controllable manner. Such tunability opens promising avenues for designing nanoscale devices based on spin and valley filtering, as well as for potential applications in information storage and processing within spintronic and valleytronic platforms.

We study the quantum Wasserstein distances introduced by De Palma and Trevisan associated with quadratic cost operators generated by families of self-adjoint observables. We first show that an arbitrary positive semidefinite cost operator is completely determined by the restriction of the corresponding Wasserstein distance to pairs of pure states. This allows geometric invariance of the pure-state distance to be translated directly into invariance of the cost operator. Within the class of nonzero quadratic costs generated by at most $d^2-1$ observables on a $d$-dimensional Hilbert space, we prove that the Wasserstein isometry monoid consists exactly of the Wigner symmetries, that is, unitary and antiunitary conjugations, if and only if the distance is invariant under unitary conjugations on pure states. Equivalently, the cost operator intertwines the adjoint representation of the unitary group and is a positive scalar multiple of the identity on the traceless subspace. We further construct explicit mutually inverse maps between quadratic cost operators generated by observables and Hilbert--Schmidt frame-type operators formed from their traceless parts. Under this correspondence, isotropy of the cost is equivalent to the tight frame property of the associated Hilbert--Schmidt operator. Consequently, a nonzero isotropic cost requires at least $d^2-1$ self-adjoint generators, and equality holds precisely when their traceless parts form, up to a common scale, a Hilbert--Schmidt orthonormal basis. Thus the geometric, representation-theoretic, operator-theoretic, and frame-theoretic notions of symmetry all determine the same one-parameter family of quantum Wasserstein distances.

Quasiperiodic lattices can host critical eigenstates, whereas nonreciprocal hopping in non-Hermitian lattices can induce non-Hermitian skin effect. In this work, we investigate localization phenomena in a Hatano--Nelson model with quasiperiodically modulated hopping amplitudes, where nonreciprocity arises from unequal modulation strengths of the right and left hoppings. Using a non-unitary gauge transformation, we map the non-Hermitian system into a Hermitian quasiperiodic system and obtain an exact analytical expression for the Lyapunov exponent in the thermodynamic limit. Under periodic boundary conditions, inverse participation ratios and finite-size scaling analysis are used to identify the quasiperiodic critical regimes. The comparison shows that parameter regimes hosting quasiperiodic critical states under periodic boundary conditions can exhibit the non-Hermitian skin effect under open boundary conditions. Furthermore, the non-Hermitian skin effect associated with quasiperiodic critical regimes is also observed in representative long-range hopping models and multiband extensions. Our results provide an analytically controlled perspective on how quasiperiodicity, modulated nonreciprocity, and boundary conditions jointly shape the non-Hermitian skin effect in critical regimes.

Nonadiabatic driving in ultrastrongly coupled light--matter systems is commonly regarded as a source of errors, as counter-rotating interactions convert vacuum fluctuations into real excitations through the dynamical Casimir effect (DCE). Here we show that, instead, the DCE can be harnessed as a resource for engineering nonclassical states of light. Considering a cavity mode ultrastrongly coupled to a frequency-tunable qubit, we employ optimal quantum control to design driving protocols that convert vacuum fluctuations into targeted states. Numerical optimization reveals a versatile and robust approach for the deterministic preparation of a broad class of nonclassical states, illustrated here through Fock states, squeezed states, and Schrödinger-cat-state superpositions.

The nuclear shell model is a general way of expressing the many-body nuclear Hamiltonian and deciphering the underlying nuclear structure. In today's era of modern and high-power computation, the primary limitation of the nuclear shell model is the enormous dimensionality of its Hilbert space, which far exceeds available storage capacity and prevents the diagonalization of the full Hamiltonian matrix in that space. Quantum computing offers a scalable solution to bypass this curse of dimensionality. In this work, we introduce a single-run quantum simulation capable of obtaining multiple shell-model eigenstates simultaneously. The nuclear Hamiltonian is transformed from a bit to a qubit basis using the Jordan-Wigner transformation, explicitly preserving fermionic anti-commutation. We employ a Subspace Search Variational Quantum Eigensolver (SSVQE) along with an Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT) ansatz to construct the quantum circuit required to solve the shell-model problem. The ADAPT-SSVQE algorithm uses a symmetry-preserving single and double-excitation operator pool and optimizes a weighted energy sum to obtain the simultaneous convergence of all eigenstates within a targeted MJ subspace, eliminating the need for post-processing efforts to extract excited spectra. We benchmark this approach by solving the problem for two and three identical nucleons in a j = 9/2 orbital, successfully extracting five and ten mutually orthogonal states, respectively, within a 10-qubit active space. The algorithm achieves spectroscopic accuracy, in simulation, relative to exact diagonalization and intrinsically restores total angular momentum (\hat{J}^2) symmetry.

Quantum linear solvers (QLSs) can offer the potential for exponential quantum advantage in solving quantum chemical problems, but its assessment hinges on determining the condition number ($κ$) scaling, which itself is computationally challenging. While a recent work applied the Harrow-Hassidim-Lloyd (HHL) algorithm to single-reference linearized coupled cluster equations (SRLCC), the validity of the HHL-SRLCC framework is restricted to weakly correlated regimes. A general treatment requires a formulation that can access strongly correlated regions. We thus begin by extending the QLS-SRLCC framework to its multi-reference form, which is based on the internally contracted multi-reference LCC method (QLS-icMRLCC). We then analyze $κ$ scaling using three complementary diagnostics that range from explicit computations to use of indirect structural indicators: (i) direct calculations of $κ$, (ii) scaling of the ratio of maximum to minimum diagonal entries of an A matrix, and (iii) structural analyses of the A matrices based on a recently proposed conjecture, which we adapt to the QLS-LCC problem. The three approaches yield consistent predictions, indicating a polylogarithmic $κ$ scaling in system size. This finding, when combined with our arguments on sub-linear scaling of sparsity, supports the prospects of exponential advantage using QLSs for the LCC problem. Finally, numerical calculations on potential energy curves of model systems containing up to four atoms recover the ground state energies with errors relative to benchmark classical methods not exceeding 0.009$\%$.

Diagonal gates are ubiquitous primitives in quantum algorithms, from phase oracles, hypergraph-state preparation, and multi-control logic to Hamiltonian simulation of spin models and digitized lattice field theories, where Ising interactions and local potential terms are diagonal in the encoded basis. Standard compilers, however, often lower diagonal structure into one- and two-qubit gates before neutral-atom hardware can exploit native Rydberg-mediated multiqubit controlled-phase operations. We propose a Möbius-guided compiler that maps a diagonal phase function to a phase hypergraph via subset-lattice Möbius inversion. The hypergraph retains the support and angle of each many-body phase term, allowing sparse or local high-order structure to be routed as native multiqubit controlled-phase candidates when feasible and decomposed otherwise. The neutral-atom scheduler accounts for atom motion, interaction-zone constraints, blockade feasibility, and error costs, enabling a direct comparison between native high-order execution and decomposed alternatives. Benchmarks against routed ZAP and ZX-calculus baselines show improved estimated success for algorithmic instances with exploitable three- and four-body phase terms, and comparable performance on predominantly two-body instances. These results provide a feasible compilation strategy for more fully exploiting the native capabilities of neutral-atom hardware, using atom reconfigurability and Rydberg-mediated multiqubit phase operations as practical resources for more efficient quantum computation.

We specialize Agarwal's multi-level collective spontaneous-emission formalism to the four-level case by formulating it in the fully symmetric \SU(4) representation of $N$ identical atoms. In the irreducible representation $(N,0,0)$, the occupation-number basis forms a tetrahedral weight lattice on which the six embedded $\mathfrak{su}(2)$ transition subalgebras act as ladder operators. From these algebraic factors we obtain a compact Pauli-type population-rate equation and a closed-form expression for the total emitted intensity that apply to any combination of open dipole channels. The formalism is then specialized to the seven dipole-allowed four-level topologies -- tripod, inverted tripod, Y, inverted Y, double-$Λ$, closed cascade, and diamond -- and the resulting rate equations are solved numerically for atom numbers up to $N=50$. In every case the emitted intensity develops a delayed cooperative burst whose peak height obeys a power law $I_{\mathrm{peak}}=aN^{p}$ with topology-dependent parameters $(a,p)$; the fitted exponents lie in the range $1.81\lesssim p\lesssim 1.92$, indicating a superlinear. The \SU(4) tetrahedral flow and the seven configuration-dependent transients together provide a unified geometric picture of multi-channel collective dissipation in four-level atomic ensembles.

The Baker--Campbell--Hausdorff (BCH) formula plays a critical role in many branches of mathematics and physics. It expresses the logarithm of the product of exponentials of non-commuting operators as an infinite series of nested commutators of the operators involved. The Zassenhaus formula is the dual of the BCH formula: the exponential of a sum of operators is written as an infinite product of exponentials involving the operators and their commutators. In practical computations, however, one typically has to truncate the expansions, and so understanding the error committed by the resulting approximations and eventually providing suitable bounds for this error is of paramount interest. In this work we present a general strategy to derive rigorous error bounds and explicit error constants for the BCH and Zassenhaus formulas when the operators involved are skew-adjoint, as is the case for quantum evolution problems.

The spectral condition number is a widely adopted measure of worst-case cost for quantum linear system solvers. Yet it can significantly overestimate the actual runtime for a typical problem instance. We present two quantum algorithms that produce the normalized solution $|x\rangle$ of linear system $Ax=| b \rangle$ to accuracy $ε$ with complexity independent of the condition number $κ=\lVert A^{-1}\rVert$. We focus on the standard input model where $A$ is accessed through a block encoding and $| b \rangle$ is prepared by a unitary. But we also introduce an affine dilation model that encodes $A$ and $| b \rangle$ jointly, allowing further refinements of the query complexity. Our truncation-based solver makes an optimal number of queries to $| b \rangle$ and $\operatorname{\mathbf{O}}\left(κ_{\mathrm{eff}}\operatorname{polylog}\left(\frac{κ_{\mathrm{eff}}}ε\right)\right)$ queries to $A$. We prove a family of upper bounds on the effective condition number, including $κ_{\mathrm{eff}}\leq\frac{\lVert(A^\dagger A)^{-t/2}|x\rangle\rVert^{1/t}}{ε^{1/t}}$ for positive even integer $t$ and $κ_{\mathrm{eff}}\leq\frac{\lVert A^{-1\dagger}(A^\dagger A)^{-(t-1)/2}|x\rangle\rVert^{1/t}}{ε^{1/t}}$ for positive odd $t$, overcoming the $κ$-barrier. Our filtering-based solver is extremely simple with a favorable runtime prefactor. In particular, the solver has query complexity $6\frac{\lVert A^{-1\dagger}|x\rangle\rVert}ε\ln\left(\frac{1}ε\right)$ to leading order when the solution norm is known. We then present a similarly simple solution norm estimator with the same asymptotic cost up to logarithmic factors. Our quantum linear system solvers thus substantially improve a recent algorithm of Li, enabling faster quantum linear system solving beyond the condition number.

The negatively charged boron vacancy center in hexagonal boron nitride is a premier candidate for quantum sensing, yet its performance is critically limited by longitudinal spin-lattice relaxation time ($T_1$). A microscopic understanding of spin relaxation in the high magnetic field regime remains elusive, as the relevant Zeeman transitions lie far below the optical phonon energies typically invoked to describe the relaxation process. Here, we apply an \textit{ab initio} acoustic mode spin-phonon relaxation theory to this problem and quantitatively reproduce the experimental magnetic field and temperature dependence of $T_1$ without empirical fitting parameters. We demonstrate that the relaxation dynamics are driven by a direct one-phonon emission and absorption process resonant with the Zeeman splitting. Furthermore, we identify the out-of-plane flexural phonon branch which is unique to two-dimensional hosts, as the primary source of decoherence, creating a distinct low-energy spectral function that facilitates spin relaxation. Our results provide a microscopic interpretation of the experimentally observed non-monotonic field and temperature dependence in two-dimensional quantum defect centers.

Time series analysis plays a vital role across a wide range of scientific and engineering domains but poses substantial computational challenges. A major difficulty arises from the time reparameterization invariance of time series data, which complicates the extraction of meaningful temporal features. In this work, we address the problem of time series classification by exploring the application of quantum computation techniques. We propose a hybrid quantum-classical architecture that integrates recent advances in quantum neural networks with the mathematical framework of path signatures, mitigating the impact of time reparametrization invariance. The architecture employs feature layers that compute a signature kernel between pairs of input paths, consisting of a reference path and a target path for classification, using either classical or quantum variational linear solvers (VQLS). These feature layers are followed by a Quantum Convolutional Neural Network (QCNN) to perform downstream learning tasks. We evaluate several realizations of the proposed architecture, differing in QCNN configurations, on a binary classification task involving time series representations of handwritten digits. Our experiments demonstrate the potential advantages of implementing path signature kernel layers within quantum circuits and provide an analysis of the computational limitations associated with the VQLS component.

Polarization measurements of a classical 1550-nm signal are collected and analyzed on 15-km hybrid aerial-inground fiber connections over 11 months. The spectral area and spectral moments9 of mHz-resolution Fast-Fourier-Transform (FFT) of these measurements are extracted, and related to temperature, humidity, wind speed, and time of day. Spectral area correlations show a strong11 diurnal structure: daytime maxima align with temperatures/wind speed peaks and humidity dips, with lower levels during the night. These diurnal patterns also show seasonality, with higher13 mean and variance in summer than winter. A random forest regressor is used to estimate FFT features from environmental measurements, informed by a theoretical model

Multi-stage cryogenic readout chains with a wide bandwidth and added noise within a few quanta of the quantum limit are frequently constructed using traveling-wave parametric amplifiers (TWPAs) as the first stage, and a semiconductor amplifier as the second stage. Unfortunately for highly-scaled superconducting detector arrays, or quantum information systems, and space-based observatories, the power dissipation of the semiconductor amplifier becomes problematic from the perspective of available cryogenic cooling power at \mbox{3~K to 4~K}. Here we demonstrate a readout chain based on a two-stage kinetic inductance TWPA (KTWPA). This quantum-amplifier-based-readout-chain (QARC) provides sufficient gain that a cryogenic semiconductor follow-on amplifier can be eliminated without degradation of the system noise. In this way, the QARC dissipates approximately three orders of magnitude less power than readout chains containing semiconductor amplifiers while adding noise of less than 2~quanta over a 1~GHz bandwidth. In addition, by leveraging the high power handling of kinetic inductance technology, the QARC maintains an input compression point of -93~dBm, which exceeds that of many contemporary Josephson-junction-based parametric amplifiers.

Quantum error correction compatible with continuous symmetries is a fundamental problem in quantum information and a possible route to robust analog quantum simulation. Because the Eastin-Knill theorem forbids exact codes with continuous transversal symmetries, we construct explicit $SU(d)$-covariant approximate codes that exploit permutation symmetry to spread logical information uniformly across all physical subsystems. For one-, two-, and three-qudit erasures at known locations, we prove worst-case purified-distance scaling $Θ(1/N)$, matching approximate Eastin-Knill lower bounds up to constants, and we extend the reduced-state analysis to general flagged local noise. For single-qudit erasure, we construct an explicit near-optimal decoder from the Petz recovery map. We then use these codes as building blocks for encoded analog dynamics. Symmetry-preserving Hamiltonians generate block-structured dynamical Lie algebras implementable transversally, while controlled symmetry-breaking terms serve as non-transversal resources for universal dynamics. These results provide explicit non-Abelian covariant codes and a framework for robust analog quantum simulation.

The distribution of entangled photon pairs over standard optical fiber is a fundamental requirement for the realization of the quantum internet. However, real-world deployment is severely bottlenecked by the interplay of amplitude damping (photon loss) and phase noise (birefringence). In this paper, we numerically investigate the degradation of dual-rail polarization entanglement in telecom C-band fiber links. We demonstrate a critical disparity between the physical survival of quantum correlations and their practical utility in standard communication protocols. By evaluating the unconditional logarithmic negativity against the post-selected teleportation fidelity, we identify a distinct ``operational collapse region'' -- a distance window where the channel retains true quantum entanglement, yet standard coincidence-based detection architectures fail to provide any advantage over classical strategies. Furthermore, we reveal that the width of this inaccessible region exhibits a non-monotonic dependence on the phase noise rate, implying that simply minimizing fiber dephasing does not necessarily optimize the operational efficiency of the network. These findings provide vital guidelines for the design of practical quantum communication links.

The emergence of Quantum Software Engineering (QSE) responds to the need for systematic, disciplined, and quantifiable approaches to the development, operation, and maintenance of quantum software. Within this context, quantum computer certification represents a significant challenge: verifying that quantum devices produce valid entangled states despite hardware imperfections, noise, and decoherence. This paper presents QAccCert, a hybrid certification framework developed following QSE principles, demonstrating how heterogeneous technologies like FPGAs and Artificial Intelligence can be integrated for quantum processing. The framework implements entanglement certification through CHSH inequality violation in ideal quantum simulations using Qiskit AerSimulator. Through LLM-guided optimization, the system achieves 99.94% of the theoretical maximum of $2\sqrt{2}$, evidencing more efficient parameter space exploration than random search. These simulated results illustrate how QSE methodologies, combined with strategic technology interconnection, can be applied for practical and scalable quantum certification on real NISQ hardware in future work. This study provides a concrete case study of systematic quantum software development.

We present a geometric interpretation of the sum photon blockade effect in multimode quantum optical systems, such as semiconductor microresonators. The blockade condition \(c^{(n)} \cdot v = 0\) reflects the orthogonality of the \(n\)-photon amplitude vector to a target mode vector in an \(N\)-dimensional Hilbert space, visualized as the confinement of the state to a hyperplane. A key result is the calculation of the maximum probability of the system remaining in the blockade subspace under the influence of decoherence processes (in particular, dephasing), which determines the practical feasibility and robustness of the effect. This approach extends to higher-order correlators \(g^{(2)}_Σ\) and cross-correlations, enabling the design of scalable quantum devices. We introduce the concept of "dark-state typicality": as the number of modes \(M\) increases, the dark subspace annihilated by the collective mode operator asymptotically occupies a unit fraction of the \(n\)-boson Hilbert space. This allows the transition from fragile, finely tuned mechanisms to macroscopically robust non-classical light in large multimode bosonic architectures. We consider continuum collective modes, hypotheses on correlation zeros and invariant manifolds, as well as the relationship between blockade and entanglement.

Donor spin systems host a native Hilbert space whose dimension exceeds that of a qubit, meaning they can be used as qudits. Here we study a \ce{Si{:}P} donor spin system through leakage-aware randomized benchmarking (RB) of native ququart $\mathcal{C}_4$ and encoded two-qubit $\mathcal{C}_2^{\otimes 2}$ Clifford groups. We implement adiabatic ramps to operate electron dipole spin resonance (EDSR) pulses at the ionization point, where the electron is shared halfway between the donor and the interface, and to operate electron spin resonance (ESR) pulses near the interface, motivated by the sensitivity of the effective magnetic field to charge noise at the ionization point. By placing the electron near the ionization point only during EDSR control and using sufficiently long displacement ramp durations, leakage outside the computational basis is strongly suppressed, which is crucial for optimized qudit control. We find in our analysis based on leakage RB that $\mathcal{C}_4$ consistently achieves $\sim 40$--$50\%$ lower (lower-bound) error rates $\varepsilon^{\mathrm{LB}}_\mathrm{PT}$ with respect to $\mathcal{C}_2^{\otimes 2}$, due to its reduced circuit complexity. These results indicate that donor spin qudits benefit from genuine qudit operation as opposed to imposed encoded qubit operation.

We provide a thorough study of the properties of the Boulware vacuum in the spacetime of a spherical, static thin shell with a Minkowski interior. To this end, we calculate the renormalized vacuum polarization and stress-energy tensor of massless scalar fields via the extended-coordinate prescription, paying particular attention to their scaling as the shell approaches the black hole limit. Near the surface of the thin shell, we obtain the expected leading-order singular behavior of both quantities via two independent methods: a high-frequency approximation for the modes, and a weak-field approximation. At the center of the shell we find non-local, Casimir-like contributions that remain finite in the black hole limit, and whose backreaction effects we compute via the semiclassical Einstein equations. Away from these regions amenable to analytic treatment, we obtain numerical results for a wide range of shell compactnesses and field couplings. In the black hole limit, we show that the vacuum polarization and renormalized stress-energy tensor outside the shell quickly approach the ones generated by a Schwarzschild black hole, suggesting a possible universality in the vacuum outside highly compact horizonless objects. This work addresses the conceptual and technical aspects necessary for computing renormalized expectation values in matter configurations, laying the foundations for future explorations on the subject.

A fundamental question in PAC learning is determining the number of labeled examples required to learn a concept class to a desired accuracy and confidence. In classical learning theory, this quantity is characterized by the VC-dimension, while several quantum generalizations have established analogous results when examples are provided in quantum superposition. In this work, we study a distinct quantum PAC-learning model in which concepts are functions acting on quantum states. We demonstrate that the VC-dimension, although still relevant, fails to fully capture the sample complexity of this model. To further characterize this setting, we develop a new lower bound on the required number of samples and establish an upper bound when the states in the domain are linearly independent. Remarkably, this upper bound has a form similar to the classical PAC-learning bound. We further examine a setting in which the learner receives more informative data and show that the limitations of the VC-dimension persist in this extended model.

Quantum thermometry based on single-qubit sensor configurations enables the precise estimation of the temperature of a cosmological Anti-de Sitter (AdS) spacetime. In this work, we characterize the achievable estimation accuracy using the Quantum Fisher Information (QFI) and the associated quantum signal-to-noise ratio. For the first time, we introduce an ancillary Unruh-DeWitt detector between the sensor and the thermal bath, enhancing thermometric sensitivity by channeling temperature-dependent information into the probe qubit's coherence. We examine how detector acceleration in AdS space and the choice of boundary conditions modify the probe's thermal sensitivity. Despite the differing geometries, a unified phenomenology emerges: we characterize the scaling of the QFI with respect to temperature, detector energy gap, spacetime curvature, and interaction time. Finally, we identify optimal state preparation and measurement strategies that maximize the QFI, thereby establishing the fundamental limits of precision for non-Markovian sensing in curved spacetime.

The Born rule for computing probabilities of the outcomes of measurements is an indispensable ingredient of quantum mechanics. The standard textbook description of this rule gives the impression that it implies the unitarity of time evolution. This view relies on the argument that unless the dynamics is unitary, the probabilities of finding all possible outcomes of a measurement do not add up to 1, i.e., the total probability is not conserved. We show that this argument is flawed, and that the general expression for the Born rule ensures the conservation of total probabilities even when the dynamics of a quantum system is not unitary. This applies to the dynamics of ensembles of quantum systems in both pure and mixed states. We discuss the status of the local conservation of probabilities and the arguments against the plausibility of non-unitary time evolutions that are based on the identification of the Hamiltonian operator with the energy observable.

We investigate the subsystem entanglement asymmetry in random quantum automaton ensembles, which are generated by permuting the basis states in the Hilbert space and applying global phase shifts. We compute the ensemble average of the $U(1)$ subsystem asymmetry in different connectivity geometries, showing that the late-time limit of the ensemble associated to a 2-local circuit geometry coincides with the all-to-all ensemble average. By focusing on different subsystem sizes, we demonstrate that, similarly to Haar-random circuits, the system locally symmetrizes. However, in sharp contrast to the Haar-random setting, the scale at which symmetrization happens depends on the initial state, a phenomenon we associate with the interplay of conservation of the participation entropy and the uniform exploration of charge sectors. Additionally, we connect the growth of the subsystem asymmetry to the subsystem coherence and show that their growth is characterized by the same symmetrization scale.

Designing fault-tolerant quantum circuits that are both algorithmically correct and hardware compatible remains a major bottleneck in the transition to scalable quantum computing. We introduce RubriQ, a scalable framework that formulates circuit synthesis as a large language model (LLM) code-generation task, optimized via group relative policy optimization (GRPO). Unlike conventional black-box neural critics, RubriQ employs a domain-grounded programmatic rubric as the reinforcement learning reward function, evaluating circuits for T-gate reduction, hardware topology compliance, and unitary fidelity. To support high-throughput training, RubriQ integrates GPU-accelerated CUDA-Q simulation directly into the reinforcement learning (RL) loop and is deployed on NERSC Perlmutter using DeepSpeed ZeRO2 across multinode NVIDIA A100 clusters. On benchmark tasks, RubriQ achieves a mean T-gate compression of 3.31x, significantly outperforming sparse-reward RL baselines (2.05x), converging 2-3x faster, and maintaining less than 1\% hardware-constraint violations. Validated on IBM and IonQ quantum processors, RubriQ establishes an automated, high-performance computing (HPC)-driven pipeline for generating hardware-ready, fault-tolerant quantum circuits at scale.

This study develops a hybrid quantum-classical framework for constrained vehicle routing problems, focusing on the pickup-and-delivery problem with time windows. Instead of casting the full routing problem as a stand-alone quantum optimization task, we embed shallow quantum samplers inside the repair phase of an Adaptive Large Neighbourhood Search (ALNS) heuristic. A Deep Q-Network controller decides whether each reduced repair subproblem should be handled by a classical repair heuristic or by a quantum sampler, using features that describe the local repair structure and predicted hardware reliability. IBM Heron experiments are used to calibrate an empirical noise-aware model for local quantum repair circuits. Across the tested instances, quantum repair is admissible in only about 16% of reduced repair states and is not superior on average. However, under selected matched repair budgets, quantum-enabled repair reduces the final gap relative to standard ALNS in 29 of 36 tested settings. These results suggest that near-term quantum sampling is most useful as a selective local repair mechanism rather than as a replacement for classical routing heuristics.

Accurately controlling entangling gates remains a major challenge for quantum technology applications with solid-state spin qubits. Here, we study a group-IV color-center with a strongly-coupled nuclear spin and approach the problem from a quantum control perspective. We show that there are three different types of entangling gates where the entanglement is mediated by the parallel hyperfine-coupling component, the orthogonal one or both. We derive the respective quantum speed limits (QSL) and show by means of dynamical decoupling, resonant driving of single- and double-quantum transitions, quantum optimal control and algebraic gate decomposition how these gates can be realized. We finally discuss the experimental applicability.

The performance of variational quantum algorithms depends in general on the structure of the parametrized quantum circuit, but the most common ansätze are typically based on local couplings. Motivated by the extended connectivity available with neutral atoms and trapped ions, we examine when structured long-range connectivity provides a useful resource, focusing on sparse power-of-two (PWR2) coupling graphs. Using dynamical Lie-algebra analysis, approximate unitary-design diagnostics, and finite-depth measures of expressibility and entanglement, we examine how these geometries enlarge the accessible operator space. This enlarged space alone is not sufficient to ensure trainability of the parameterized circuit for given target problems, and we explore performance across example problems with and without long-range coupling, identifying where sparse coupling graphs are or are not likely to provide an advantage. We also introduce a variational scheme that maps hierarchical long-range Hamiltonians to geometrically local ones that can be optimized with short-range circuits. Together, these results identify circuit geometry and qubit reconfigurability as task-dependent resources for variational algorithms, relevant to ongoing developments in quantum hardware with long-range connectivity.

Non-Markovian behavior in quantum systems is often studied in the context of bipartite systems consisting of a system of interest and an environment -- tracing over the environment results in non-Markovian behavior for the subsystem of interest. One may get a Markovian limit in certain regimes, which is studied using the Lindblad master equation, and corrections to this behavior can be obtained by techniques such as the Nakajima-Zwanzig formalism. In this paper, we obtain an exact non-Markovian equation for the dynamics of a simple model system that consists of a direct sum rather than a tensor product of two pieces, namely, a discrete state and an infinite ladder. This system, called the Bixon-Jortner model, was first developed in the quantum chemistry literature but has been utilized by the quantum optics community as a model system with interesting behavior, including a Wigner-Weisskopf limit of exponential decay. We attack the time evolution problem of this system directly in time-domain, and start with an integrodifferential equation describing the time evolution of the discrete state. Using tools from mathematical physics, we transform this equation to a delay differential equation, which makes the non-Markovianity completely transparent, and then we solve the delay equation using an intuitive ansatz. This allows us to obtain the analytic form of the dynamics directly in time domain, and demonstrate decay and revival behaviors coming from the aforementioned delay differential equation. We believe the explicit form of the time-domain non-Markovian equation we obtain and the accessibility the solution techniques we use make our results a useful case study of non-Markovianity in quantum systems.

We propose a novel approach to the minimax estimation of high-order functionals from the perspective of quantum computing. Specifically, for any real number $α\gg 1$, we present two estimators, one for the classical functional $\mathrm{F}_α(P) = \sum_{i=1}^S p_i^α$ of a discrete distribution $P$ and the other for the quantum functional $\mathrm{F}_α(ρ) = \operatorname{tr}(ρ^α)$ of a mixed state $ρ$. These functionals have close connections with the Rényi entropy and the Tsallis entropy. We show that both estimators achieve the minimax optimal $L_2$ rate $α\mathsf{n}^{-1}$ in the range $α\lesssim \mathsf{n} \lesssim α^{3-o(1)}$, where the support size $S$ of $P$ or the dimension of $ρ$ can be much larger than the number of samples $\mathsf{n}$. As a result, both estimators achieve the \textit{optimal} sample complexity $\mathsf{n} \asymp α$, improving upon the prior best upper bounds $O(α^2)$ established by Jiao, Venkat, Han, and Weissman (IEEE Trans. Inf. Theory 2017) for classical functionals and Chen and Wang (COLT 2025) for quantum functionals. Our estimators are constructed under a unified framework using quantum primitives and run in linear time on a quantum computer. This work reveals an unexpected path from quantum computing to statistics, suggesting a conceptually new methodology for functional estimation. It adds to the growing list of quantum proofs for classical theorems.

We consider a multiplexed quantum repeater that distributes entanglement between two end nodes. Multiplexing is achieved through optical integration of many quantum chips. Each chip hosts an optically addressable communication qubit and a separate memory qubit. The communication qubit serves as an entanglement generation interface between different quantum chips, and the memory qubit can be used to store entanglement. The quantum chips on the repeater are interconnected using a reconfigurable router, which makes it possible to dynamically assign quantum chips for entanglement generation with either of the two end nodes in every end-to-end communication cycle. We propose a dynamic multiplexing policy in which after an entangled link has been established with one of the end nodes, all remaining quantum chips are assigned to the opposite end node. We compare this dynamic policy to a policy in which the assignment of quantum chips to end nodes is fixed. We consider a parameter regime where on average less than one entangled link is generated per end-to-end communication cycle, which is the relevant regime for near-term quantum networks. We show that in this regime, the dynamic multiplexing policy can lead to a significant improvement in fidelity over a fixed policy, while marginally improving the rate. Moreover, even though the dynamic multiplexing policy requires a deeper, and hence, more lossy, router than the fixed policy, it can still achieve higher secret key rates in the parameter regime studied. This makes dynamic multiplexing with a many-quantum-chip repeater especially relevant for the development of near-term quantum networks.

With a single contested exception, every NISQ-era flagship demonstration of "quantum advantage" has been classically reproduced, or closed by a simulability theorem, within eighteen months of its announcement. Six theoretical results from 2024 through April 2026 explain the pattern: the regions of circuit-space NISQ hardware can run with sufficient fidelity coincide with the regions classical algorithms compress efficiently, because the features that admit one (low effective depth, strong algebraic structure, geometric locality) are the features that admit the other. This reading dates the NISQ programme from its 2018 articulation as an interim retreat from the unmet conditions of the 1996 threshold theorems, characterises the eight years that followed as a closed loop in which the demonstrations the hardware could run were drawn from the only regions classical methods could already attack, and locates the exit from the loop where the threshold theorems originally located it: in fault tolerance. The empirical pattern could in principle break with a demonstration that escapes the current simulability results. After eight years and more than thirty advantage-class announcements, the burden of producing such a demonstration falls to the defenders of NISQ.

Isospectrally patterned lattices exhibit a composite band structure with a tunable ratio of localized versus delocalized eigenstates that is controlled by the underlying phase gradient. We show that the lattice Hamiltonian can be interpreted as that of a single spin exposed to a rotating magnetic field which is allowed to hop with a spin-flip across the lattice. In the low- and high-energy part of the band the localized states show an envelope of oscillatory character separated by quasi-nodes. Spin peaks occur at the locations of these quasi-nodes and provide a unique spin texture to the eigenstates which becomes increasingly complex with increasing degree of excitation. The crossover from localization to delocalization and vice versa leaves its fingerprints in the Fourier spectrum of the eigenstates: the original bimodal frequency distribution widens with increasing degree of excitation, moves across the spectral window and finally culminates in an extremely narrow frequency peak. In the course of this evolution the spin texture undergoes a rearrangement transition involving different characteristic (ir)regular patterns which we quantify by considering the total variation of the local spin fluctuations. Our results demonstrate the variety of the spectral properties of isospectrally patterned lattices which holds great prospect in particular when considering higher lattice or cell dimensions.

We investigate pattern formation in a finite chain of bosonic modes whose dynamics is governed by a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation. The model combines local parametric driving and nonlinear damping with nonlocal dissipative couplings between modes that work on different discrete spatial scales. In the classical limit, these mechanisms generate a reaction-diffusion-like dynamics, allowing the emergence of Turing-type instabilities. The key aspect of the analysis is the coexistence and competition of different unstable spatial modes. Depending on the range of parameters, the system may select different stationary nonuniform configurations, oscillatory wave-like states, or regimes in which multiple modes interact before a dominant pattern is established, thus providing a mechanism for pattern selection. We compare the deterministic bifurcation scenario, generated by a reaction-diffusion-like system derived from semiclassical drift dynamics, with the quantum dynamics, derived via the GKSL master equation, using phase-space methods and reduced Wigner functions. The results show how Turing instabilities, mode competition, and pattern selection can be extended to multimode open quantum systems, providing a bridge between nonlinear dynamical systems, dissipative quantum mechanics, and spatial self-organization.

Light-electron interactions generate synthetic momentum-space dynamics that can be used to engineer free electron quantum states. Here we develop coherent control protocols in which the optical phase acts as the controllable hopping phase of a Floquet-Bloch momentum lattice. Pontryagin optimization designs phase-only waveforms that prepare selected momentum populations and coherent few-sideband superpositions with programmable relative phases. In a complementary Bragg regime protocol, dynamical phase matching selectively couples neighboring sidebands and enables deterministic sequential state synthesis. Full wave-packet simulations based on the minimal-coupling Hamiltonian identify the tolerance window set by phase noise, detuning, and finite momentum spread. The two protocols expose a speed-selectivity tradeoff between ultrafast multilevel interference control and slower resonant engineering, establishing programmable free electron sidebands as a platform for ultrafast quantum state synthesis.

Engineered loss, gain, and non-reciprocity can sharply amplify a sensor's response, and exceptional points and the skin effect are widely proposed as routes to more precise quantum sensors. Some predict an exponentially large quantum Fisher information, the quantity that sets the best achievable precision, yet whether this amplified response is genuine measurement information has remained unsettled. We prove that it is not. For any open sensor whose parameter is imprinted coherently by a Hamiltonian, with loss, gain, non-reciprocity, and readout held fixed, the quantum Fisher information is capped by a single quantity, the spread between the largest and smallest energy the generator can impart, independent of the non-Hermitian dynamics. Amplification enlarges the response but not the information. The reported exponential gains arise only when that spread is unbounded, and any finite spread, such as a photon-number cutoff, restores the cap. The same limit governs dissipative probe preparation and spectral singularities. For photonic sensors the cap takes an operator form in which the information of any probe, classical or entangled, is set by the photon's dwell time at the perturbation, and it contains the recently derived scattering limits as special cases. Non-Hermiticity thus shapes a sensor's dynamics but does not source its precision, and the generator's spread and the attainable dwell time benchmark future non-Hermitian sensing proposals.

Solving linear differential equations is a fundamental task in scientific computing and an important primitive for quantum computing. A recent one-ancilla quantum differential equation solver provides a hardware-friendly and locality-preserving approach with provable performance guarantees, making it highly suitable for the early fault-tolerant and near-term regimes. Its simple circuit structure comes with a natural trade-off: the maximum single-run circuit depth scales as $O (1/ε)$ in the target accuracy $ε$. In this work, we reduce this depth by combining the solver with classical step-size postprocessing. By running the one-ancilla solver at a logarithmic number of finite time step sizes and using classical post-processing to cancel leading discretization errors, we reduce the maximum single-run circuit depth to $O(\mathrm{polylog}(1/ε))$ without adding quantum ancillae or sacrificing locality. Technically, extending extrapolation ideas beyond Hamiltonian and Lindbladian dynamics requires regularity estimates for observable maps under nonunitary evolution, which we obtain through a holomorphic extension of the adjoint evolution. Numerical experiments on the Hatano-Nelson model (ODE) and the convection-diffusion equation (PDE) demonstrate the effectiveness of the approach.

The Quantum Control Processor (QCP) bridges the gap between compiler toolchains and control electronics, and is responsible for translating compiled quantum circuits into executable instructions that directly manipulate qubits and handle measurement feedback. However, existing designs rely primarily on customized instruction sets, limiting design reuse and requiring significant effort to build supporting toolchains. Furthermore, efficiently addressing qubits and scheduling operations in highly scalable scenarios remains a critical challenge. In this work, we present a vectorized quantum control approach built upon the RISC-V Vector (RVV) engine with a quantum-oriented extension. Leveraging the high parallelism of RVV, our approach can address up to 128 qubits in a single instruction. We also embed parameterized rotation information into the instruction set, enabling dynamic tuning of gate rotations in hybrid quantum-classical programs. To support mid-circuit measurements, we design a hardware-based halt-resume protocol that resumes pipeline execution within 80 $ns$ of receiving the measurement result. Comprehensive evaluation using both RISC-V toolchains and FPGA prototypes demonstrates that our design achieves up to 2.52$\times$ speedup over the baseline in program execution time, with excellent scalability.

I formulate black-hole-horizon-induced decoherence of charged branch codes as the leading-soft QED restricted to an exterior algebra, formulated as an open quantum system. The fixed-history Feynman--Vernon identity ${\cal F}[J,J]=1$ remains exact. Decoherence enters through the unequal-history influence factor that survives exterior monitoring and belongs to the complementary horizon output. In the coherent eikonal regime, I derive the completely positive Schur channel $({\cal E}_H^{(0)}ρ)_{ab}=\langleΦ_b^{H,(0)}|Φ_a^{H,(0)}\rangle \, ρ_{ab}$. The leading soft input is the eikonal factor, projected onto the horizon radiative algebra. The channel yields Gram-positivity constraints, an exterior quantum-eraser bound, finite-time non-Markovianity tests, soft/hard scaling criteria, and a charged-qutrit interferometer measuring a leading-soft Bargmann holonomy. The holonomy phase is the rephasing-invariant symplectic area of a triangle in horizon soft phase space. I show that its orientation, common-mode, triangulation, and completely positive determinant identities render falsifiable tests beyond pairwise two-path visibility.

Nonlinear dynamics is ubiquitous in nature, ranging from chemical pattern formation to ocean circulation, yet its simulation on quantum computers is fundamentally limited by the unitary nature of quantum evolution. We propose the quantum Koopman method, a data-driven framework that embeds nonlinear dynamics into a learned linear representation and implements the resulting evolution using shallow quantum circuits. This method learns Koopman observables from trajectory data, projects the lifted dynamics onto a finite-dimensional subspace, and decomposes the corresponding non-unitary propagator into parallel spectral channels. We utilize the Koopman method on a superconducting processor to simulate three distinct nonlinear systems, comprising reaction-diffusion dynamics, fluid motion on a sphere, and satellite-derived observations of Gulf Stream currents, employing up to 32 parallel circuits of 10 qubits. These quantum simulations capture the dominant multiscale patterns and statistical signatures of the underlying dynamics, and reveal a transition from performance limited by hardware noise in weakly nonlinear systems to performance limited by finite-dimensional Koopman representations as nonlinear scale interactions increase. This transition identifies a practical boundary for quantum-amenable nonlinear dynamics, establishing a hardware-validated route for simulating moderately nonlinear dynamics on near-term quantum hardware.

Large-scale combinatorial optimization remains demanding for classical heuristics, particularly when dense Quadratic Unconstrained Binary Optimization (QUBO) formulations induce large memory footprints, high CPU utilization, and long execution times. While near-term quantum processors cannot yet deliver unconditional quantum advantage, hybrid architectures can provide practical value by reducing the resource burden. This paper presents a resource-efficiency study of Hybrid Quantum Neighborhood Selection (HQNS), a framework that decomposes large dense QUBO instances into bounded-width quantum subproblems via stochastic frontier selection. We evaluate HQNS on the Maximum Diversity Subset Selection Problem (MDSSP), focusing on the trade-off between solution quality retention and resource consumption. Benchmarks up to N=1000 candidates show that HQNS preserves 99.9908% of the mean diversity score of an 11-restart parallel Simulated Annealing baseline, while reducing wall-clock time by 94.91%, peak CPU utilization by 64.68%, and peak memory usage by 88.61%. The QPU execution time remains bounded within a 6-7 second envelope across scales, indicating that the quantum component is decoupled from the global QUBO dimension when the frontier size is fixed. These results suggest that HQNS provides a resource-aware pathway for deploying hybrid quantum optimization in practical large-scale settings, serving as an efficient architecture for incorporating near-term quantum processors into classical optimization pipelines.

The study of non-Markovian quantum processes has attracted significant interest in recent decades, giving rise to several competing notions of quantum non-Markovianity. These notes serve as an introduction to the topic for graduate students familiar with quantum mechanics and probability theory. Owing to the vastness of the literature, we focus on two prominent characterizations of quantum Markovianity based on the divisibility of quantum channels and monotonically decreasing state distinguishability. The correspondence between classical concepts (stochastic matrices, Chapman-Kolmogorov equation) and their quantum analogs (dynamical maps, CP-divisibility) is emphasized throughout.

The quantum boomerang effect (QBE) is a unique dynamical signature of Anderson localization, characterized by a launched wavepacket that initially drifts but ultimately returns to its initial position due to fundamental quantum interference. In this work, we theoretically establish and quantitatively characterize the QBE in a time-crystalline structure using a periodically driven quantum particle in a one-dimensional potential well. By constructing maximally localized Floquet-Wannier states and introducing temporal disorder, we rigorously map the continuous Floquet dynamics onto a discrete disordered tight-binding lattice. By positioning a detector at a fixed spatial coordinate, we monitor the temporal evolution of the wavepacket, to extract the mean temporal center of mass of the probability density in a time-crystalline structure. This mean temporal center of mass exhibits an initial ballistic expansion, followed by a pronounced U-turn, and ultimately returns to its initial temporal position after long-time evolution. These results confirm the existence of the complete QBE in the time domain. They also demonstrate that non-trivial dynamics can be explored within time-crystalline systems, even though these structures already possess an inherent temporal periodicity.

We study a quantum implementation of non-Abelian Thouless pumping in Lieb lattices using Rydberg synthetic dimensions. The lattice is encoded in twelve selected microwave-coupled Rydberg levels, forming a three-cell structure with six degenerate zero-energy states. These zero-energy states define the working subspace for cyclic modulation of the microwave couplings, while the remaining bright states provide the dominant leakage channels at finite evolution time. To choose the relative timing of the Gaussian pulses, we introduce a global adiabatic criterion (GAC), which evaluates the mean value and temporal fluctuation of a nonadiabatic factor obtained from a representative $Λ$-type transfer paradigm. With the resulting timing applied to the full twelve-level pumping dynamics, composing two elementary pumping cycles in opposite temporal orders produces distinct projected population maps. It is exactly consistent with noncommuting matrix-valued adiabatic operations in the zero-energy subspace. We numerically simulate the non-Abelian Thouless pumping using the Lindblad master equation with state-dependent Rydberg loss and representative perturbations. The results show that the GAC-selected timing within the same Gaussian pulse family gives higher target-state population than two literature-adapted Gaussian pulse schedules over the simulated parameter ranges. This quantum implementation of non-Abelian Thouless pumping, enabled by the GAC, marks a major milestone in finite-time geometric control and paves the way for transformative applications in holonomic quantum computing with Rydberg synthetic lattices.

This short report explores the (non exhaustive) current state of quantum technologies, their potential applications, and the challenges that must be addressed to harness their full potential. In particular we will focus on the quantum computer architecture and its ecosystem. Such architecture represents a complex, multi-layered system that integrates quantum and classical components to enable the execution of quantum algorithms. This manuscript is then organized as follows : first we will introduce the quantum processing unit, the lowest layer of a quantum computer. Then we will progress from the lowest to the higher layer of the system architectures : measurement, circuit control, error correction and mitigation system, the quantum compiler and finally the software stack, with particular emphasis on the interactions between these components

Achieving a genuine quantum advantage relies on two distinct non-classical resources that restrict efficient classical simulation: entanglement and magic (nonstabilizerness). We investigate the interplay between these resources by characterizing the Pareto frontiers of extreme magic at fixed entanglement for systems of two qutrits ($d=3$) and two ququints ($d=5$). Unlike the case of two qubits, the Schmidt spectrum for two qutrits features two independent entanglement parameters, resulting in two-dimensional Pareto surfaces. For the lower frontier, we recast the minimal magic as a compact function of concurrence and negativity, with a maximal value of $\ln 2$. For the upper frontier, we determine the maximal stabilizer Rényi entropy to be $M_2 = \ln(81/17) \approx 1.561$, which tightens the previous theoretical bound of $\ln 5\approx 1.609$ and improves on earlier numerical estimates. The maximum magic is achieved at eighteen distinct maxima categorized into three families of six permutation-equivalent spectra. We provide analytical expressions for the maximal magic in the neighborhood of each maximum and for the corresponding maximally magical states which turn out to be Weyl-Heisenberg-covariant fiducial states for mutually unbiased bases. Finally, numerical analysis of two ququints ($d=5$) reveals six permutation-inequivalent maxima with a peak magic value of $M_2 = \ln(625/49) \approx 2.546$. Based on these findings, we conjecture that the maximal magic for a bipartite system of two qudits with prime dimension $d$ is given by $\ln [ d^4 / (2d^2 - 1) ]$, which reproduces the previously known value for qubits, as well as the values derived here for qutrits and ququints.

Entanglement between two spatially separate matter particles can be generated via many means and often resides in the internal states of particles. Here, via Rydberg blockade in two spatially separate neutral atoms, we find that the photon recoil in Rydberg excitation can push one atom microns away provided the other atom exerts a state-dependent Rydberg-mediated blockade. When the atoms are recaptured by optical traps, a position-position entangled state between two spatially separate atoms can emerge. This realizes a Bell state of two atoms, where the entanglement exists in the position of each atom and the distance between the two possible locations of each atom can be in the hundred-micron regime.

Dynamical structure factors (DSF) measured with neutron-scattering experiments provide key insights into the structure of materials. Their computation requires both the preparation of an equilibrium state and the implementation of Hamiltonian dynamics. We demonstrate the feasibility of computing DSF on the Quantinuum Reimei trapped-ion quantum computer, comparing the DSF of 1D Heisenberg model on $20$ sites, and that of the copper sulfate crystal. To that end, we introduce a pumping approach for computing the DSF $S(q,ω)$ on quantum computers that enables targeting specific arbitrary values of frequencies $ω$. This method time-evolves the initial state using a time-dependent Hamiltonian perturbed by a source term oscillating at the target frequency $ω$. When targeting only a few frequency values, this approach provides a significant reduction in shot overhead compared to previous methods.

Exotic helium atoms act as unique atomic traps for heavy, negatively charged particles, protecting them from nuclear annihilation and nuclear capture on timescales long enough to enable high-precision laser spectroscopy. Such measurements serve as stringent tests of three-body quantum electrodynamics and offer a direct route to determining fundamental particle masses. Motivated by upcoming spectroscopic efforts targeting pionic ($π^{-\,4}\mathrm{He}^+$) and kaonic ($K^{-\,4}\mathrm{He}^+$) helium, we present a rigorous theoretical evaluation of the collisional and density effects governing these systems. Using an ab initio potential energy surface and coupled-channel quantum scattering calculations, we study the collisional stability of the candidate metastable states against inelastic quenching in a cryogenic helium buffer gas. Furthermore, we provide theoretical reference values for the pressure broadening and pressure shift coefficients of the targeted transitions. These results establish an essential benchmark for future experiments, paving the way for refined determinations of the pion and kaon masses.

We propose a method to create a room-temperature maser operating at approximately 2.9~GHz frequency using an ensemble of negatively charged nitrogen-vacancy electronic spins (NV) in diamond, without requiring population inversion. Our method considers a DC magnetic field of a few milli-Tesla (mT) applied along the perpendicular direction of an ensemble of NV spins aligned along a common axis. This perpendicular magnetic-field creates superposition states of $|m_{\mathrm{s}}=-1\rangle$ and $|m_{\mathrm{s}}=+1\rangle$ of the NV spin's ground state triplet levels and thereby makes it possible to drive all three transitions in the NV spin ground state. We model the system by including optical pumping of the NV spins, near-resonant driving of two transitions, and coupling the third transition to a near-resonant microwave resonator. Numerical estimates using experimentally realizable parameters show that inversionless masing can be achieved inside the microwave resonator using our method. As an application, we show that the output intensity of an inversionless maser ($1.1\times10^{14}$ spins) can be used for magnetic field sensing with a DC sensitivity on the order of a hundred pT/$\sqrt{\mathrm{Hz}}$. Our study opens a new direction in room-temperature diamond NV maser devices for quantum technological applications without the requirement of a strong bias magnetic field, as in conventional NV diamond masers.

Efficient single-photon frequency conversion is investigated in a two-giant-atom waveguide-QED system, where a two-level giant atom and a $Λ$-type three-level giant atom couple to a common one-dimensional waveguide. While the $Λ$-type atom provides the inelastic channel, the two-level atom induces secondary coherent coupling, creating multi-path interference for the converted photon. Using the real-space approach and within the Markovian approximation, we derive analytical four-channel scattering amplitudes and reveal that the inelastic transmission spectrum, governed by three complex resonance poles, exhibits a multi-peak interference pattern. By introducing a local single-pole approximation, we reduce this complex spectrum to a local Fano lineshape, decomposing it into a coherent superposition of a local background term and a single-pole resonant term. The interplay between these two terms-controlled by the photon propagation phase between the giant atoms' coupling points-determines the conversion efficiency, with the background suppression condition leading to a Lorentzian reduction. Based on the single-pole resonance weight, we formulate a phase-selection criterion for highly efficient conversion. Compared with both the small-atom and single $Λ$-type giant-atom models, the two-giant-atom scheme achieves substantially enhanced inelastic transmission over a broader frequency-conversion range. This work reveals how phase-controlled local Fano resonance enables high-efficiency frequency conversion, establishing a general paradigm for engineering resonant light-matter interactions in structured quantum systems.

In a symmetry-restoration quantum Mpemba effect, an initial state with stronger local symmetry breaking can lose that memory faster than a state that starts closer to the symmetric manifold. We test whether this local ordering reversal is organized by chaotic thermalization in a clean U(1)-conserving spin chain, comparing spectral level statistics with crossings of the entanglement asymmetry for the same Hamiltonians. We find that Gaussian orthogonal ensemble (GOE)-like level statistics alone do not determine whether Mpemba crossings occur. Across field textures, GOE-like spectra can occur with or without entanglement-asymmetry crossings, and crossings can also appear away from the GOE reference. A near-staggered detuned control further shows that even an inversion of the total charge-sector coherence need not produce an entanglement-asymmetry crossing. Thus the crossing response is controlled not by spectral chaos alone, but by how local charge-sector coherence enters the reduced density matrix.

Recurrence Plot (RP) is a method employed to analyze the periodicity, chaoticity, and nonlinear characteristics of complex systems. Quantum Principal Component Analysis (QPCA), on the other hand, achieves dimensionality reduction of sample data using density matrices based on quantum circuits. We improve the distance threshold function of the recurrence plot algorithm using a density operator conceptually equivalent to the covariance matrix, integrate it with quantum circuits, and thereby develop a Quantum Recurrence Plot (QRP) algorithm. This algorithm achieves ultra-high efficiency in parallel computing, reduces computational costs, and simultaneously upgrades the traditional grayscale recurrence plot to colored heatmaps, enabling a better revelation of the system's dynamical characteristics.

We report an improved absolute frequency measurement of the $^{176}$Lu$^+\,(^{3}\mathrm{D}_1)$ optical frequency standard, evaluated via a remote link to the NRC-FCs2 caesium fountain primary frequency standard. Operating a single ion clock with 94.2% uptime over 10 days, and using an ambiguity-resolved precise point positioning (PPP-AR) link over the Global Positioning System (GPS), we determine an absolute frequency of $353\,638\,794\,073\,800.33(9)\,$Hz at a fractional uncertainty of $2.6 \times 10^{-16}$. This agrees with our previous result, which underpins the CIPM recommended frequency value, and reduces the uncertainty by a factor of 3.6.

We study lower bounds for Bayesian quantum parameter estimation, with a particular focus on qubit models. While several lower bounds on the Bayes risk have been proposed, including the Bayesian symmetric logarithmic derivative (B-SLD) type bound and the Bayesian Nagaoka-Hayashi (B-NH) bound, there is no definite proof available to show they are attainable except for special cases. Thus, identifying attainable bounds together with their corresponding optimal measurement strategies remains a central open problem in Bayesian quantum estimation. In this work, we introduce a new Bayesian lower bound, referred to as the Bayesian Gill-Massar (B-GM) bound, inspired by the logic of Gill-Massar bound in point estimation. We derive an analytical closed-form expression of the bound and show that it is attainable for any qubit model. In particular, we prove that the optimal Bayesian strategy can be realized by a projection-valued measure associated with a single effective direction determined by the weight matrix and the B-SLD-type Fisher information matrix. We provide numerical comparisons between the B-GM, B-NH, and B-SLD-type bounds in higher-dimensional models. Our results show that the B-GM bound has a limitation in high-dimensional models with few parameters, since it can be negative.

We formulate the geometric structure of non-compact bosonic quantum systems in regimes where vacuum instability renders the relevant quantum states non-normalizable, causing conventional state-space quantum geometry -- described by the Berry connection, curvature, and quantum metric -- to become ill-defined. To overcome this breakdown, we develop a formulation of quantum geometry at the level of canonical operator frames, allowing for complexified Bogoliubov-Valatin transformations that lift the requirement that creation operators be Hermitian conjugates of annihilation operators. Canonical operator frames are defined as choices of bosonic creation and annihilation operators realizing the canonical commutation relations. A natural equivalence relation among such frames generalizes the phase ambiguity of quantum states and determines a parameter space that analytically extends the stable-regime parameter space. The space of canonical operator frames forms a principal bundle over parameter space -- the operator-frame bundle -- equipped with a natural Ehresmann connection that defines parallel transport while preserving the canonical commutation relations. In the stable regime, this construction reduces to the Berry connection, while more generally it yields a well-defined operator-space quantum geometric tensor (QGT) that remains valid across vacuum instabilities. Using the framework of rigged Hilbert spaces, we define a notion of quantum frame vacuum and obtain a consistent state-space QGT. Focusing on a single bosonic mode, we demonstrate analyticity of the QGT across the quantum frame-vacuum phase transition and present the corresponding phase diagram on the complexified squeezing-parameter plane. We further introduce a realistic physical setting that allows continuous paths connecting stable and unstable regimes, along which the QGT evolves smoothly across Stokes lines.

Macroscopic optomechanical systems offer a promising testbed for distinguishing whether gravity acts as a quantum interaction or as a classical field. Schrodinger-Newton (SN) theory is the nonrelativistic limit of semi-classical gravity where quantum matter couples to classical gravity. Based on SN theory, this work investigates how classical self-gravity affects continuous quantum state tomography of a macroscopic mechanical oscillator monitored by variable-angle homodyne detection. In the Schrodinger-Newton (SN) theory, the measurement record arises from a different conditional test mass dynamics from that in quantum-gravity (QG)/standard quantum mechanics, consequently, applying the QG-optimised reconstruction map introduces an additional state-dependent contribution. We show that this contribution makes the reconstructed covariance depend on the chosen set of tomography angles and can drive the SN covariance--after QG filtering--outside the standard Gaussian-covariance domain set by the Heisenberg uncertainty principle. We quantify the resulting QG-SN distinguishability via the Hellinger distance and analyse its dependence on measurement strength and temperature. We then formulate the same issue in the broader setting of nonlinear quantum mechanics: when the system's conditional dynamics during the readout process depends on the state being inferred, the tomographic map acquires nonlinear, model-dependent corrections to the usual Radon or Gaussian reconstruction map.

We introduce a quantum algorithmic framework based on probabilistic mixtures of unitary channels that, similar to the framework of quantum singular value transformations, enables the application of arbitrary polynomials of hermitian operators onto arbitrary initial states. We show that our framework supports a flexible tradeoff between sample- and query complexity ranging from optimal query complexity, meaning logarithmic in the error, and exponentially scaling sample complexity to sub-polynomial query complexity in the error and polynomial sample complexity. Combined with the considerably lower quantum circuit complexity, compared to quantum singular value transformations with a linear combination of unitaries block encoding, we argue that our framework can be seamlessly scaled from NISQ to fault-tolerant quantum computing.

Superradiant lasers promise continuous, narrow-linewidth coherent emission at the bare atomic transition frequency, enabling frequency references of exceptional precision. Recent experiments have advanced the field, but achieving truly continuous operation remains technically challenging. Here we propose an alternative route to an active optical frequency reference with fewer emitters using all-to-all dipole-dipole interactions mediated by a nanophotonic waveguide. We show that selectively pumping only a sub-ensemble of emitters, rather than the full ensemble, substantially improves emission characteristics. The collective interactions with unpumped emitters provide narrowband frequency selection and establish an effective feedback mechanism analogous to the role of a macroscopic cavity. We find directional superradiant emission with strongly phase-synchronized emitter correlations and a narrow output spectrum close to the bare emitter resonance. Our results demonstrate a strong metrological gain from selective partial pumping of quantum emitters with the second-order intensity correlation $g^{(2)}(0)\simeq 1$, indicating reduced equal-time intensity fluctuations, and open a route to waveguide-based optical frequency references using small clock-atom ensembles for chip-scale precision metrology.

We study the localization of excitations in positionally disordered spin or atom networks coupled via the realistic resonant dipole-dipole interaction (RDDI), which does not conform to a simple power law, as the spatial dependence and dissipative character distinguish it from conventional short or long-range models. Despite its partially long-ranged and radiative nature, positional disorder in the RDDI coupling leads to strong spatial localization of excitations. The interplay between coherent and dissipative couplings gives rise to nontrivial interference effects that stabilize localized modes even in open geometries. Our results uncover a photon wavelength-induced transition from extended to localized excitation dynamics, establishing RDDI networks as a unique setting to explore the emergence of localization in realistic quantum optical systems. Our analysis of the localized modes induced by RDDI has potential applications in coherent photovoltaics, excitonic circuits, quantum memory, and quantum sensors.

Quantum sensing is a promising technology capable of demonstrating clear advantage over comparable classical techniques for precise measurement. One application of quantum sensing is in function estimation, which can be done using a network of entangled quantum sensors, allowing for measurements with greater optimal sensitivity than unentangled sensing protocols. In cases where quantum sensor networks will be used to measure data that should remain private (e.g., biomedical data), it is imperative that these protocols include a privacy mechanism to hide sensitive information. In this work, we show that entangled sensor networks are vulnerable to certain privacy-violating attacks. To mitigate these attacks, we introduce secure sensing protocols endowed with differential privacy. We reconcile differential privacy with retaining Heisenberg-limited scaling, and introduce several protocols achieving varying balances between the two. We show that our main protocol, an $n$-node network sensing protocol that injects noise directly into the sensing Hamiltonian, exhibits a tradeoff between the desirable $O(1/n^2)$ Heisenberg scaling of the mean-squared error of the function estimate and the level of privacy attainable. Under assumptions on the network (a common source of randomness and a constant fraction of honest parties), we show that this protocol is locally implementable and achieves $(O(1), δ)$-differential privacy for arbitrarily small $δ$ while retaining Heisenberg scaling of the mean-squared error. We prove that our protocols are resilient to attacks by broad classes of classical and quantum adversaries, and find advantages in the privacy-utility tradeoff when using quantum techniques.

Interest in using quantum computers for the purpose of predicting chaotic partial differential equations (PDEs) has been growing with the advent of newer low-error quantum computers and robust simulation tools. In this paper, we present a method that utilizes a quantum reservoir network (QRN) to predict latent space representations of the high-dimensional chaotic 1-D Kuramoto-Sivashinksy (KS) system. This hybrid approach takes advantage of advancements in classical machine learning (ML) through the use of a classical autoencoder as well as techniques from quantum metrology through the use of a unitary that creates metrologically-useful states. Through rigorous simulation and analysis, we show that the proposed method outperforms alternative QRN implementations without this metrologically-useful state preparation, and also show better performance than classical echo-state networks when weight regularization is not used. Finally, we bring to light potential issues that can arise when using autoencoders within QRC pipelines.

We present the design and benchmarking of RP000, a quantum photonic processor capable of encoding a quantum system in the degrees of freedom of single photons, based on standard CMOS-compatible manufacturing processes, and working at room temperature. We benchmark it against machine learning tasks, evaluating three quantum-classical architectures of increasing complexity. Our experimental results and simulations show that RP000 achieves higher accuracy than classical networks of comparable size in multiple use cases. Compared to a superconducting quantum processor, RP000 exhibits superior noise tolerance. These findings demonstrate that RP000 can provide a scalable route toward efficient quantum applications.

We investigate universal entanglement properties inherent to superpositions of randomized states. We find that an $m$-fold superposition of typical states may be classified into two distinct entanglement classes via the 2nd Rényi entropy density $s_2$. The maximally entangled regime is defined by $s_2 \sim \ln (2)$, for which superposition adds no additional entanglement. The sub-maximally entangled regime, $s_2<\ln 2$, instead constrains the reduced density matrices of independent components to be orthogonal in the thermodynamic limit, which fixes the entanglement of the superposition to a logarithmic enhancement $ΔS(m)=\ln (m)$. As a consequence, an exponentially large number of superpositions is required to transition from the sub-maximally entangled class to maximal entanglement. We explicitly calculate $s_2$ and the logarithmic enhancement, and demonstrate orthogonality for two canonical examples of the sub-maximally entangled regime (superpositions of pure Gaussian states and of random matrix-product states). We also examine the entanglement of superpositions of random stabilizer states, and discuss their relaxation to the Haar limit.

Given that quantum computers are naturally suited to simulate the behavior of quantum many-body systems, an immediate question arises: can one formulate physically motivated quantum machine learning (QML) tasks that exhibit learning separations? We address this problem by studying the learnability of quantum many-body dynamics from the perspective of probably approximately correct (PAC)-learning. Concretely, we devise a supervised learning problem where the training set consists of specifications of randomized stabilizer probe states, evolution times sampled uniformly from a polynomially large time interval $[0,T]$, coupled with expectation values of certain observables evaluated on the resulting time-evolved state under an unknown Hamiltonian. For this learning task, we provide an efficient quantum procedure whose training phase learns the underlying Hamiltonian from short-time training samples, and whose deployment phase combines Hamiltonian simulation with the classical shadows protocol to perform inference on a newly given data point. By contrast, the existence of $O(\mathsf{poly}(n))$-time instances ensures classical hardness: by embedding a $\mathsf{BQP}$-complete computation into the polynomially long time-dynamics of a low-intersection variant of the Feynman-Kitaev clock Hamiltonian construction, we show that, for a certain family of input distributions, no randomized classical polynomial-time algorithm can fulfill our learning condition, unless $\mathsf{BQP}\subseteq\mathsf{P/poly}$. Furthermore, we show that the classically hard instance maintains quantum learnability. We also give an interpretation of our results in learning-assisted certified quantum simulation. Taken together, our results demonstrate a rigorous learning separation for a natural ML task based on Hamiltonian evolution, while building connections between quantum learning theory, quantum simulation, and QML.

Continuous measurements can prepare macroscopic mechanical oscillators in conditional quantum states, but their covariance is difficult to verify. The conventional retrodictive estimator assumes a forward--backward covariance symmetry and can be biased, because physical dynamics such as feedback damping reduces the observability of the state from future records. Here, we derive an exact linear-Gaussian estimator from causal, retrodictive, and smoothed trajectories. For a milligram-scale mirror, it agrees with a Riccati prediction based on parameters fixed independently, while the conventional estimate exhibits a large bias in the covariance-space metric, $d_M \sim 5$. Our method paves the way toward unbiased testing of macroscopic entanglement within a calibrated linear-Gaussian model, which will be applicable to tabletop mirrors as well as gravitational-wave kg-scale test masses.

Unitary encoding of a single parameter provides quadratic enhancement in precision, with the quantum Fisher information scaling quadratically with the encoding time. However, when estimating multiple parameters simultaneously, this fundamental scaling is not guaranteed. Here, we establish a universal geometric obstruction that dictates when multiparameter quantum metrology fails to achieve simultaneous $t^{-2}$ scaling. By decomposing the Hamiltonian derivatives into components that commute and do not commute with the system Hamiltonian, we prove that linear dependence among the commuting components inevitably generates a slow parameter direction whose Fisher information remains bounded as O$(t^0)$, limiting the overall estimation precision. We demonstrate this mechanism in both discrete- and continuous-variable setups, including collective spin magnetometry and a generalized quantum harmonic oscillator, and contrast it with the Lipkin--Meshkov--Glick model where $t^{-2}$ decay is preserved. Remarkably, while the slow direction fundamentally limits the achievable precision, the measurement incompatibility between fast and slow directions decays as $1/t$, rendering the symmetric logarithmic derivative bound asymptotically saturable. Our framework provides a readily computable diagnostic, given by the Gram matrix of the diagonal generators, for identifying such obstructions in arbitrary multiparameter estimation problems. We further show that the bottleneck can be circumvented by relegating slow directions to nuisance parameters or by employing adaptive quantum control.

Bosonic quantum error correction (QEC) relies on non-Gaussian bosonic encodings whose preparation cost is a central practical constraint. In this work, we use stellar rank as a resource measure to design and benchmark bosonic codes under finite non-Gaussian resources. For fixed cat and Gottesman--Kitaev--Preskill (GKP) code families, we show that finite stellar rank creates a trade-off among state approximability, energy, and logical protection under photon loss and photon-number dephasing, evaluated with optimal recovery. This trade-off implies that codewords with better ideal error-correction properties need not be optimal once finite-rank preparation constraints are imposed. Going beyond fixed-target codewords, we directly optimize bosonic encodings at fixed stellar rank, revealing noise-adapted code structures and concrete resource thresholds. Grid-like encodings emerge under photon loss, whereas approximately rotation-symmetric encodings arise under dephasing. In the optimized search, stellar rank k=2 suffices to surpass break-even for all dephasing strengths considered, while under photon loss the required rank increases with the loss rate. These results establish stellar rank as an operationally meaningful resource measure for bosonic QEC under practical state-preparation constraints.

Attosecond metrology is the ability to measure ultrafast optical light-wave oscillations, yet its approach has been limited to classical fields. Hence, the influence of the fluctuations of a quantum field on attosecond measurements has remained unexplored. Here, we close this gap by showing that the attosecond streaking measurement of bright quantum light is sensitive to quantum fluctuations of the optical field on the attosecond timescale. The distinct sub-cycle modulations allow to extract the properties of the squeezed field quadrature in regimes where conventional state tomography approaches reach their limitation. With the full quantum optical attosecond streaking scheme developed here, we provide a certification method that can measure quantum squeezing below the shot noise limit, thereby overcoming the problem of tomographically measuring bright quantum light. This opens the way towards quantum optical metrology of field fluctuations with attosecond temporal resolution.

Hole spin qubits in undoped Ge/SiGe quantum well structures have advanced rapidly in performance and scalability. However, stringent multi-layer patterning and overlay requirements of conventional overlapping-gate devices create a bottleneck for academic proof-of-concept experiments involving few-qubit devices. Here we present fabrication and measurements of Ge/SiGe spin qubit devices with a global accumulation gate and single-layer depletion fine gates, which substantially reduce fabrication complexity. With careful design of the gate-2DHG capacitance, we demonstrate RF-based single-shot spin readout and coherent control of two single-spin qubits. We also characterize the spin coherence times and exchange tunability, which are similar to those reported in recent overlapping-gate Ge/SiGe spin qubit devices. By simplifying fabrication without sacrificing performance, our approach offers a more accessible device design for spin-based quantum technology research.

A graph with Laplacian matrix $L$ is called Laplacian integral if the eigenvalues of $L$ are all integers, and it is called $\{-1,0,1\}$-diagonalizable if $L$ has a full set of eigenvectors with entries from $\{-1,0,1\}$. We herein develop a structure theorem for both Laplacian integral graphs and $\{-1,0,1\}$-diagonalizable graphs of prime order, and combine it with some novel computational techniques to characterize all such graphs for orders larger than was previously possible. For example, we enumerate all Laplacian integral and $\{-1,0,1\}$-diagonalizable graphs of order $13$ or less, all $\{-1,0,1\}$-diagonalizable graphs of prime order $23$ or less, all regular integral graphs of order $15$ or less, and all regular $\{-1,0,1\}$-diagonalizable graphs of prime order $53$ or less. As an immediate byproduct of our work, we show that the $S_{n,n}$ conjecture for Laplacian integral graphs is true when $n = 12$, thus making $n = 16$ the smallest open case; additionally, we disprove two related conjectures regarding Laplacian spectra. We also establish an exponential lower bound on the number of connected $\{-1,0,1\}$-diagonalizable graphs of order $n$, thus beating the previously best-known (subexponential) lower bound. Finally, we show that every bipartite $\{-1,0,1\}$-diagonalizable graph is regular (a fact that fails to generalize to Laplacian integral graphs).

Differential privacy provides a rigorous framework for quantifying privacy leakage in data analysis, while its quantum extensions have become increasingly relevant with the development of quantum computing and quantum machine learning. In this work, we introduce and study quantum probabilistic local differential privacy, a relaxation of quantum local differential privacy in which the privacy constraint is allowed to fail on a spectral violation event with low probability. This quantity can be interpreted as the probability under the quantum superoperation of a quantum privacy-loss violation, and is closely related to the acceptance probability of the quantum Neyman-Pearson test at a small threshold. We investigate the basic structural properties of this privacy notion and clarify its relationship with existing forms of quantum differential privacy. We show the properties of quantum probabilistic local differential privacy under tensor-product composition and unitary post-processing, while it is in general neither convex nor closed under post-processing by arbitrary quantum channels. We further characterize when depolarizing noise satisfies quantum probabilistic local differential privacy under several representative scenarios. Finally, we connect quantum probabilistic privacy constraints with statistical inference by deriving a lower bound on probabilistically privatized contraction coefficients in terms of the hockey-stick divergence. As an application, we obtain sample complexity bounds of probabilistically privated asymmetric and symmetric quantum hypothesis testing. These results provide a systematic foundation for studying probabilistic privacy guarantees in quantum information processing and their operational consequences for private quantum statistical inference.

We investigate how cavity-mediated attractive electron-electron interactions modify the excitation gaps of fractional quantum Hall states within the composite-fermion framework. We compute both the neutral magnetoroton excitation spectrum and the charged excitation gap relevant to transport experiments for the Laughlin $ν=1/3$ and $ν=1/5$ states. We consider a spin-polarized lowest-Landau-level model in which the interaction is mediated by a cavity mode with a spatially uniform vacuum-field gradient and a finite interaction range controlled by a long-distance cutoff. Finite-size scaling reveals that the transport gap is consistently enhanced by the cavity-induced interaction, with the gap enhancement scaling quadratically with the electron number and with the fourth power of the vacuum-field gradient. By contrast, the magnetoroton spectrum exhibits a richer dependence on the interaction range. The high-$k$ magnetoroton gap is enhanced for all interaction ranges considered, consistent with its close connection to the charged excitation gap, even with the long-range character of the interaction.

We introduce a mapping between the ground state of interacting fermionic Hamiltonians and the non-equilibrium steady state of a purely dissipative open quantum system. Within the framework of third quantization, we map the Fermi-Hubbard Hamiltonian onto Lindblad jump operators acting on Majorana fermions. Remarkably, both hopping and interaction terms map onto jump operators that preserve the Gaussianity of Majorana fermions along individual quantum trajectories. As a result, the dynamics can be unravelled and each trajectory can be simulated efficiently using only two-point correlation functions, with a computational cost that scales polynomially with system size. We further show that finite particle number requires negative dissipative rates, leading to an intrinsically non-Markovian dynamics. The corresponding trajectory unravelling involves both positive and negative stochastic weights and exhibits a sign problem and large fluctuations, so that convergence requires an exponentially large number of trajectories. The overall computational cost remains exponential in system size despite the efficient Gaussian representation of individual trajectories, but is crucially dependent on the computational complexity of the non-Markovian unravelling, motivating further studies on the efficiency of such unravellings.

We nonperturbatively compute Rényi entropies for strip-shaped subregions in the three-dimensional O(4) model at finite density on the lattice. By using a dual variable representation and a tailored worm algorithm, we circumvent the sign problem when sampling the grand canonical ensemble. In the limit of large subregions, we also establish a direct, quantitative relationship between the derivative of entanglement entropy with respect to the size of the entangling region and the thermal entropy density for general quantum field theories, providing a new way to study their thermodynamics. We corroborate this argument with our lattice results by demonstrating that, in the appropriate limit, the derivative of entanglement entropy satisfies the same Maxwell relation as the thermal entropy density.

Braiding statistics of $p$- and $q$-dimensional topological excitations is conventionally defined in $p+q+2$ spatial dimensions. We find a novel statistical process $W_N(X,Y)=(Y^{-1}X^{-1})^N(YX)^N$ for two order-$N$ excitations in $p+q+1$ dimensions, detecting the Bockstein response $A\smile β(B)$. This new statistics and fermionic loop statistics exhaust all loop statistics in three dimensions whose fusion rules form an Abelian group $G$, classified by $H^5(B^2G,U(1))$. Surprisingly, conventional three-loop braiding goes beyond this classification, so it must have non-Abelian fusion rules. We suggest viewing three-loop braiding as particle-loop braiding together with exotic fusion rules between loops and point-like defects. We also try to clarify the relationship between statistics and symmetry anomaly.

Spin-photon interfaces based on silicon quantum emitters offer a scalable platform for quantum computing and networking. However, achieving coherent photon emission remains a primary challenge due to stringent material quality requirements. To overcome this, we utilise high-purity molecular-beam epitaxy (MBE) to epitaxially incorporate single T centres in silicon-on-insulator (SOI) wafers. We demonstrate single T-centre emission coupled to a nanophotonic waveguide and observe significant suppression of homogeneous broadening, yielding optical linewidths as narrow as 30 MHz using natural silicon for crystal growth. These results establish epitaxial T centres as a robust foundation for coherent spin-photon interfaces in silicon quantum photonics.

Synthetic quantum matter provides a highly tunable route to fractional quantum Hall physics beyond the constraints of conventional electronic materials. However, previous theoretical studies have mostly focused on their ground state properties. It remains unclear to what extent such platforms could reveal key excitation properties of fractional quantum Hall states. Here, we study charge-neutral collective excitations in a non-abelian lattice fractional quantum Hall state realized in the bosonic Harper-Hofstadter model at unity filling factior, realizing a Moore-Read ground state. Combining full exact diagonalization, band-projected exact diagonalization, and matrix-product-state simulations, we demonstrate the existence of a long-lived chiral graviton mode, probed by chiral 3-body correlators, for the first time on lattice non-Abelian states. The graviton signal is topological sector-independent and could be observed via geometric quenches in small open droplets directly relevant to current cold-atom experiments, while other neutral modes, such as the magnetoroton and neutral fermion, are less resolved at presently achievable volumes.

Wigner function learning is a central tool for characterizing continuous variable quantum systems. A fundamental challenge in this setting is to infer a continuous phase-space function from sparse pointwise measurement data, a task that becomes increasingly demanding as the effective dimension enlarges. Here, we develop a general machine learning framework to reconstruct Wigner functions directly as continuous functions from sparse phase-space data. For states with sparse Fock-space or coherent-state representations, such as binomial code states and cat states, we devise provably efficient regression models whose measurement complexity scales only logarithmically with the effective Hilbert-space dimension. For more general states, such as the Gottesman-Kitaev-Preskill (GKP) states, we design a deep learning model that reconstructs the Wigner function from sparse measurements and generalizes to arbitrary phase-space resolution. We demonstrate the broad applicability of our framework on both simulated data and experimental data from a circuit quantum electrodynamic (circuit-QED) system. Interestingly, on experimental data, we find that our model reconstructs Wigner functions of GKP code states across multiple rounds of quantum error correction and identifies the dominant error process using significantly fewer measurements than conventional estimation techniques.

Parameterized quantum circuits (PQCs) are increasingly used as policies and value functions in quantum reinforcement learning, yet it remains unclear when and why quantum policies generalize. We give a PAC-Bayesian account in which generalization is governed not by the raw number of circuit parameters, but by the effective dimension of the Fisher geometry induced by the circuit. This quantity is inflated by entanglement, making entangling connectivity an independent axis of complexity.In controlled experiments that fix the number of trainable rotations and vary only entanglement, we find that circuits with larger Fisher effective dimension exhibit larger train-test gaps, while parameter count is a weak predictor. The resulting bound acts primarily as a ranking certificate: it correctly orders circuits with identical parameter count, which parameter-counting bounds cannot do. We validate this mechanism across supervised classification, quantum contextual bandits, and value-function generalization, where entangled circuits consistently generalize worse than non-entangled circuits of equal parameter count, with gaps shrinking as sample size increases.Our strongest evidence comes from low-variance decision models, including single-observable classifiers, value heads, and one-step policies. In end-to-end multi-step policy learning, entanglement effects remain statistically significant but high return variance leaves the full ordering only partially resolved. Partial-correlation analysis shows that Fisher effective dimension screens off entangling pattern, and controls for training accuracy, readout, and optimizer rule out major optimization confounders. The effect also persists on an IBM Heron quantum processor under real noise. Overall, our results reframe quantum policy design around an entanglement--generalization trade-off rather than expressivity alone.

Rising energy demand from data-centre and AI applications has renewed interest in reversible computation, where logic need not dissipate heat at every step if information is uncomputed. Implementations have so far been classical: adiabatic CMOS reduces dissipation by slowing charge motion but is still limited by the threshold physics of transistors. Here we propose classical reversible logic implemented by coherent spin dynamics in a spin quantum-dot array, with inputs and outputs in classical basis states and no algorithmic use of superposition. The same spin stores, transports, and computes, with unitary rotation replacing irreversible switching. The universal building block is an iToffoli gate driven by DC voltage pulses and anisotropic exchange in Ge/Si hole spins. Simulations with experimental parameters reproduce the Toffoli truth table and yield a testable error landscape. Because shuttling transports the bit without measurement, logic and data movement remain reversible until readout. Millivolt pulses on femtofarad gates yield a gate energy below the 4~K Landauer scale, about five (eight) orders of magnitude below a room-temperature CMOS Toffoli with (without) 4 K cooling overhead. The same semiconductor hardware is therefore dual-use, supporting quantum algorithms when superposition is used and classical reversible logic otherwise.

We investigate the estimation of bath-induced coherence in a finite quantum system interacting with thermal reservoirs. Enhancement of coherence estimation is transient and the estimation precision totally disappears at the steady state despite the system retaining finite coherence. By analyzing the full Liouvillian eigenspectrum, we demonstrate that the optimal sensing window emerges from the competition between identifiable contributory modes' temporal relaxation and statistical importance. Neither is the linear inverse scaling of Liouvillian gap with transient optimal time a signature of unimodal contribution to optimal sensing, nor is the existence of multimodal dynamics a signature of nonlinear scaling. The inverse Liouvillian gap does not obey any general scaling with the optimal sensing time of coherence and we prove our numerical results analytically using a general Markovian framework. We further show that coupling the finite system to a quantum cavity and maintaining a thermal bias, transforms the transient metrological optimization into a sustained steady-state resource.

We characterize the Tanner graph spectrum of hypergraph-product (HGP) / lifted-product (LP) codes and bivariate-bicycle (BB) codes, informing qubit routing for three-dimensional reconfigurable qubit architectures. Syndrome-extraction routing depth on HGP/LP Tanner graphs reduces to a single SVD on the base parity-check matrix, using a spectral ratio $β_\text{HGP} = (1 + β_\text{base})/2$ where $β_\text{base} = σ_2(H)/σ_1(H)$ for the base parity-check matrix, and a diameter identity $D_T = 2 D_\text{base}$ where $D_\text{base}$ is the base Tanner graph diameter. Fourier spectral reduction reveals that the BB Tanner graph spectrum equals the union, over the $l \times m$ grid of characters of $\mathbb{Z}_l \times \mathbb{Z}_m$, of the singular values of a single $2 \times 2$ symbol matrix built from the two defining polynomials. This reduces spectral analysis from an $O((lm)^3)$ diagonalization of the $4lm$-node Tanner graph to $lm$ independent $2 \times 2$ SVDs. These results compose into a multi-layer three-dimensional AOL routing protocol with one-time setup cost $T_\text{Valiant} = O(\log N)$ atom rearrangements amortizable over a memory experiment of $R$ rounds. For a Tanner graph chromatic index $χ'$ and $L_\text{layers}$ stacked AOL planes, the per-syndrome-cycle depth is $\lceil χ'/L_\text{layers} \rceil$ AOL pattern activations with no atom motion, an $8\times$ step-count reduction at $L_\text{layers} \geq χ' = 8$. Contingent on multi-layer AOL hardware, this yields an estimated $\sim50-300\times$ per-cycle wall-clock advantage over a single-layer AOD baseline (degrading to $\sim5-100\times$ under AOD-crosstalk overhead), reducing to equality in the single-layer limit. This paper therefore presents a route toward practical routing improvement for future quantum hardware incorporating multi-layer reconfigurable qubit architectures.

CP bias in proton--antiproton diffractive dissociation can be viewed from several philosophical perspectives, notably stochastic realism and stochastic epistemicism. When combined with the presumption of temporal symmetry, stochastic realism suggests that the laws of physics allow the possibility of thermodynamic antisystems, although whether antisystemic characteristics can be physically realised in nature remains an open question. Here, this bias is interpreted as apparent, indicating significant non-unitary contributions and a distinction from fundamental CP violations arising from unitary Hamiltonian dynamics. Such apparent effects may arise from intrinsic stochasticity, from environmental interactions, or from interference between the two. This work investigates the relevant mechanisms and determines conditions for creating, transmitting, or screening a CP bias. In the environmental branch, an equilibrated radiation bath may transmit a CP bias from matter-dominated surroundings, although causality constraints may limit this possibility. In the intrinsic branch, the observed bias is consistent with subleading antisystemic effects required by CPT invariance. Further experiments are needed to distinguish between these mechanisms.

We study the quantum decoherence of a bound state interacting with a reservoir of strongly interacting matter within the framework of open quantum systems. The bound state is modeled as a quantum harmonic oscillator whose parameters are tuned to reproduce the root-mean-square radius of $J/Ψ$ particle. The surrounding medium, representing the many degrees of freedom of strongly interacting matter, acts as an environment that induces dissipation and decoherence through system-reservoir coupling. By analyzing the time evolution of the reduced density matrix, we quantify the loss of quantum coherence and its dependence on medium properties. Subsequently, we extend the model by introducing a time dependence in the system-thermal bath coupling, thereby simulating a temperature evolution similar to that occurring during the expansion of a fireball in the central region of heavy-ion collisions. We find that a temperature evolution has a relevant impact on the way the system loses coherence through the coupling with the expanding medium. Finally, we estimate the impact of the time-dependent temperature on the decoherence process, also analyzing a scenario that includes viscous effects without finding a significant change with respect to ideal hydrodynamical evolution.

We present a new design for quantum packet routing within the emerging Quantum Internet, highlighting how a little-used feature of Internet Protocol Version 6 (IPv6), namely Extension Headers, can lead to a significant amount of quantumness within the IP layer. Taking a minimalist approach to alterations of established standards, we outline the changes required in order for quantum teleportation, quantum routing, and superpositions of these processes to be enabled. Relative to other proposals for routing within the Quantum Internet, the architecture we propose enables a wider range of outcomes allowed by quantum mechanics. We do not claim any optimally in our design, but rather a pathway to invoke new quantum routing outcomes via small additions to the current IPv6.

The Mpemba effect refers to the counterintuitive phenomenon that an initially hot system can freeze faster than an initially warm one. Recent years have brought major advances in both classical and quantum realizations, with the asymmetric bistable potential emerging as the paradigmatic classical benchmark because its mechanism is especially transparent and controllable. Yet for precisely this benchmark problem, the impact of quantization remains unexplored. Here we show that quantization shifts Mpemba behavior to qualitatively new regimes, moving it to ultra-cold temperatures that are orders of magnitude lower than those relevant for classical thermal barrier crossing. In addition, quantization produces inverse and double inverse Mpemba effects that are absent in the corresponding classical dynamics. Our results establish quantization as a robust route to quantum-enabled Mpemba effects inaccessible in classical regimes.

Generating images directly from quantum systems is an attractive but unresolved goal on NISQ hardware. Existing quantum generators face several coupled obstacles: barren plateaus that block trainability, expensive quantum circuit preparation, and hardware noise that erodes quantum information with depth. A further difficulty is producing image-scale output without a classical decoder, whose use would otherwise break the end-to-end quantum advantage. We propose SQGen, a full quantum generator built on a quantized tensor train (QTT) with a latent modulation architecture. Specifically, SQGen promotes the QTT bond index of the target pixel distribution to ancilla bond qubits, so that each circuit site operates locally on a bond register plus the two physical qubits that carry the row- and column-bit of one image scale. We further introduce latent modulation: each re-uploading rotation is factorized at the angle level into a trainable main path plus an additive latent term, reducing to the trainable main path when the latent term is disabled. During training, we create a differentiable model in the classical system under gate-compatibility constraints, with a torus prior as the latent distribution. After training, every operator maps one-to-one to a native quantum gate, yielding a compact, deployable quantum circuit with no classical decoder in the inference path. Together, these design choices address the obstacles raised above. Extensive experiments on image datasets and synthetic data demonstrate that SQGen trains stably, generates images end-to-end from a shallow circuit with no classical decoder, and shows promising feasibility on real quantum hardware.

We study genuine multi-entropy as a diagnostic of multipartite entanglement in the toric code, which provides a controlled setting for probing multipartite structures in topologically ordered states. Our main question is whether genuine multi-entropy captures information that is not reducible to conventional lower-party entropic data, such as topological entanglement entropy. We first analyze toric-code ground states that admit a stabilizer-state description, where the relevant quantities can be evaluated exactly. In this sector, genuine multi-entropy reflects the topological structure and symmetries of the toric code, while exhibiting highly constrained relations to lower-party multi-entropies. We conjecture that, for stabilizer states and ${q}\ge4$, the ${q}$-partite genuine multi-entropy at replica index $n<{q}$ collapses to a linear combination of multi-entropies involving at most ${q}-2$ parties. We establish this pattern explicitly for ${q}=4$ in the toric code stabilizer sector: for $n=2,3$, the genuine multi-entropy is proportional to the tripartite information $I_3$ and, for the Kitaev--Preskill partition, contains no independent genuine four-partite information beyond that captured by the topological entanglement entropy. At $n=4$, however, this reduction breaks down: the genuine multi-entropy is no longer proportional to $I_3$, but remains a topological invariant of the toric-code stabilizer ground states. For generic non-stabilizer superpositions within the ground-state manifold and for coherent superpositions of local excitations, the low-$n$ reduction also fails. These results show that genuine multi-entropy probes multipartite entanglement structure beyond the tripartite information, and hence beyond the topological entanglement entropy in the Kitaev--Preskill partition, whereas for stabilizer states at low replica index it reduces to lower-partite entropic data.

Light polarization is a primary degree of freedom for encoding quantum information. The scaling up of photonic quantum networks and computer architecture depends crucially on its precise characterization. This is typically achieved by placing external waveplates, polarizers, moving mounts, and recently metasurfaces, on top of the detectors. All these solutions complicate integration and scaling. Here we break convention with traditional architecture and present a monolithic, self-aligned metal-superconductor nanowire single photon detector (M-SNSPD) possessing intrinsic full polarization selectivity. Gold nanowires, co-fabricated atop NbTiN superconducting nanowires within the same lithographic footprint, act as polarization-selective plasmonic metamaterials inducing resonant absorption in the NbTiN. U-shaped wires provide linear polarization selectivity, while S-shaped meanders distinguish circular polarization, while retaining the high-count rates and low dark count rates of conventional SNSPDs. By arranging them into a four-pixel array we realize simultaneous projection onto four polarizations and demonstrate continuous polarization state tomography with an ensemble average fidelity exceeding 98%. Our approach opens new avenues towards scalable detector arrays with integrated plasmonic functionalities, for single photon polarimetry, imaging and spectroscopy.

There are several possible ways to encode random variables in a quantum state. The basis encoding of bit strings has paramount importance because it allows to load the values of a random variable through the superposition of corresponding basis states, and to then exploit quantum parallelism in processing algorithms. The basis encoding offers a natural way to represent an unsigned integer random variable, and extends to signed integers, as well as to fixed-point and floating-point variables. Each quantum representation of fractional numbers, however, involves a trade-off between accuracy and depth of manipulation circuits. Here, an efficient hybrid quantum-classical representation of quantum floating points is introduced. It combines a quantum register containing the values, with a classical register storing global information about the variable, namely the range and approximation tolerances. The sum and product operations are defined, in such a way as to ensure they are performed without overflow. By taking advantage of the stored classical information, the precision degradation that occurs due to rounding after repeated data manipulations, can be significantly reduced compared to known strategies. Ad hoc examples show up to around $90\%$ reduction in approximation, compared to previous techniques, after repeated additions. The method finds application in many algorithms of practical relevance and constitutes a significant advance in the design of arithmetic circuits with low depth and high accuracy.

We present an implementation of a three-state BB84 protocol with time-bin encoding, one decoy state and a simplified measurement scheme that uses passive basis choice. Our system simplifies the state characterization with respect to previous iterations. We also adapt the loss-tolerant method to our protocol, thus dealing with the measured state preparation flaws. We compare the obtained phase error rate and secret key rate when including the state imperfections and when assuming perfect states. Our results highlight the importance of characterization and implementation security.

Naseri et al. [Phys. Rev. A 106, 062429 (2022); arXiv:2205.13610] studied which quantum resources in initial states are essential for the probabilistic Bernstein-Vazirani (BV) algorithm, defining its performance as the optimal average success probability over all measurements. In this work, we consider a variant of BV algorithm, which is called the initialization-free (IF) BV algorithm, in which an arbitrary ancilla state as the oracle register is allowed, to improve the performance. We derive an explicit formula for the performance of the probabilistic IF-BV algorithm and obtain a necessary and sufficient condition for an initial state to achieve maximal performance. We further prove that, under a suitable ordering assumption on the coefficients of the initial state, the probabilistic IF-BV algorithm outperforms the standard probabilistic BV algorithm.

Lattice-based post-quantum cryptography relies on the hardness of the Learning With Errors (LWE) and Module Learning With Errors (MLWE) problems. This work introduces a constructive framework for encoding small MLWE instances as Quadratic Unconstrained Binary Optimization (QUBO) models suitable for quantum annealing. The formulation jointly represents secret coefficients and explicit error variables within a unified binary optimization structure, enabling their simultaneous recovery from the ground-state solution. Beyond the encoding, we develop a stability analysis of the resulting optimization landscape under additive perturbations. We show that the admissible noise region forms a convex polytope defined by competing candidate secrets, and establish an equivalent characterization in terms of the QUBO energy gap between the optimal and second-best solutions. Numerical experiments on low-dimensional benchmark instances using exact simulation demonstrate correct recovery of both secret and discretized error vectors, and confirm consistency between geometric stability regions and energy-gap behavior. We further quantify the scaling of logical variables and embedding overhead with increasing MLWE dimensions to assess feasibility on quantum annealing architectures. The results establish a systematic connection between MLWE problems and quantum optimization while providing a framework for analyzing robustness properties of QUBO formulations. Although current quantum annealing hardware remains insufficient for cryptographically relevant parameters, the proposed methodology offers a structured basis for studying lattice-based problems in quantum optimization settings without implying a practical threat to standardized post-quantum schemes.

Quantum theory fundamentally forbids the perfect copying of an arbitrary unknown quantum state, according to a principle known as the no-cloning theorem. Nevertheless, it is possible to construct a deterministic quantum map that produces multiple approximate copies of an unknown quantum state. This task is referred to as universal quantum cloning, further facilitating numerous quantum technologies such as quantum cryptography and quantum communication. In this work, we theoretically verify that the universal quantum cloning cannot be realized within a noncontextual theory, highlighting its intrinsically nonclassical nature. Our verification first {focuses on revealing that} $1\rightarrow2$ cloning scenario {is fully contextual}, and {further covers general examples to observe the contextual behavior of} $N\rightarrow M$ scenario. We believe that our results regarding quantum cloning serve a key role for understanding both quantum foundation and application.

Highly collimated laser beam with excellent spatial quality is essential for quantum sensing experiments, where even small residual beam divergence can accumulate over distance and introduce significant systematic errors. In this article, we present the design and detailed characterization of a high precision laser beam collimator developed for a cold-atom Gravimeter system, capable of producing an expanded laser beam with a diameter of 16 mm while achieving microradian level collimation accuracy through a five-degree-of-freedom (5-DOF) adjustment mechanism. The beam quality is evaluated using an ISO11146 compliant beam propagation measurement combined with Gaussian beam analysis to extract key parameters, including the beam waist, divergence angle, Rayleigh length, and beam quality factor $M^{2}$. The measured divergence angles of 0.006° (105 micro-radian) along the $x$ axis and 0.007° (122 micro-radian) along the $y$ axis confirm stable and well controlled collimation over long propagation distances. The demonstrated collimation architecture and characterization methodology provide a robust and scalable solution for cold-atom Gravimetry and other precision optical applications that require stable, high quality laser beams maintained over extended distances.

A topological invariant based on polar-decomposition of matrices correctly captures the topology of finite non-Hermitian chains exhibiting the non-Hermitian skin effect, provided that an appropriate crop-length parameter is chosen. This parameter, which sets the cutoff used in the calculation of the invariant, is usually chosen empirically and becomes especially important near topological phase transitions, where finite-size effects are strongest. Here we show that the required crop-length is controlled by physical decay (localization) lengths. For nearest-neighbor and pure longer-range hopping Hatano-Nelson-type chains, the crop-length is set mainly by a single localization length and is well approximated by a scalar multiple of that length. For more general longer-range hopping models, it is governed instead by a multichannel root structure of the characteristic polynomial. Random-forest regression captures finite-size and near-boundary corrections while preserving this decay-length interpretation. Trained on one set of Hamiltonians, the predictor accurately generalizes to unseen Hamiltonians and complex base energies, reproducing crop-lengths across full phase diagrams. We further show that the predictions learned from clean nearest-neighbor hopping chains remain stable under moderate hopping disorder. These results provide a practical and physically interpretable way to choose the crop-length, which in turn determines when the real-space invariant can reliably capture the topology of finite non-Hermitian chains.

Tile codes are a family of planar quantum low-density parity-check (qLDPC) codes with weight-6 stabilizers and open boundary conditions, offering an encoding efficiency $kd^2/n$ of up to four times that of the surface code. In this work, we develop an exhaustive search algorithm for finding SWAP-based routing schemes that implement syndrome extraction for four tile-code families using only nearest-neighbor interactions on a two-dimensional square lattice, matching the connectivity of the surface code. Using explicitly constructed routed syndrome-extraction circuits decoded with BP+OSD, we estimate the circuit-level thresholds of these code families. For the SI1000 noise model, the threshold without such a connectivity constraint is obtained in a range 0.23%-0.31%, while it decreases to 0.11%-0.13% with routing, representing a reduction factor of around two to three. Despite this threshold penalty, our resource-footprint analysis shows that routed tile codes require fewer physical qubits per logical qubit than the surface code at sufficiently low physical error rates: Under the SI1000 noise model, we find a crossover near $p^*\approx 0.08\%$, below which routed tile codes become more qubit-efficient, with an advantage that grows monotonically as the physical error rate decreases.

Nonlinear differential equations play a crucial role in modeling a wide range of phenomena, yet their solutions remain notoriously difficult to obtain. With the rapid development of quantum computing, quantum algorithms for efficiently solving such equations are actively being explored. One promising approach is based on Carleman linearization, which transforms nonlinear differential equations into linear systems. However, this method suffers from exponential divergence beyond a certain time scale. By reformulating the solutions in terms of eigenvalues and eigenvectors, we identify that this divergence originates from the Laurent expansion outside its neighborhood of convergence. To address this issue, we insert a regularized function to the divergent solution hinted by analytical continuation. We validate this divergence-correction method on both the logistic equation and some other partial differential equations like KPP-Fisher equations and Phase-Field models under periodic conditions. We implement our method for the logistic equation using the Linear Combination of Unitaries (LCU) quantum algorithm, providing a detailed complexity and error analysis.

Barrios Hita et al. [Phys. Rev. Lett. $\bf{136}$, 240202 (2026)] argued that quantum mechanics can be formulated over the real numbers by replacing the tensor-product postulate with a quotient-space construction, and concluded that complex numbers are therefore a matter of convenience. We show that the operational content of this construction is not that of a generic real Hilbert-space theory. Empirical equivalence requires a distinguished real linear operator $J$ with $J^2 = -\mathbb{1}$, and all physical effects, instruments, and dynamics must preserve the corresponding $SO(2)$ gauge. Moreover, the composite-system rule is a balanced tensor product over this hidden complex structure, not the ordinary tensor product over $\mathbb{R}$. In multipartite network scenarios, this changes the meaning of source independence: canonical real representatives are not source-factorizable in the usual tensor-product sense. Thus, the construction is best understood as standard complex quantum mechanics written in real notation, not as an independent real-amplitude theory. This clarifies what is, and is not, excluded by experiments testing the necessity of complex numbers.

A resource theory of quantum measurement can be addressed in terms of quantum coherence and measurement sharpness, respectively. The former analyzes the off-diagonal structure of POVM elements in a predetermined basis while the latter analyzes the deviation from trivial, state-independent, measurements. We establish a direct connection between the two resource theories by identifying measurement sharpness as the maximal coherence that is achievable under all possible unitary changes of the reference basis. For a broad class of POVMs whose elements share a common eigenbasis, we show that the maximal distance-based coherence of measurement coincides exactly with the corresponding distance-based sharpness monotone. We further extend this equivalence, with element-additive distances, to POVMs whose elements admit a common mutually unbiased basis structure. These results provide a measurement-theoretic analogue of the maximal-coherence \& purity correspondence for quantum states. We also show that the maximal coherence of measurement is faithful with respect to trivial measurements and is monotonic under fuzzifying operations for dichotomic measurements, as well as under mixed-unitary and unitarily covariant preprocessing channels. Finally, we illustrate the operational meaning and limitations of the equivalence through qubit POVMs, single-photon phase sensing, and noisy photon-number resolving detection. In particular, the maximal Fisher information in a Mach-Zehnder interferometer is shown to be determined by the squared maximal coherence of the measurement, while in an imperfect photon-number resolving detector the maximal coherence behaves as a proper sharpness monotone, unlike conventional PVM-based unsharpness measures.

Real-time decoding is a major bottleneck in scaling quantum error correction (QEC) from noisy intermediate-scale quantum (NISQ) devices to fault-tolerant quantum computing. We present an adaptive confidence-gated decoding framework for the rotated surface code that treats decoding as a two-stage inference problem. A lightweight feed-forward neural network performs fast-path decoding for the majority of syndrome measurements, while only low-confidence predictions are escalated to a minimum-weight perfect matching (MWPM) refinement stage. We benchmark the framework on rotated surface codes with distances $d \in \{3,5,7,9,11\}$ under circuit-level depolarising noise using the Stim stabiliser simulator. The evaluation characterises logical accuracy, confidence-controlled accuracy-latency trade-offs, decoding throughput, per-shot latency, and decoding-graph resource scaling. Routing only 3.3%-6.2% of syndromes to the refinement stage improves logical accuracy from 99.21% for the neural-only baseline to 99.81% at a confidence threshold of 0.95 while incurring only a bounded increase in average decoding cost. Neural-decoder throughput saturates near $4.6 \times 10^{5}$ samples s$^{-1}$ at batch size 512 on commodity CPU hardware, indicating that the neural fast path is not the dominant throughput bottleneck beyond code distance $d=7$. We release the complete benchmarking pipeline, trained models, raw benchmark data, and source code, and explicitly distinguish the experimentally validated contributions from the broader hardware-aware QEC co-design roadmap, including hardware-constrained code discovery, GPU-accelerated inference, and multi-noise optimisation, which remain directions for future work.

Dilution refrigerators are the enabling infrastructure of superconducting quantum computers, yet their fault diagnosis is still dominated by threshold alarms that report that something is wrong, not what. We present Onnes, a physics-grounded digital-twin simulator of a dilution refrigerator (a forward physics model with a learned real-fridge noise fingerprint) that drives a live multi-agent LLM operations layer, and use it for a controlled head-to-head between a zero-shot LLM agent panel and a supervised ML classifier on cryogenic fault diagnosis. The twin couples a real dilution-cooling floor, a noise-and-correlation fingerprint learned from real BlueFors logs, and six physics-grounded fault classes, three engineered to overlap on temperature but separate on flow and pressure. Across a 1000-turn evaluation the zero-shot panel shows no significant difference from the classifier on detection but trails on classification, its errors concentrating on the confusable faults. Curated contrastive few-shot demonstrations and self-consistency voting then raise classification accuracy from 0.685 to 0.990, matching the supervised classifier (0.985) with no parameter updates and six labeled demonstrations; an ablation attributes the gain almost entirely to the demonstrations. Run as a continuous monitor across a nine-run fault-by-seed sweep, the agent catches every developing fault within one poll interval, and a confidence gate suppresses pre-onset false alarms whose rate is backend-dependent. As a first sim-to-real check, a detector trained purely on real BlueFors telemetry posts a real-hardware false-alarm rate of 6.4% and 100% recall on physics faults injected onto real held-out windows. All numbers are drawn verbatim from released run logs.

We introduce population-transfer dynamics as a practical validation observable for active-space-derived reduced Hamiltonians in multistate reaction-center chemistry. Using a cytochrome P450-inspired Fe-complex model, we construct a reaction-coordinate-dependent effective Hamiltonian from state-averaged complete active-space self-consistent field (SA-CASSCF) calculations, map it to a quantum-circuit representation suitable for current hardware, and propagate dynamics from the reactant-side ground state. The reduced Hamiltonian reproduces the SA-CASSCF reference with an RMS deviation of 0.030 eV and a maximum absolute deviation of 0.143 eV. As a dynamics-based diagnostic, the product-manifold population p_P(t) identifies a pronounced near-degeneracy region around x = 0.3, where state mixing is strongest. Classical exact time evolution yields a product population of 0.488 at x = 0.3 after 10 fs, compared with 7.26 x 10^-2 at x = 0.2 and 5.90 x 10^-3 at x = 0.0. To enable execution on current trapped-ion hardware, we examine the trade-off between dynamical fidelity and circuit resources through coupling pruning and first-order Trotterization. A coupling cutoff of 0.02 eV reduces the non-zero coupling set from 32 to 7 while preserving the dominant transfer pathways, and M = 30 provides the best practical operating point. Finally, we demonstrate the workflow on Quantinuum's trapped-ion quantum computer Reimei. The hardware reproduces the key reaction-coordinate trend identified by the classical model, including the maximum at x = 0.3, where the measured product population is 0.42 on hardware and 0.43 on the matched emulator. This work establishes a dynamics-based framework for assessing active-space-derived reduced Hamiltonians and demonstrates chemically interpretable multistate electronic dynamics on current trapped-ion hardware.

Fast single-qubit gates on weakly anharmonic transmons are limited by leakage to noncomputational states, and standard mitigations such as DRAG (derivative removal by adiabatic gate) act on the leakage amplitude at the end of the gate. We show that this endpoint amplitude and the transient leakage exposure accumulated during the gate are two distinct control objectives that can be assigned to separate modules. The endpoint is a single sample of the drive spectrum, $|\tildeΛ(η)|^2$; the exposure is a band integral about $η$ and governs leakage under dephasing, and the spectral-null condition $\tildeΛ(η)=0$ constrains only the former. We realize this split in a path--endpoint separation pulse (PESP): a path-shaping pulse suppresses the exposure, and a two-tone endpoint-cancellation pulse cancels the residual amplitude. For a $10$ ns $R_{X}(π/2)$ gate at $η/2π=0.2$ GHz, in numerical simulations the path-shaping pulse reduces the dephasing exposure by ${\sim}21\%$ relative to cosine DRAG and the independently simulated Lindblad excess leakage by ${\sim}20\%$, consistent with $P_{\mathrm{excess}}^φ\simeqγ_φT\bar{P}_{A}^{\mathrm{deph}}$, whereas matched-budget endpoint-only and spectral-null controls leave it essentially unchanged. The residual endpoint floor splits exactly into a $|2\rangle$ back-action and a $|3\rangle$ cascade, which the two tones cancel one-to-one, driving the floor at the path-exposure knee from ${\sim}7\times10^{-7}$ to ${\sim}3\times10^{-8}$ without perturbing the path. By separating transient exposure from endpoint leakage, PESP turns leakage suppression in fast weakly anharmonic gates into a modular, interpretable control problem: dephasing-induced leakage and the coherent residual error are reduced by separate, individually verifiable modules.

Chiral quantum emitters interact with light only in one propagation direction, allowing them to be linked into cascaded systems in which photons mediate ordered, long-range interactions. Such systems are predicted to host novel regimes of many-body physics of light and matter. Exploring these regimes requires arrays of identical quantum emitters with directional, low-loss coupling to guided photons, a combination that has thus far remained experimentally out of reach. Here we realize a cascaded network of superconducting qubits using an architecture that overcomes these bottlenecks. We implement a four-qubit chain spanning two modules, with separations ranging from millimeters to half a meter, and exploit the shared waveguide as a dissipative resource to stabilize reconfigurable entanglement, reaching a genuinely multipartite regime unavailable in reciprocal baths. By scattering weak pulses off the chain, we observe photons sorted in time by photon number, a signature of the strong photon-photon interactions mediated by the emitters. Together, these results provide experimental access to many-body light-matter regimes that are beyond the reach of reciprocal systems.

Quantum techniques, developed in recent decades, provide new approaches to achieving high-precision measurements beyond the classical bounds. In this paper, we theoretically demonstrate a metrology method for improving the sensitivity of the interferometric optical gyroscope, robust against the loss, by using coherent-light stimulated two-mode squeezed beams as the light source. The detection protocol is based on a simple intensity measurement, and the quantum noise is far below the shot-noise limit. The enhancement factors for different coherent light fields are analyzed in detail. Additionally, the influence of loss during the propagation in the optical path is studied, and the conditions for achieving sub-shot-noise measurement sensitivity are obtained. We also find that the phase sensitivity of the proposed gyroscope scheme becomes closer to the quantum Cramér-Rao bound with increasing of the photon number of the coherent beams.

Quantum LDPC memories can encode many logical qubits, but dimension alone does not make them usable: applications need explicit conjugate logical operators with structured labels and physical representatives. For hypergraph-product (HGP) codes this structure is transparent, since the input matrices are binary and can be row-reduced over $\mathbb{F}_2$. Abelian lifted-product codes are subtler. Their seed entries are shifts, or sparse sums of shifts, in a group-algebra ring rather than a field, so pivot blocks need not be invertible and global row reduction can fail. We address this with \emph{logical spectroscopy}, a spectral construction that replaces global row reduction by finite-field computations in the Frobenius character packets of the Abelian lift group. The Chinese remainder theorem (CRT) decomposes the group algebra into these packets. In each packet, we compute kernels, quotients, and product-complex homology; we then lift the resulting representatives back with CRT idempotents and pair $X$ and $Z$ logicals through reciprocal trace-dual packets. This gives complete addressable conjugate logical bases for finite Abelian lifted products $\mathsf{LP}(A,B)$. The same packet data also gives design diagnostics. Packet ranks show how logical sectors split, the lifted representatives give certified upper bounds on the width of the constructed conjugate basis, and whole-orbit erasures decompose into packet-attributed erased-logical dimensions. Thus, CRT packets also serve as working coordinates: they label logical sectors, certify the constructed basis width, and attribute structured erasure failures. Under bounded seed-shape and group-basis-support assumptions, this construction gives Abelian lifted-product qLDPC families an HGP-like feature while preserving the layout freedom of group-algebra lifts.

I construct the Type-IIB axion--dilaton wormhole partition function from charge-sector data. In a chosen axion charge, equivalently form-field flux sector, the long-distance saddle calculation supplies a two-end operator term with coefficient matrix \(C^{ij}_ν\). The labels \(i,j\) label end-insertion operators; the labels \(A,B\) label parent universes. Reduction data \(b\) convert this matrix into scalar coefficients \(W_ν[b]\). The wormhole partition function in the theta variable is \(Z_{\rm wh}(θ;b)=\sum_νW_ν[b]\e^{iνθ}\). I analyze properties and constraints this coefficients satisfy: discrete-symmetry covariance, phase, absolute bounds, moment positivity, Cauchy--Schwarz inequalities for the unreduced coefficient matrix, complex-\(θ\) domains, charge-lattice tails, and the dilute Bessel/Skellam limit. The \(θ\)-dependence of the wormhole partition function is the Fourier transform of the charge-sector scalar coefficients.

Coherent control of energy transport in a non-equilibrium steady-state (NESS) in a reaction-center-connected donor-acceptor pair is proposed. The pigments are considered to be continuously interacting with incoherent radiation and a phonon bath while being driven by phase-controlled coherent fields. Coherent excitation of the donor-acceptor pair is shown to induce interference between excitation pathways, resulting in phase dependent modulation of the flux. As a consequence one can enhance or suppress energy transfer via interference, e.g. an optical energy switch. The persistence of such interference enables coherent control at a NESS in dissipative regime suggests an extension of the operational scope of quantum control from traditional transient domain with low dissiaption to noisy environment NESS at room temperature.

Characterizing a quantum state through the lens of quantum resources provides an information-theoretic perspective on many-body systems. While quantum entanglement serves as the paradigmatic example of a quantum resource, recent studies have shown that quantum magic, a resource for universal quantum computation, can capture aspects of many-body states complementary to those described by entanglement. For instance, in spin systems, conformal field theory (CFT) analysis of the stabilizer Rényi entropy has revealed universal features of nonstabilizerness that are qualitatively distinct from entanglement. In bosonic and fermionic systems, however, a comparable formulation for their computational resource, non-Gaussianity, has yet to be established. In this work, we introduce a unified measure, the magic Rényi entropy (MRE), to quantify computational resources in spins, bosons, and fermions on an equal footing. This allows us to reveal common universal aspects of nonstabilizerness and non-Gaussianity in critical many-body states. In particular, our CFT analysis shows that the universal contribution to the MRE appears as the size-independent term determined by the Affleck-Ludwig boundary entropy. We find that non-Gaussianity can continuously renormalize this universal contribution or drive a boundary phase transition through bulk-induced boundary renormalization-group flows. As a concrete demonstration, we present a detailed CFT analysis of non-Gaussianity in interacting spinless fermions described by the Tomonaga-Luttinger liquid, showing boundary transitions at the Luttinger parameters $K=1/3$ and $K=3$. We perform numerical calculations that confirm our field-theoretical predictions. These results provide a unified field-theoretical understanding of many-body magic across spins, bosons, and fermions.

A core task in quantum anomaly detection is to compute an anomaly score that quantifies how strongly a test quantum state deviates from a given quantum dataset assumed to be normal. Classically, principal component analysis (PCA) for centered data computes the anomaly score by evaluating the test sample relative to the subspace spanned by the selected leading eigenvectors. However, for quantum data that lack a standard centering, explicitly recovering principal eigenvectors, constructing full Gram matrices, or loading quantum-random-access-memory-style data can be more costly than estimating the anomaly score itself. To avoid these costs, we propose Quantum Spectral Anomaly Detection (QSPADE), which computes PCA-like anomaly scores directly from the spectrum of the average state of the normal dataset. By replacing hard PCA rank selection with a smooth, temperature-controlled spectral threshold, QSPADE makes near-threshold spectral components contribute partially to the anomaly score. This makes the score vary continuously rather than jump when a borderline component is included or excluded, and makes it less sensitive to noise or arbitrary hard cutoffs near the threshold. In the zero-temperature limit, QSPADE recovers the hard-projector PCA score. The proposed measurement-based quantum detector can be calibrated with a sample complexity independent of the data dimension. Numerical simulations show that QSPADE behaves like kernel-PCA on encoded classical data and detects changes across a transverse-field Ising transition without predefined order parameters. Consequently, QSPADE gives an efficient framework for both quantum-kernel anomaly detection on encoded classical data and the monitoring of quantum-native systems where diagnostic observables are unknown.

State Krylov, or spread, complexity is a property of a pair $(H,\ket{K_0})$ rather than of the Hamiltonian alone. Thus, changing the initial state at fixed $H$ generally changes the Lanczos coefficients and the ordered Krylov basis. We solve this relative initial-state problem for normalized polynomial filters, $\ket{ψ_Q}=Q(H)\ket{K_0}/\sqrt{N_Q}$ with $N_Q=\langle K_0|Q(H)^\dagger Q(H)|K_0\rangle$. The filtered spectral measure is the positive polynomial modification $|Q(E)|^2\mathrm dμ(E)/N_Q$, and orthogonality turns this measure change into a finite-band transfer from reference Fourier-orthogonal-polynomial moments to shifted Krylov amplitudes. We derive exact finite sums for individual amplitudes and projected Christoffel-Darboux kernels for cumulative probabilities and spread complexity. The formulae cover confluent roots, complex seed coefficients, support loss, and terminal quotients in finite dimensions. We evaluate the construction in three canonical Jacobi families, the Heisenberg--Weyl/Charlier oscillator, the compact $SU(2)$/Krawtchouk spin, and the constant-coefficient tight-binding/Chebyshev chain, with a Hermite central-limit scaling of Charlier as a continuous-spectrum check of this Christoffel jump machinery. Finite seed families are organized by a matrix-valued parent measure whose scalar compressions recover the individual shifted problems. The fixed-inner-product construction carries over to operator Krylov complexity after the replacement \(H\mapsto\mathcal L\) and \(\ket{K_0}\mapsto O\); polynomial seeds then become nested-commutator descendants \(Q(\mathcal L)O\). The result is an exact relative calculus in which a solved cyclic problem generates a family of polynomially related initial-state dynamics without repeating Lanczos in the original Hilbert space.

Present-day quantum computing is cloud-based, where a user submits a circuit to a service provider's proprietary backend hardware. While providers may wish to hide implementation details, scheduling choices, or even which physical device was used, noisy finite-shot outputs can carry backend-specific fingerprints: information imprinted in the classical output distribution that can reveal the backend identity. So far, such fingerprints have mostly been studied from a benchmarking perspective, with limited attention to privacy considerations for users and providers. This work develops the first formal framework for backend identifiability and its privacy implications. We introduce a backend-identifiability game and use it to formalise routing anonymity as a security notion for quantum cloud services. We show that backend identifiability is a hypothesis-testing problem and prove that, under passive i.i.d. access to a single backend, routing anonymity decays exponentially at the Chernoff rate. We also establish a utility-anonymity trade-off, imposing fundamental limits on how much backend-specific information can be removed from classical outputs without degrading their usefulness. In addition, we observe that, for noisy quantum hardware, identifying fingerprints are inherently an intermediate-depth phenomenon, and establish a depth principle using Pauli-transfer-matrix tools. We complement the theory with experiments on Amazon Braket on AWS, using ion-trap and superconducting quantum processors. We observe 87-90% classification between superconducting backends and 96-100% classification across physical platforms, and find that identifiability can survive natural forms of post-processing. Overall, these results establish routing anonymity as a distinct security requirement for quantum cloud computing, and provide a framework for quantifying and controlling the utility-anonymity trade-off.

We formulate a tangent-space method for algebraic varieties of matrix product states (MPS) to study excitation spectra of non-uniform quantum many-body systems with open boundary conditions. We further introduce a rank tomography of the MPS tangent space, which characterizes its expressivity in terms of particle-sector rank profiles of the underlying MPS variety. Using the Bose--Hubbard model as a benchmark, we illustrate that the method reproduces low-lying excitations and captures finite-size precursors of the Mott-insulator to superfluid transition.

We develop a framework for quasi-holonomy in non-adiabatic quantum time evolution of subspaces along loops in a complex Grassmannian. By factoring the Schrödinger evolution into dynamical and connection-induced contributions in a moving basis, we obtain an effective geometric generator that depends explicitly on the dynamical propagator. This quasi-connection does not define a genuine connection on the original Grassmann bundle, since its gauge transformation law acquires a history-dependent, nonlocal term. Other ways of factoring the Schrödinger evolution are briefly discussed. All these approaches suffer from the same type of history-dependence, thereby defining transport of subspaces in which geometric and dynamical effects are generally intertwined, just as in the case of the quasi-holonomy. Our work sheds light on the issue of separating quantum evolution of subspaces into holonomic and dynamical parts from an essentially gauge-theoretic perspective.

Circular states in Rydberg atoms offer a promising platform for quantum computation, quantum simulation and quantum sensing. However, the final step of their preparation - termed as circularization, a process that involves the transfer of a large amount of angular momentum quanta to the valence electron by means of radio-frequency (RF) pulses - remains as a major bottleneck for all technological applications based on interacting circular Rydberg atoms. Even though successfully implemented to circularize an atom cloud in the dilute regime, previous efforts to speed up the circularization process have focused on the single-atom case, thereby neglecting the interactions which constitute one of the main resources for quantum simulation and computation. In this theoretical work we show how interactions between two atoms disturb the efficiency of pulses designed for single atoms and identify shifts induced by the interactions on relevant transition energies as the dominant disturbance. We demonstrate that the initial efficiency of single-atom pulses can be restored by adapting them to these shifts. Our approach is based on a simple functional form depending only on two linear parameters, which we derive analytically. The adapted pulses prepare two $^{87}$Rb atoms after $65 \,$ns in a $n=52$ circular state with a fidelity of at least $95\,\%$ for interatomic distances down to $6.5\,μ$m and for all angular configurations, while also complying experimental amplitude and frequency constraints. Finally, we show that when combining our adapted pulses with Krotov's pulse-shaping algorithm we obtain high-fidelity pulses for any pair arrangement with interatomic distances larger than $5.9\,μ$m. This work demonstrates that fast RF pulses can circularize interacting Rydberg atoms, paving the way toward their technological application.

We define and analyze hockeystick divergences and $f$-divergences for normal positive functionals on general von Neumann algebras, generalizing and unifying previous work in classical probability and finite-dimensional von Neumann algebras. All the main properties of these state distinguishability measures (including in particular monotonicity, convexity, semicontinuity, bounds, state discrimination, data processing inequality) are derived from properties of the Jordan decomposition of selfadjoint normal functionals. This is done by representing the $f$-divergences as integrals over hockeystick divergences, and their significance in quantum hypothesis testing is reviewed. The $f_0$-divergence given by the information function $f_0(t) = t \ln t$ is shown to coincide with Araki's relative entropy, extending results of Frenkel to general von Neumann algebras.

Quantum matter emerges from the interplay of fluctuations, topology, and entanglement, which - in equilibrium - governs quantized transport, universal criticality, and topological classification. Non-Hermitian systems, widely explored in platforms ranging from electric circuits to photonics, are intrinsically out-of-equilibrium, and display fundamentally new phenomena, including complex spectra, spectral winding, exceptional topology, and non-unitary dynamics. A central challenge is understanding how the complex single-particle spectrum governs universal many-body behavior. We introduce a symmetry-protected dynamical topological index derived directly from the complex spectrum. Through the lens of algebraic topology, more specifically Morse theory, we identify critical points in the spectrum with topological defects, whose curvature and stability are protected under continuous deformations. This links spectral geometry to many-body observables, unifying non-Hermitian band topology, entanglement, and transport. We demonstrate that non-Hermitian quantum criticality in non-interacting systems is controlled by gain-and-loss-selected non-equilibrium steady states, which dynamically generate an emergent imaginary Fermi surface whose Fermi points host scale-invariant gapless modes with logarithmic entanglement scaling and algebraic correlations. Our work establishes a unified framework for non-Hermitian quantum matter, connecting spectral topology to Morse theory, revealing a topological foundation of non-equilibrium quantum criticality.

In variational Monte Carlo (VMC) calculations of $N$-site quantum systems with arbitrary all-to-all two-body interactions, evaluating the local energy generally costs $O(N^3)$. We introduce a new framework that reduces this cost to $O(N)$ for tensor network states, capable of scalable and accurate computation of real-time dynamics and ground states. As a result, we obtain accurate simulations of the adiabatic real-time protocol of a $10\times10$ dipolar XY model realized in a Rydberg simulator [C. Chen et al., Nature 616, 691 (2023)], which was previously beyond the reach of classical simulation. Going beyond quantum experiments, we also directly perform ground state VMC to compare with the adiabatic state preparation. Our work demonstrates tensor network VMC as a powerful classical simulator for long-range quantum platforms such as Rydberg and ion-trap simulators, which are currently in urgent need of scalable classical benchmarking tools. As a separate technical contribution, we resolve the pathology of evolving from product states within of tensor network VMC.

It is known that a one-dimensional (1D) quantum walk gives a local space-time discretization of the massless Dirac equation with a single quasi-energy cone (no fermion doubling at low energies), keeping the fundamental symmetries (chiral and time-reversal) of the continuum theory. We show that the analogous 2D construction is fundamentally more fragile. Local two-band quantum walks can have an unpaired Dirac cone, but the protecting symmetries then cease to be ordinary on-site symmetries: they become non-symmorphic, involving half-lattice translations, and are broken by generic spatial inhomogeneities. In particular, we demonstrate that the 2D Dirac quantum walk based on the Ho-Chalker network model can be gapped by potential scattering.

In space based quantum key distribution (QKD) protocols, the quantum channel will be dynamic in nature and the channel loss will change with respect to the zenith angle. In the context of continuous variable (CV)-QKD, this will cause issues with parameter estimation and for a transmitted local oscillator in particular it will also fluctuate the shot noise. Therefore, it is vital to characterise this channel loss and the sources of this loss. In this paper the varying channel loss is characterised under practical assumptions. This is shown for various different scenarios, turbulence strengths, as well as wavelengths. This work shows, for the channel parameters considered, it is possible to generate a positive secret key if restricted Eve security assumptions are made.

Transversal logical gates provide a direct route to fault-tolerant quantum computation, but the Eastin-Knill theorem forbids a universal transversal gate set within a single quantum error-correcting code. We propose a hybrid architecture based on the tetrahedral three-dimensional color code and its Hadamard-transformed counterpart, which we call the H-tetrahedral code. The two encodings support complementary transversal non-Clifford operations. Combined with bitwise Hadamard transformations that switch between the two encodings and a one-way transversal logical CNOT from the tetrahedral code to the H-tetrahedral code, these operations realize an almost-universal transversal logical gate set that enables both the creation of entanglement and logical states with magic. We complete a universal gate set through a pieceably fault-tolerant round-robin construction of a logical controlled-$Z$ gate between two H-tetrahedral codes. This logical entangling gate is interleaved with reduced-overhead Steane-type syndrome extraction using logical two-dimensional color-code auxiliary qubits. Our construction provides a new route toward implementing classically hard-to-simulate quantum algorithms where magic and most entangling operations are transversal while the resource overhead is concentrated in a small number of non-transversal Clifford entangling operations.

Matrix Brownian motion provides a powerful framework for studying crossover ensembles in quantum chaos and quantum transport, as well as thermalization and information scrambling in many-body dynamics. Here, we develop a unified diagrammatic framework to characterize Brownian ensembles for orthogonal and symplectic random matrices, which describe systems with particle-hole symmetry. We compute polynomial averages up to fourth order and construct an orthogonally invariant interpolation for the disconnected $\mathrm{SO}^-(q)$ sector of the orthogonal group. We consider applications relating to the fields of quantum information, quantum chaos, and quantum transport.

We introduce a superconducting digital-to-analog converter (DAC) that filters control noise, provides native multiplexing, performs quantum gates in nanoseconds, and can be controlled by CMOS. This is achieved by transducing a trapezoidal drive pulse into a superconducting soliton, which is then held in the DAC load loop, applying flux to a mutually-coupled superconducting qubit or gate coupler. The analog flux output by the DAC can be easily controlled by varying the soliton hold time, or with a DC-biased tunable DAC-qubit coupler, allowing the DAC to perform a fixed-time, high-fidelity gate that's robust to fabrication variance or flux offsets in the quantum circuit. Our initial demonstration shows that the DAC can successfully perform 5.6 ns S-gates on transmons. We measure the DAC-induced quantum state excitation probability per gate to be 0.05%, and find that the DAC-induced relaxation rate from the qubit 1 state is below the intrinsic T1 rate limit of the transmon. Quantum simulations show qualitative agreement with the measured data, and predict that the DAC excitation rate can be lowered 10 times further by overdamping the Josephson junction (JJ) in the DAC load loop. may be limited by a Interleaved Randomized Benchmarking (IRB) sequences on an observer qubit reveal that, when scaling to many qubits, the DAC's performance may be limited by a non-local, DAC-induced phase error of 1.6% per gate, appearing in ancilla qubits that are not directly coupled to any of the 30 DACs on the chip. We discuss strategies for future layouts of multi-DAC chips that focus on mitigating the source of these non-local, high-frequency electromagnetic interactions (EMI), and how to incorporate a DC-tunable coupler for phase correction.

Macroscopic observables allow the recovery of intrinsic dynamics from stationary quantum states. I show that, by interpreting the squared amplitude as the probability density for each definite value of intrinsic time, a curvature emerges in the time direction. For example, from the perspective of intrinsic quantum time, the Friedmann-Lemaître-Robertson-Walker cosmological model emerges from spherically symmetric stationary solutions in four-dimensional Euclidean space, without presupposing gravity. If there is no unique direction of time, curvature emerges in all spacetime dimensions, without presupposing gravity, from the variable amplitude of the stationary wavefunction alone. This opens a new possibility that general relativity or some modification of it emerges from intrinsic time observables.

Large-scale quadratic unconstrained binary optimization (QUBO) formulations of constrained combinatorial optimization problems often exceed the input-size limit of present Ising machines or suffer from degraded solution quality as the number of binary variables increases. Large neighborhood search (LNS) mitigates this difficulty by sequentially optimizing restricted subproblems, but the structural factors that distinguish subproblems beyond the number of binary variables remain insufficiently characterized. In this study, we examine vehicle routing problems and compare a construction based on the vehicle routes of the current solution, denoted by LNS-K, with a construction based on QUBO variables and constraint relations, denoted by LNS-Q, while controlling the number of binary variables in the subproblems. Under the tested conditions, LNS-K obtained shorter total distances than LNS-Q in the matched-size comparisons, and the position variance, a measure of the spatial spread of the selected customers, decreased during the iterations in LNS-K. These observations suggest that subproblem design for sequential optimization with Ising machines should consider not only subproblem size but also semantic and geometric structures inherited from the current solution.

Accurate determination of hyperfine structure constants in atomic systems provides important insight into the interplay of electron correlation and relativistic effects in the nuclear region. Although sodium (Na) is a relatively light atom, previous all-order relativistic many-body calculations of the magnetic dipole hyperfine constants for the low-lying states of $^{23}$Na show noticeable discrepancies with experiment. To address this, we calculate the ionization potentials and hyperfine structure constants of $^{23}$Na using relativistic coupled-cluster theory with explicit inclusion of triple excitations. We further incorporate corrections from the Breit interaction, quantum electrodynamics, and the Bohr-Weisskopf (BW) effect. Results from lower-order methods are also presented to assess the importance of different physical contributions across states. Our calculations demonstrate that contributions from the lower-order relativistic and BW effects play almost similar roles with the electron correlation effects, including triple excitations, and are essential for reconciling theoretical predictions with experimental observations. This study can also serve as a useful guide for understanding the role of triples in heavier alkali systems.

Canonical quantization provides a systematic procedure for constructing quantum models from classical Hamiltonians. Here, we apply this principle to a fundamental computational primitive of machine learning: the neuron. Specifically, by viewing a neuron as a composition of an energy function and an activation function, we quantize this model by replacing the energy function with a quantum Hamiltonian and applying the activation function to it through matrix functional calculus. This results in an activation observable that can be measured on an input quantum state. We investigate the use of these quantized neurons for function approximation, where the objective is to learn an unknown observable from labeled quantum data. For this purpose, we develop hybrid quantum-classical algorithms for training and evaluation, including procedures for measuring the activation observable and estimating gradients of the squared loss error. Our algorithms for gradient estimation rely on basic primitives like classical random sampling, the Hadamard test, and Hamiltonian simulation, and those for measuring an activation observable rely on quantum algorithms known as the power of one qumode and Schroedingerization. Numerical experiments demonstrate that our quantized neurons exhibit enhanced expressive capabilities relative to corresponding classical neurons on representative learning tasks. Our work establishes canonical quantization as a principled framework for constructing quantum machine learning primitives and provides a foundation for developing neural architectures tailored to quantum data.

In this Letter, we show that constrained many-body dynamics in Rydberg atom arrays naturally gives rise to a quantum hashing mechanism. By encoding ternary strings into deterministic trajectories in the state space, the classical information space is mapped onto a quantum state ensemble in the Hilbert space with an induced geometric structure. Statistical analysis reveals that this ensemble exhibits high probability near-orthogonality, random-like distribution, and broad geometric coverage. These geometric features naturally give rise to the essential cryptographic properties of quantum hashing, including low collision probability, one-wayness, tamper sensitivity, and privacy preservation. Our results demonstrate that the cryptographic functionality of quantum hashing need not rely on deliberately engineered algorithms, but can instead emerge naturally from constrained many-body dynamics, identifying quantum dynamics itself as a physical resource for cryptographic information processing.

The Bloch sphere is an elegant tool for representing single-qubit states. However, a widely accepted generalization for multi-qubit systems with entanglement remains absent. We propose a novel geometric model extending the Bloch sphere representation to arbitrary $N$-qubit systems using $2^N-1$ spheres. We demonstrate that any pure 2-qubit state is uniquely described by three spheres: two for individual qubits and a third encapsulating bipartite entanglement. Generalizing this, we establish an $N$-qubit parameterization through the hierarchical application of controlled rotation gates along the $Z$ and $Y$ axes. We formally prove a strict bijection between the standard state vector representation and our model's angular parameters. This framework provides an intuitive visualization of multiple entanglement, offering potential computational advantages for quantum simulators and new analytical perspectives on quantum gates.

Laser cooled and trapped atoms have been the workhorse of atomic physics for the past four decades. The predominant method has been the highly versatile Magneto-Optical Trap. We describe an alternative laser trap involving a simple geometry of collimated laser beams that provides both a velocity and position dependent restoring force such that a dense cloud of cold atoms is formed. This technique produces similar atom number ($>10^6$) and density ($10^{10}$\,atoms/cm$^{3}$) to the Magneto-Optical Trap, albeit with \emph{no magnetic field}. The beam geometry is compatible with conventional sub-Doppler cooling techniques, allowing the trapped cloud to be cooled to $< 10~μ$K. We demonstrate the validity and robustness of the trap by capturing $^{87}$Rb atoms directly from the background vapor and provide a theoretical discussion of the underlying principles. This trap has many unique properties that make it highly suitable for quantum sensing, timing, and computing applications as well as a new tool in fundamental science and metrology.

The contraction coefficient of the trace distance is a central tool in quantum information, quantifying how strongly a quantum channel degrades the distinguishability of states. However, being an extremal ratio, it captures only the most optimistic behaviour of the channel and is often trivial, even for very noisy channels. Moreover, a single scalar is poorly suited to describe how contraction accumulates under channel composition. In this work we introduce the \emph{contraction and expansion values}, two monotone sequences that refine the contraction and expansion coefficients in the same way singular values refine the operator norm. They arise from a min--max variational principle over subspaces of traceless Hermitian operators, admit an operational interpretation in terms of two state-discrimination games, and are shown to coincide with the Gel'fand or Bernstein numbers of the channel restricted to traceless operators. This identification places the sequences within Pietsch's theory of $s$-numbers and yields, in particular, bounds under channel composition that the contraction coefficient alone cannot provide. We establish their main structural properties and compute or estimate them for single-qubit channels, $d$-dimensional amplitude damping channels, and direct-sum channels.

We investigate the use of twin optical fingerprints derived from correlated physical unclonable functions (PUFs), as a hardware-based platform for cryptographic key generation and distribution. Each fingerprint is associated with a random, yet reproducible speckle pattern, generated when coherent light is scattered by a disordered optical structure. We consider a pair of correlated optical PUFs, and study the conditions under which two honest parties can establish a common secret key, despite fabrication-induced variability and environmental noise. An explicit information-theoretic key-agreement protocol is developed, incorporating secure sketches, error reconciliation, and privacy amplification. We quantify information leakage due to public helper data, and derive lower bounds on the length of the final secret key. The analysis identifies the noise regimes in which secure key agreement is feasible, and examines the performance of both practical and near-capacity reconciliation schemes. Finally, we discuss how twin optical PUFs could be integrated into quantum key distribution (QKD) networks, as a mechanism for establishing an initial pre-shared secret key between two honest users, without relying on computational assumptions or trusted third parties.

Quantum machine learning (QML) could have the potential to leverage advantages of quantum over classical computing but still lacks strong evidence of actual improvements and scalability, partly due to phenomena such as barren plateaus. In this paper, we employ a hybrid quantum neural network (QNN) on a dataset on cloud microphysics, containing processes for phase transitions of water in the atmosphere and its related temperature changes, which are highly relevant for accurate climate predictions and projections. To reach optimal performance of our QNNs, we employ a rich and trainable frequency spectrum together with expressivity enhancing classical postprocessing. We find that our QNNs strongly benefit from extensive hyperparameter optimization and thereby demonstrate the feasibility of applying QNNs to complex physical systems. At the same time, the QNNs are outperformed by classical baselines in the form of simple fully-connected neural networks. We discuss identified bottlenecks of this class of quantum models to learn the full complexity of the cloud microphysics dataset to show that there is a need to further understand and improve variational quantum models for machine learning such that they might fill the gap where classical models fail or are inefficient.

Virtual distillation is a promising error-mitigation technique that exploits multiple copies of a noisy quantum state to estimate observables as if measured on a purified state. Although originally introduced in the context of bosonic many-body systems under the name of virtual cooling, its development and applications have largely focused on qubit-based quantum computation. Here, we establish a framework for virtual distillation in bosonic quantum information processing and continuous-variable quantum computing. Building on a diagonalization of cyclic shift operators implemented with passive linear-optical interferometers, we derive experimentally accessible protocols for estimating virtually distilled expectation values of observables relevant to bosonic architectures. In particular, we show how to recover noise-mitigated expectation values of number operators, phase-shift operators, and arbitrary quadratures from multi-copy measurements. For number operators, we further demonstrate the estimation of virtually distilled correlators of arbitrary order through the characteristic function of the photon-number distribution. We apply the framework to states affected by photon loss and dephasing, two of the dominant noise mechanisms in bosonic quantum computation, and quantify the resulting suppression of noise contributions. Our results extend virtual distillation beyond its original setting and provide a practical route toward error-mitigated measurements in bosonic quantum processors using experimentally available linear-optical resources.

In this paper we argue that, in addition to the statistical structure of quantum theory, another structure, referred to here as the ``Noether structure," is necessary to describe the composition of systems and to define completely positive operations. A Noether structure reflects the dual role of Hermitian operators as observables on the one hand and as generators of symmetry transformations on the other. This idea has been expressed in a similar form in the works of Alfsen and Shultz, who investigated the conditions under which the Jordan product can be extended to an associative product of operator algebras. Our investigations into the Noether structure and the composition of systems are limited to the finite-dimensional case and establish a connection to completely positive operations. In the case of pure operations, the latter can be characterized as orientation-preserving maps.

Photonic cluster states are a key resource for photonic quantum information processing. So far, deterministic generation of these states has been limited to the near-infrared wavelength range. To achieve quantum advantage in communication while maintaining compatibility with silicon photonics, operation in the telecom wavelength range is required. In this work, we demonstrate deterministic cluster state generation directly in the telecom C-band. This is achieved through repetitive excitation of a hole spin confined in an indium-arsenide quantum dot subjected to an external magnetic field. We characterize the quantum process that generates the cluster state by measuring its process map, obtaining a fidelity of $\mathrm{F} = 0.71 \pm 0.01$ to the ideal case. As part of this characterization, we observe spin--photon polarization entanglement with a negativity of $\mathrm{N} = 0.27 \pm 0.02$. The emitted photons exhibit indistinguishability of at least 83%, demonstrating the potential for future fusion gates necessary for photonic cluster state generation beyond linear connectivity.

In advanced complementary metal-oxide-semiconductor (CMOS) quantum chips, compact gate stacks make it difficult to connect lithographic geometry, electrostatic confinement and many-electron spin filling in one transparent model. This connection is central to design-technology co-optimization (DTCO). Here we develop a reduced-order analytical framework for asymmetric multigate silicon quantum-dot devices. Its electrostatic core, the Poisson-kernel coupled-interface Green-function (PK-GF) model, agrees with an independent finite-volume solution at the millivolt scale for the matched two-dimensional problem, without fitting to that solution. We then pass the gate-derived confinement, rather than a harmonic or fitted potential, to a spin-valley many-body calculation for a jellybean quantum dot with N = 2-17 electrons at B = 5 T. The unrestricted Hartree-Fock (UHF) solution supports occupation-dependent, Wigner-molecule-like charge localization but likely overestimates spin polarization. Complete active-space configuration interaction (CASCI) supports a low-spin branch within the tested active spaces, which aligns with the experiments. The workflow therefore connects CMOS layout, device electrostatics, and potential-determined quantum observables, providing an auditable modelling layer for CMOS-based qubit design and DTCO.

The probabilistic nature of quantum measurement provides a direct window into the structure and complexity of many-body wave functions. When only part of a system is measured, the remaining degrees of freedom form an ensemble of post-measurement states whose statistical structure can reveal a stronger form of thermalization, known as deep thermalization. Recent numerical evidence suggests that this phenomenon is characterized by convergence of the projected ensemble to the Scrooge ensemble, a maximally random ensemble compatible with a given density matrix. In this Letter, we use the solvable Sachdev-Ye-Kitaev (SYK) model to unveil the mechanism by which the Scrooge ensemble emerges in many-body systems. By formulating measurement probabilities and post-measurement states in terms of path integrals, we analytically characterize all moments of the projected ensemble and show that they exactly match those of the Scrooge ensemble, even at short evolution times. We further connect this result to the saddle-point structure of the measurement path integral, which naturally generates the replica permutations underlying Scrooge statistics. Our results establish the solvable SYK model as a tractable setting for exploring universal statistics of quantum measurements in chaotic many-body dynamics.

Quantum Architecture Search (QAS) automates the design of parameterized quantum circuits for variational quantum algorithms, yet existing benchmarks organize instances by molecular identity or qubit count -- criteria agnostic to Hamiltonian structure -- and rely solely on energy accuracy, which cannot detect structural failures such as over-parameterization on near-product ground states. We introduce HamQASBench, a Hamiltonian-informed diagnostic benchmark organizing 11 molecules into five structural tiers via fingerprints derived from the Pauli operator basis, computational basis representation, and ground-state entanglement. A post-hoc critical-structure extraction procedure identifies minimal circuits consistent with each tier's requirements, complementing energy-based evaluation with per-qubit entanglement analysis and pairwise state fidelity. Benchmarking five QAS methods across four paradigms reveals failure modes invisible to conventional metrics: over-parameterization in the minimalism regime, eigenstate commitment under degeneracy, a representation bottleneck in strongly correlated systems, topology-induced routing failure, and circuit search space growth as a scalability bottleneck.

While complex-pole hierarchical equations of motion (HEOM) have dramatically expanded the reach of numerically exact quantum dynamics simulations of open quantum systems, they suffer from numerical instabilities rooted in the non-Hermitian structure of their Liouvillian. Yet, the origin of this structure remains obscure. Here, we report a previously unknown gauge freedom in complex-pole HEOM: a continuous family of analytically equivalent Liouvillians, all encoding the same bath correlation function, whose numerical properties vary dramatically. This gauge controls both the eigenspectrum and non-normality of the hierarchy generator, revealing spectral divergence and non-normal error amplification as two distinct instability mechanisms. By optimizing this gauge, we introduce GO--HEOM, which eliminates divergences in strongly coupled Brownian oscillator environments and extends numerically exact simulations of sub-Ohmic dynamics -- including through the delocalized-to-localized quantum phase transition -- to previously inaccessible coupling strengths. Because this gauge transformation is independent of the bath-correlation decomposition scheme, our GO--HEOM becomes a general, broadly compatible strategy for accessing numerically exact quantum dynamics of open quantum systems over arbitrary coupling and highly non-Markovian regimes.

Finite quantum environments can relax local probes without acting as canonical baths. We study this distinction for a probe qubit coupled to a programmable bath of ($N$) qubits under excitation-number-conserving dynamics. The conserved charge partitions the Hilbert space into sectors. We characterize probe-level bath emergence using the sector-resolved late-time population ($p_e^{(q)}$), the sector-memory variance ($M_N$), and a global Gibbs-fit error ($Δ_G^{\mathrm{global}}$). Exact simulations with Haar-random pure states in each complete fixed-charge sector yield sector-dependent populations close to the maximally mixed-sector benchmark ($p_e^{(q)}=q/(N+1)$), producing a nonzero Gibbs obstruction. We then construct charge-preserving Floquet circuits using ($R_z$) phases and ($XX+YY$) exchange gates, validate them with ideal and noisy Qiskit simulations, and implement finite-depth experiments on IBM Fez. For ($N=4$) and ($ε=0$), the hardware data give ($M_N \simeq 0.044$), ($Δ_G^{\mathrm{global}} \simeq 0.558$), and charge preservation near 0.90 after readout mitigation. A paired symmetry-breaking scan using bath ($R_x(ε)$) rotations reduces both diagnostics while increasing charge leakage, but does not erase sector ordering over the accessible depths. These results show that equilibration within constrained sectors is insufficient to produce a single sector-independent Gibbs state for the probe.

We present a theoretical study of spin- and valley-resolved quantum transport in monolayer MoS$_2$ under the combined influence of mechanical strain and an external scalar potential, a combination whose simultaneous unexplored. Within an effective massive Dirac Hamiltonian that incorporates intrinsic spin--orbit coupling, strain induces valley-dependent momentum shifts that lift the degeneracy between the $K$ and $K'$ valleys and strongly modify the transport characteristics. The scalar potential modifies the tunneling spectrum, leading to pronounced changes in resonant transmission, Fabry--Pérot interference, and conductance. We show that the interplay between strain and electrostatic potential enables efficient control of both valley and spin polarization of the transmitted current. In particular, we identify a dual-knob control scheme in which the barrier width governs the frequency of conductance oscillations while strain independently controls their phase and amplitude. Furthermore, we predict electrostatic spin inversion -- a sign reversal of spin polarization achievable purely by gate tuning at finite strain, requiring no geometric reconfiguration. Depending on the strain orientation, the transmission probability and conductance can be selectively suppressed or enhanced, resulting in highly tunable valley- and spin-polarized transport. These findings demonstrate that strain and potential engineering provide orthogonal and independently operable mechanisms for controlling conductance as well as spin and valley degrees of freedom in monolayer MoS$_2$, offering promising prospects for spintronic and valleytronic device applications.

Bound states in the continuum (BICs) are counterintuitive localized states that lie within the continuum of extended states. While extensively realized and utilized in classical wave systems, it is still unclear what a close analog of BICs would be, and how to extract their experimental signature in quantum-optical settings -- where the wave field itself is quantized into bosonic excitations. Here, we present a paradigmatic quantum-optical model consisting of a driven multi-level Jaynes-Cummings (JC) system, featuring few quantum degrees of freedom yet capable of hosting a BIC. Using the concept of a Fock-state lattice (FSL), this model can be mapped to an extended structure comprising two semi-infinite inhomogeneous Su-Schrieffer-Heeger (SSH) chains coupled to a common continuum. An appropriate quantum superposition of two topological zero modes from the separate chains forms a BIC that remains perfectly localized in the Fock-state dimension within the continuum spectrum, due to complete decoupling from the common continuum via destructive quantum interference. We further develop a method to extract the spectroscopic signature of the BIC -- a discrete peak embedded in a continuous background -- by Fourier-transforming the time-dependent dynamics of the system's chiral-symmetry operator. A highly feasible experimental proposal using a single trapped ion is provided. Our work bridges BIC physics with quantum optics, opening a pathway to harnessing such exotic states at the quantum limit.

Strengthening light-matter coupling has become a central challenge in cavity quantum electrodynamics (QED), enabling ultrafast gate operations, qubit protection, and deterministic nonlinear optics. As the coupling increases, even the simplest configuration, a two-level atom interacting with a quantized field, requires careful treatment, as exemplified by the gauge-invariant quantum Rabi model (QRM). Here we propose a magnetic graph model for single-atom cavity QED, which enables the interpretation of quantum dynamics across the ultrastrong coupling regime through graph connectivity. We demonstrate that the generalized QRM maps onto a complex bipartite graph of identical sites under Floquet boundary conditions. This framework captures the crossover from weak to deep-strong coupling via a single metric: the cost of disconnecting a nonmagnetic subgraph. We examine the mechanism underlying this connectivity transition, establishing phase frustration induced by subgraph topology as the primary driver. Scalable to many-body systems, this approach bridges graph theory and cavity QED, revealing highly complex-graph dynamics even in the simplest setting.

Graph-theoretic frameworks have been widely employed in quantum physics to address the high-dimensional complexity of quantum systems. Although open quantum dynamics incorporates system-bath coupling via numerous interacting operators, it has been formulated algebraically with a partial set of jump operators or statistically universal reservoirs, leaving the underlying connectivity structure largely unexplored. Here, we propose a universal graph-theoretic framework for Markovian quantum dynamics. The framework maps open quantum dynamics onto two uniquely defined graphs, where the quantum master equation is rigorously interpreted as the average wave characteristic of operator-valued signals across the graphs. Applying this framework to the open quantum Rabi model, we demonstrate an open-system generalization of Fock-state lattices, characterize graph-topological signatures of dissipation, and classify the weak-to-ultrastrong coupling transition. Building on these representations, graph pruning reveals the backbone of open quantum dynamics, which enables superior graph neural-network learning. Our results bridge graph theory and open quantum dynamics, achieving efficient data-driven analysis of high-dimensional complexity.

Coherent perfect absorption (CPA) extinguishes optical fields through interference and dissipation, but conventional implementations rely on material loss that is largely fixed after fabrication. Here we demonstrate all-optically controllable CPA based on frequency conversion in a periodically poled lithium niobate waveguide resonator. Pump-driven frequency conversion couples a resonant signal field at 1581 nm in the main system to a non-resonant environmental mode at 780 nm, creating a dynamically tunable effective loss channel. The nonlinear cavity acts as a tunable lossy beamsplitter without intrinsic material absorption. Under coherent two-sided signal injection, we observe up to 92 % absorption. We further introduce environment-assisted CPA by injecting an external field into the frequency-converted environmental mode, turning the environment from a passive loss reservoir into an addressable coherent control port. Our results establish a frequency-conversion-based platform for all-optical control of dissipation in CPA, combining pump-tunable loss with environment-assisted coherent control.

Quantum gate teleportation enables distant parties to implement nonlocal quantum operations without physically transferring the participating qubits, making it a promising primitive for distributed quantum computing. We introduce a general framework for deterministic quantum gate teleportation based on path superposition, in which the target nonlocal operation is specified through the phase of a preshared maximally entangled resource and a suitable family of path-dependent local unitary operators. The framework establishes general design conditions that guarantee deterministic teleportation after measurement of the control qubits and the application of local correction operations. As representative realizations, we construct teleportation protocols for controlled-NOT (CNOT) and controlled-Z (CZ) gates, demonstrating that different nonlocal operations can be implemented within the same protocol architecture through appropriate choices of the design parameters. We further outline a proof-of-concept photonic realization based on spatial-path and polarization degrees of freedom. The proposed framework identifies path superposition as a versatile resource for quantum gate teleportation and distributed quantum information processing.

Hamiltonian estimation is an effective approach in studying the structure and dynamical evolution of quantum systems. The difficulty in estimating the Hamiltonian is that an $N$-qubit Hamiltonian has $4^N-1$ unknown parameters, requiring exponentially many equations for information extraction. In this paper we develop a method based on compressed sensing to estimate the Hamiltonian of a multi-qubit system. We identify a problem where as $N$ increases, the common sufficient condition (Restricted Isometry Property) for compressed sensing often fails, obstructing the application of compressed sensing in ($N\geq 3$)-qubit Hamiltonian estimation. To solve this problem, we propose a ``scale transformation" technique to restore RIP and ensure a compressive estimation of a $k$-sparse Hamiltonian using only $O(k\log(4^N/k))$ equations. In the numerical examples, we estimate the Hamiltonians of two 6- and 30-qubit systems, demonstrating the effectiveness of the method.

We investigate phase transitions in the extended Su-Schrieffer-Heeger (SSH) model with next-nearest-neighbor hoppings and an imaginary staggered chemical potential. In the presence of small non-Hermiticity, exceptional points emerge in pairs from the gap-closing momenta near the topological phase boundaries of the Hermitian limit. Utilizing the Krylov spread complexity and entanglement entropy, we analyze two dynamical protocols: (i) preparing the non-Hermitian ground state via a unitary transformation, and (ii) evolving the system under the non-Hermitian Hamiltonian. We show that the spread complexity, and long-time spread complexity as well as entanglement entropy can effectively signal phase transitions in the first and second protocols, respectively. To unravel the detailed structure of the transitions, we introduce the momentum-resolved complexity that identifies the characteristic modes and tracks their evolution with the driving parameter. In the regime where the system possesses a purely imaginary spectrum, we further identify dynamical phases based on the saturation behavior of the spread complexity. The entanglement entropy is also found to exhibit similar saturation behavior, thereby providing a more experimentally accessible probe of the dynamical phases.

Quantum networks can exhibit nonclassical correlations that cannot be explained by classical models with independent sources. While the role of entanglement is well understood, the impact of measurement design remains largely unexplored. Here we develop an operational framework for certifying network nonlocality in the bilocal Alice--Bob--Charlie network using ancilla-assisted meters to evaluate the nonlocal observables required for bilocal and fully network nonlocal (FNN) witnesses. The approach successfully reproduces both bilocal and FNN correlations in simulation. On the 156-qubit superconducting processor \textit{ibm\_kingston}, we observe bilocal nonlocality with $\mathcal{S}_{\rm BLHV}=1.067(6)>1$ after readout-error mitigation, while the FNN witnesses reach $99\%$ and $96\%$ of their certification thresholds, implying the substantially stronger requirements for FNN certification. We further show that Bob's joint measurement determines the accessible level of network nonlocality: bilocal and FNN certification are optimized by different measurement settings, while both violations can disappear even for maximally entangled states. These results identify measurement geometry as an independent resource for network nonlocality and provide a practical route toward its certification on programmable quantum processors.

Expressive parameterized quantum circuits (PQCs) are often designed under a dilemma: the growth of expressibility and entangling power (EP) that improves Hilbert-space coverage is also expected to randomize an ansatz and activate barren-plateau (BP) conditions. We show that this dilemma is not a one-dimensional tradeoff. The usual picture collapses three inequivalent objects -- parameter-ensemble coverage, fixed-circuit entangling response, and local gradient moments -- into one scalar narrative. For a fixed circuit probed by Haar-product inputs, EP is a global two-copy mean of the output-entanglement distribution, whereas entangling-power deviation (EPD) is a global four-copy fluctuation descriptor. Gradient variance, however, is a local two-copy contraction selected by a parameter light cone and a cost observable. This moment hierarchy yields an analytic separation: equal EP need not imply equal trainability, as witnessed by equal-EP circuits with different EPDs and different gradient variances. These separations turn EP and EPD into a two-dial design rule for PQC ansatzes: EP measures how far the circuit has moved along the coverage dial, while EPD monitors whether input-dependent variability remains. We find that ansatz routes can reach high, Haar-like coverage before EPD and gradient variance collapse, showing that coverage and BP activation are distinct crossover events. The EP/EPD framework thus breaks the apparent one-dimensional expressibility-trainability tradeoff into a practical design rule: search for highly expressive PQCs in the window where coverage is high but BP-like homogenization has not yet erased trainable structure.