Quantum Physics Paper Analysis

The linear advection operator is an ubiquitous building block in fluid and plasma problems. We develop a quantum algorithm for enacting the operator. When the advection velocity is constant in space, our algorithm is exponentially more efficient per time step than classical and avoids spurious oscillations near steep gradients. The algorithm is most cleanly illustrated using the one-dimensional advection equation on a uniform spatial grid with periodic boundary conditions, which can be extended to higher dimensions. The algorithm uses a first-order upwind scheme, which captures discontinuities in the wave envelope but is not unitary. We embed the non-unitary upwind scheme using Linear Combinations of Unitaries (LCUs), and develop an efficient quantum gate decomposition of the upwind unitary, which performs one step of advection using $O(n^2)$ two-qubit gates, where $N=2^n$ is the number of spatial grid points, as opposed to a classical computer which costs $O(N)$. Although LCUs introduces a small bounded probability of failure per time step, we show that the accumulation of failures does not lead to exponential-in-time complexity as one would naively expect. Moreover, when LCUs fails, we develop a probabilistic scheme to recover from the failure state, which avoids a full restart of the simulation. The failure recovery scheme uses quantum Fourier transform (QFT) and effectively achieves quantum indefinite integration of an unknown quantum state. The recovery, which can itself fail, is more efficient than a full restart if the wave envelop is well-resolved to include only low Fourier modes. We emulate our scheme classically and demonstrate small problems on Quantinuum's trapped-ion qubits. Our quantum algorithm provides a subroutine for physics simulations that involve linear advection.

In quantum networks, nodes are connected via sharing of Einstein-Podolsky-Rosen (EPR) pairs, ideally with high fidelity and high rate. However, the fidelity of EPR pairs degrades due to imperfect generation and decoherence errors. Entanglement Distillation is a method that increases the fidelity but operates probabilistically and may destroy all involved EPR pairs upon failure. This failure reduces available EPR pairs for application use, thereby decreasing the service rate. Quantum Error Correction (QEC) is another mechanism to protect EPR pairs against error by forming what we term as Coding-Enhanced Memory (CEM). While effective, CEM requires extra time and resources to form the code, which also reduces the service rate. Existing methods often use static combinations of distillation and CEM, ignoring demand variations. This results in a low service rate without significant fidelity gain. Limited resources together with this rate-fidelity tradeoff make it essential to schedule when to run distillation, form CEM, or serve requests. We propose ReFINE, a demand-aware preemptive scheduler that based on application requirements either serves an available EPR pair immediately or preserves it in CEM. This selective use of CEM, only when needed, enables a better balance for rate-fidelity tradeoff than always using CEM. Between request arrivals, ReFINE either schedules distilling EPR pairs or forming CEM to protect distilled pairs, following one of the three priority policies: ReFINE-D (Distillation-First) first generates EPR pairs for distillation and then forms the CEM, prioritizing service rate. ReFINE-M (Memory-First) first forms the CEM, then generates the EPR pairs for distillation, prioritizing fidelity. ReFINE-C (Concurrent) performs both distillation and CEM formation concurrently, balancing between fidelity and service rate.

Molecular profiling from routine histopathology could expand access to precision oncology when sequencing is unavailable, tissue is limited, or training cohorts are small. We developed a hybrid quantum-classical strategy that replaces softmax attention in a transformer for histopathology-based gene expression prediction with a quantum-derived doubly stochastic matrix (QDSM). Across 29 cancer cohorts from The Cancer Genome Atlas and an independent pancreatic cancer cohort from the Clinical Proteomic Tumor Analysis Consortium, QDSM attention produced selective gains, with the largest relative improvements in smaller, data-limited cohorts, including adrenocortical carcinoma and uveal melanoma. Rather than improving transcriptome-wide performance uniformly, QDSM redistributed predictive accuracy across genes and pathways, improving biologically relevant targets in some tumor contexts while worsening others. In adrenocortical carcinoma, preferentially improved genes were enriched for adverse overall-survival associations, linking enhanced molecular inference to prognostically relevant biology. In pancreatic cancer transfer experiments, QDSM improved selected metabolic and lineage-associated genes but did not consistently improve performance under cross-cohort shift. Leave-one-cancer-out mixed-effects analysis showed that baseline molecular features predicted part of the gene-level benefit, while residuals identified cancer-specific programs that improved more or less than expected. Separate experiments on IBM quantum processors recovered the doubly stochastic matrix primitive underlying the attention mechanism. These findings position QDSM attention as a context- and target-dependent strategy for image-based molecular profiling and molecular triage when direct testing is unavailable, incomplete, or impractical.

Quantum Darwinism explains objective information through redundant environmental records. Earlier work established that imperfect records can be amplified and that environment self-evolution can enhance or suppress their formation. We investigate how preparation, interaction angle, and field disorder combine in an imperfect-CNOT model with random Gaussian couplings and pure, noninteracting environment qubits. We find that, without fields, a single alignment parameter $Λ$ determines the preparation and interaction-angle dependence of conditional-state distinguishability. Increasing interaction imperfection or local field strength can improve or suppress recording. We explain this nonmonotonic response through the geometry of conditional branch separation. For the pure initial environments considered here, the $Z$ basis remains optimal for Holevo information, so field-assisted recording requires no change of the recorded system observable. Comparing uniform local field strengths with Gaussian-distributed strengths at equal root-mean-square strength shows how disorder broadens both beneficial and detrimental field effects. Exact expressions for fragment information and numerical simulations with up to 24 environment qubits quantify the distinction between high mean information and reliable records across fragments and throughout a finite observation window. These results connect the geometry of local information acquisition to the fragment sizes needed for robust recording. The branch-distinguishability analysis itself requires only the conditional evolution of each environment qubit and extends to other interactions that preserve a system pointer basis.

Conventional quantum advantage in many-body dynamics is based on avoiding the simulation cost on a classical computer that arises from the extensive exponential complexity of the global wavefunction. Local observables, however, do not inherit this extensive complexity and may instead be governed by an intrinsic local complexity that is independent of the total system size. This distinction is particularly relevant in thermalising systems, where local observables lose memory of microscopic details and relax towards equilibrium values determined by only a few parameters. Here we introduce a variational time-evolution principle that exploits this distinction by replacing global-state fidelity with a cost function defined on local reduced density matrices. The resulting evolution retains coherent short-time dynamics while exploiting the simplification produced by thermalisation at later times. The concrete algorithm we propose is based on locally optimising matrix-product states and admits closed-form equations of motion analogous to the time-dependent variational principle. We show that the same variational principle has a quantum-classical counterpart, combining quantum evaluation of the local cost with an optimisation strategy robust to both shot and hardware noise. Proof-of-principle implementations on Quantinuum H2 and IBM Heron processors recover the characteristic local dynamics.

Quantum channel discrimination plays a crucial role in quantum information theory. Of particular interest is the case in which the channels can be discriminated perfectly. In this work, we focus on the perfect quantum channel discrimination task in a parallel scheme. We develop an SDP formulation combined with a bisection procedure to compute a quantum state for perfect discrimination in time linear in the number of copies. In addition, we obtain the minimal number of copies of quantum channels to achieve perfect discrimination. Thanks to that, we settle in the affirmative Conjecture 1 of Duan, Guo, Li and Li [arXiv:1605.02294, IEEE ISIT 2016], which characterizes the number of parallel uses needed to discriminate perfectly a distinguished family of operator subspaces. All our results are obtained using the notion and basic properties of the numerical range. In particular, the key fact that we prove and use is that the minimal angle of the numerical range of a tensor product of matrix subspaces equals the sum of the minimal angles of the numerical ranges of the individual subspaces.

We construct explicit families of asymptotically good quantum locally testable codes over qubits. More precseily, we construct explicit quantum LDPC CSS codes over qubits having constant rate, constant relative distance and constant weight local testers with constant soundness.

Hole spin qubits in semiconductor quantum dots (QDs) enable high-fidelity all-electric control, but conventional electric dipole spin resonance (EDSR) can require substantial rf drive power at the low magnetic fields that are favorable for qubit coherence and readout. In planar Ge hole spin qubits, this can reach -27 dBm at the device, posing challenges for scalable architectures due to heating and crosstalk. Here, we demonstrate a flopping-mode (FM) qubit in Ge, where a single spin is delocalized in a double QD, combining first-order protection against charge noise with exceptionally efficient electric driving. By mapping out coherence sweet-spots as a function of magnetic field orientation we achieve $T_2^*= 1.4μ\mathrm{s}$, $T_2^{\mathrm{Hahn}}= 11.5 μ\mathrm{s}$, $T^{φ, \mathrm{CPMG32}}_2= 130 μ\mathrm{s}$, and $T_1= 226 μ\mathrm{s}$, and a single-qubit gate fidelity of up to 99.76$\%$ for a gate time $t_{Xπ} = 88$ ns. Importantly, these results are obtained at a nearly in-plane magnetic field of 5 mT using only -52 dBm drive power at the device. We further find that qubit relaxation in this regime is consistent with a two-photon Orbach process, providing a route for further optimization. Our results demonstrate that FM-EDSR supports ultra-low-power, high-fidelity single-qubit operations, improvements that could benefit scalable hole-spin-based architectures and hybrid spin-photon interfaces.

The concept of causal (non)separability describes whether the causal order between parties that perform local quantum operations is well-defined or indefinite. Causal (non)separability in the general multipartite setting was introduced and studied in [Oreshkov and Giarmatzi, New J. Phys. 18, 093020 (2016); Wechs, Abbott, and Branciard, New J. Phys. 21, 013027 (2019)]. We resolve an open problem from these earlier works by showing -- using a novel "coherent teleportation technique" -- that a sufficient condition for causal separability identified in [Wechs, Abbott, and Branciard, New J. Phys. 21, 013027 (2019)] is also necessary, and thus provides a complete characterisation of multipartite causal separability. A consequence of this result is that all causally separable processes admit a realisation as generalised quantum circuits in which the order between the operations is classically controlled, known as "quantum circuits with classical control of causal order".

Gowers, Green, Manners, and Tao (Annals '25) recently resolved Marton's polynomial Freiman-Ruzsa conjecture. We give an algorithmic counterpart to their result: given uniform sampling and membership-oracle access to a set $A \subseteq \mathbb{F}_2^n$ with doubling constant at most $K$, our algorithm outputs a subspace of size at most $|A|$ whose $K^{O(1)}$ translates cover $A$. The algorithm runs in $\textsf{poly}(n,K)$ time. As applications, we obtain polynomial-time algorithms for a variety of learning problems, including quadratic Goldreich-Levin, improper agnostic tomography of stabilizer states, and tomography of quantum states with bounded stabilizer extent.

Simple analytic pulse-shaping techniques are of great practical utility in quantum control, with prime examples being the DRAG method for suppressing leakage in superconducting microwave gates and the transitionless-driving approach to shortcuts-to-adiabaticity. Standard versions of these methods require two orthogonal control channels, with the second channel effectively breaking time-reversal symmetry. This appears to rule out their use in settings with only a single real-valued control field, such as the kind of baseband flux control that is common in many superconducting circuit architectures. We show here that a simple analytic pulse-shaping technique derived via a Magnus expansion is effective even with just a single baseband control channel. We demonstrate its efficacy by simulating a two-qubit gate between transmons realized with a tunable coupler and baseband flux pulses. Our corrections dramatically reduce non-adiabatic leakage caused by ramping the coupler: for realistic device parameters, leakage in a fast iSWAP gate is suppressed by up to three orders of magnitude. Our approach is general, goes beyond simply suppressing unwanted spectral weight at leakage transitions, and can be applied to a variety of platforms.

Among the processes governed by open-system and dissipative quantum dynamics, environment-induced superselection, or einselection, is particularly foundational, since it describes the formation of a preferred set of pointer states through environmental monitoring and ultimately the emergence of classicality. Especially in the context of Quantum Darwinism, einselection can be studied in terms of the motion of an observable towards its pointer value. To this end, we derive a quantum speed limit for observables for finite-dimensional systems governed by differentiable time-local open dynamics. We identify two mechanisms through which non-Markovianity can enhance observable speed: direct dissipative motion supported by population retention or revival, and indirect enhancement through restoration of the asymmetry available for coherent motion. For permanent einselection, this delays the emergence of the pointer basis due to accumulated negativity.

We prove that hypercontractivity implies entropy contraction for a single quantum channel, without a detailed balance condition. For primitive quantum Markov semigroups that are KMS-symmetric with respect to a faithful invariant state \(σ\), we obtain the modified Log-Sobolev bound $α_1\geq \fracλ{(2+\log\|σ^{-1}\|_\infty)}$ where $λ$ is the spectral gap. This removes the assumption of \(L_p\)-regularity for the comparison through the log-Sobolev constant. As an application, we show that the hypercontractivity of an average of two conditional expectations implies the approximate tensorization of relative entropy.

The Mermin-Peres magic square provides a simple example of a system of linear equations over $\mathbb{Z}/2\mathbb{Z}$ which has no classical solutions but does have a finite-dimensional operator solution. For a long time, it was not known how to construct similar examples over $\mathbb{Z}/d\mathbb{Z}$ with $d$ odd. In this paper, we construct, for every integer $d\ge2$, a linear system over $\mathbb{Z}/d\mathbb{Z}$ that has a finite-dimensional operator solution but no classical solution. For an odd prime $p$, our operators act on two $p$-dimensional qudits and generate a finite $p$-group obtained by adjoining diagonal polynomial phase operators to the generalized Pauli group. Classical inconsistency follows from an elementary linearity argument comparing assignments on abelian subgroups.

On the span of the first $N$ oscillator modes, Gauss--Hermite quadrature gives an exact change of basis between mode coefficients and $N$ weighted position space samples. We implement this transform with $O(N\operatorname{polylog}(N,1/\varepsilon))$ logical gates and polylogarithmic quantum width. The operator-error bound $\varepsilon$ holds on arbitrary superpositions and includes all auxiliary registers. The construction uses signed averages on adaptive windows to convert uniform-grid samples into weighted Hermite-root samples. Their varying widths control the amplification cost, giving the near-linear bound.

Blind quantum computation (BQC) allows low-resource clients to securely delegate computations to a quantum server, but server resource costs scale with the computation size, posing a bottleneck for implementations. By leveraging Pauli-based computation (PBC), we achieve BQC with a server whose size depends only on the non-Clifford gate count. Our protocol inherits fault tolerance and qubit virtualization from PBC and reveals that classical-client BQC is possible even in the absence of classical simulability. Finally, we present an entanglement-based dual protocol that performs a resource state computation with a dramatically reduced execution cost.

Mutually unbiased bases capture perfect complementarity between two quantum measurements. Extensions beyond pairwise unbiasedness have been proposed, but essentially no non-trivial higher-order constructions are known. We introduce $k$-fold unbiased measurements ($k$-UMs), extending the $k$-fold unbiased bases notion of [arXiv:1706.04446] from rank-one basis measurements to arbitrary-rank projective measurements, and show that this higher-rank setting supports a much richer theory. We develop the notions of algebraic and spectral $k$-UMs and prove that they coincide for rank-one measurements and triples of measurements (3-UMs). We establish strong no-go results for higher-order rank-one constructions and three-outcome 3-UMs, but obtain infinitely many higher-rank triples using Hadamard matrices and Clifford algebras. We then give these structures an exact operational interpretation in terms of measurement incompatibility. For 3-UMs with any number of outcomes, we determine their generalised incompatibility robustness exactly and construct an explicit joint measurement for their noisy versions at the compatibility threshold. Finally, we implement the symmetry reduction of the sum-of-squares hierarchy recently introduced in [New J. Phys. 28, 064509 (2026)] and give numerical evidence that the noise thresholds arising from the $k$-UM analysis may characterise the asymptotic behaviour of this hierarchy. In particular, with very high precision, we numerically show that our constructed four-outcome 3-UMs are among the most incompatible triples of four-outcome measurements.

We present a quantum algorithm for simulating classical oscillator networks characterized by non-Markovian dissipation and time-varying material properties, extending recent speedups for undamped harmonic systems to viscoacoustic and viscoelastic media. We embed the history-dependent dynamics into a Markovian state space governed by a non-Hermitian operator by approximating memory kernels through a Prony series. We then use linear combination of Hamiltonian simulation to estimate the instantaneous kinetic and potential energy for a subset of oscillators at time $t$ within error $ε$ using a number of queries to the oscillator system that scales as $\widetilde{\mathcal{O}}(α_{\rm tot} t/ε)$, where $α_{\rm tot}$ is polynomial in the strength of the dissipation, spring constants, inverse masses, and sparsity of the connections in the network. We further show that this energy estimation task is in the worst-case classically hard (i.e., a corresponding decision problem is $\mathsf{BQP}$-complete), even in the presence of strong dissipation. For time-dependent materials, we show that changes in material properties appear as effective dissipation or growth in the energy representation. Additionally, we prove the infeasibility of exponential quantum advantages in locally coupled topologies through a novel form of Lieb-Robinson-like bounds that apply to differential equations. This allows our quantum algorithms to provide quartic speedups for locally coupled damped oscillator systems in three dimensions, raising the possibility of practical quantum speedups for realistically damped oscillator networks and approximated wave equations.

Threshold analyses of quantum error-correcting codes are well established for stochastic error models, in which errors occur randomly with given probabilities. However, errors in actual devices can also be coherent, such as unwanted $Z$ rotations due to imperfect control, which are not captured by stochastic error models. For the surface code, numerical studies have indicated threshold behavior even under coherent errors, but a rigorous proof of threshold existence is lacking. Here we prove that a positive threshold for coherent $Z$-rotation errors exists for quantum low-density parity-check codes with a bounded number of logical qubits, including the surface code and other topological codes. Specifically, we show that the maximum-likelihood Pauli recovery suppresses the entanglement infidelity exponentially in the code distance up to a prefactor linear in the number of physical qubits whenever the rotation angles lie below a constant that is independent of the code size. The proof combines Fourier analysis to retain the interference among the amplitudes of coherent errors with the cluster expansion of abstract polymer models. Our results expand the theoretical foundation of quantum error correction and offer a statistical-mechanical description of quantum error correction beyond stochastic errors.

The study of entanglement inevitably leads to the concept of regularization, where measures are evaluated on infinitely many copies of a state. Single-letter formulas try to make these asymptotic entanglement quantities accessible through a calculation on one copy of a state, but are rarely available. We introduce a decreasing hierarchy of computable upper bounds on the asymptotic relative entropy of entanglement with respect to positive-partial-transpose (PPT) states. The regularization of every fixed hierarchy level equals this asymptotic quantity. Additivity at any level therefore yields a single-letter formula, even when the usual one-copy relative entropy is nonadditive. We establish such additivity at the first nontrivial level for two broad multiparameter families, both containing all Werner states. The upper-bound construction also extends to sandwiched Renyi divergences. The hierarchy motivates $k$-multinegative states, a generalization of binegative states and the associated $k$-multinegativity, which gives explicit upper bounds on both the asymptotic relative entropy and exact PPT entanglement cost. We construct states which are $k$-multinegative at arbitrarily large depths $k$ that separate consecutive levels of the previously introduced entanglement-cost hierarchy, disproving its conjectured finite collapse. These results provide state-dependent single-letter formulas while identifying a limitation of universal finite-level characterizations.

Detecting phases of matter in general relies on identifying the correct order parameter - a task that remains notoriously difficult for unknown transitions and traditionally is guided by physical intuition and educated guess. Neural networks have recently offered an alternative route by locating phase transitions in known models without any a priori physical knowledge. Yet these approaches remain black boxes and only identify phases without elucidating their properties. Moreover, they often struggle when confronted with realistic, noisy experimental data, which constitute the ultimate testbed for automated methods in physics. Here, we bridge these perspectives by introducing TetrisCNN, a convolutional architecture with parallel branches of differently shaped filters, reminiscent of Tetris blocks, that learns sparse, interpretable latent representations directly in terms of spin correlators. Applied to experimental snapshots of two-dimensional Ising and XY quantum simulators measured in multiple bases, the network not only detects phase transitions and crossovers but also expresses its latent representation and decision boundaries as symbolic formulas built from experimentally measurable spin correlators. This framework opens the way to integrating interpretable neural networks with quantum simulators to uncover and understand new phases of matter.

Godsil, Roberson, Šámal and Severini conjectured that the quantum chromatic number of the categorical product of two graphs equals the minimum of the quantum chromatic numbers of the factors. We disprove this conjecture: we construct explicit finite graphs $G,H$ with \[ χ(G\times H) \leq 1538 < 1539 = \min(χ_q(G),χ_q(H)).\]The graphs are obtained from Zhu's counterexample to Hedetniemi's conjecture by using a base graph for which the Lovász theta number of the complement, and not only the fractional chromatic number, is large. The lower bound for the first factor is the theta bound. For the second factor we adapt Zhu's argument to projections that do not commute: the step that fixes the colors of a clique is replaced by identities between operators. Both lower bounds hold for colorings by projections in an arbitrary nonzero unital $C^*$-algebra. Hence the conjecture also fails for the spatial, approximate, commuting-operator and $C^*$-algebraic variants of the quantum chromatic number. We also give smaller counterexamples certified by exact integer data. The graph constructions, the certificates and the counterexample statements in the projective formulation are formalized in Lean~4.

We prove RE-completeness of the quantum homomorphism problem parameterised by families of graphs derived from the classic metric association schemes. These include Kneser graphs, $q$-Kneser graphs, and the complements of Johnson, Grassmann, and Hamming graphs. Our proof develops a spectral method for establishing non-contextuality of quantum polymorphisms. It combines an equality analysis of Roberson's bound on the projective packing number in terms of Schrijver's theta with a structural argument inspired by Erdős-Ko-Rado theory.

Starting from the entrance of a welded tree, a quantum walk algorithm can find its exit vertex exponentially faster than any classical algorithm. However, it has been an open question whether any quantum algorithm is able to efficiently find a path from the entrance to the exit. We answer this by proving an exponential quantum query lower bound for finding such path. Specifically, for trees of height $n$, any quantum query algorithm requires at least $Ω(2^{n/24})$ queries in order to succeed with constant probability. Our proof uses the compressed permutation oracle technique in order to construct databases which track the graph information an algorithm has learned and forgotten, and show that no efficient quantum algorithm can build an entrance-to-exit path in these records.

Does quantum mechanics allow for deterministic amplification schemes that simultaneously behave uniformly for all angles of bosonic phase space (i.e. phase preserving) and are nonlinear in the underlying field operators? Would such a scheme have some utility to quantum information science? In this paper we answer both questions with a resounding yes. Such amplifiers exist, but their form is highly constrained compared to the more general set of noise limited nonlinear amplifiers previously studied in the literature. This enables us to characterize the entire class of bosonic noise-limited nonlinear phase preserving amplifiers, and identify their utility: namely, the optimal amplification of Yurke-Stoler cat states and Kerr kitten states.

The accessible information of any given quantum ensemble quantifies the maximum amount of Shannon information that can be extracted from the ensemble by any quantum measurement. Almost three decades ago, Shor conjectured that the accessible information of any quantum dichotomy, that is, an ensemble of two states, is attained by a projective measurement. Recently, a proof of this conjecture restricted to the qubit case was published by Keil. Here, we conclusively settle this longstanding open problem. First, we show that Shor's conjecture follows, in arbitrary dimension, from a recent result by Fang, Fawzi and Fawzi, and we provide a self-contained, elementary proof. Second, for any given dichotomy and measurement, we provide the explicit construction of a projective measurement that outperforms such a measurement in extracting information from the given dichotomy. Third, while the computation of the accessible information is known to be non-convex in general, we frame the computation of the accessible information of dihotomies as a convex problem.

A verified Kubo-Martin-Schwinger (KMS) relation, after a drive has ceased, is not sufficient evidence to prove equilibrium. We demonstrate this in a large-$N$ large-$q$ Sachdev-Ye-Kitaev (SYK) quench protocol. Although all post-quench fermion correlators are exactly thermal, a second quench back to the initial Hamiltonian reveals hidden memory of the initial state. It is encoded in correlators connecting to times before the first quench. This memory is an extensive nonequilibrium (NEQ) witness with its decay rate being the Lyapunov exponent $λ_L$. Thus $λ_L$ sets the rate at which the state becomes effectively indistinguishable from a Gibbs state. Despite being a unitary interacting many-body system, the complete NEQ real-time evolution is obtained exactly in the large-$N$, large-$q$ limit, making the setup ideal for analytically studying thermalization.

Continuous-variable quantum key distribution (CVQKD) is compatible with telecommunication infrastructure, but implementing composable security with experimentally practical resources has remained challenging, particularly for discrete-modulated (DM) protocols. We report the first experimental demonstration of a DM CVQKD system that generates composable secret keys against general attacks with finite-size block lengths on the order of $\sim 10^{6}$ rounds via a quadrature phase shift keying (QPSK) system. Our implementation follows a variable-length, general security framework enabled by modern entropy accumulation techniques and conic optimization, whose experimental pipeline allows real-time operation on near-commercial hardware.

Fault-tolerant quantum computing (FTQC) is essential for large-scale quantum computation, but realizing useful application throughput requires coordinating resource preparation, assignment, routing, and logical execution under strict hardware and timing constraints. Many FTQC compilation approaches construct offline schedules using nominal or fixed magic-state factory throughput. Such schedules cannot respond to stochastic resource-preparation and teleportation outcomes, leading to execution stalls and hardware underutilization. In this work, we introduce FT-Weave, a stage-aware real-time FTQC compilation framework that jointly coordinates resource preparation, resource assignment, teleportation routing, and correction handling. By adapting to runtime resource availability and hardware constraints, FT-Weave allows preparation, communication, and logical execution to overlap. We instantiate FT-Weave on two representative neutral-atom, early FTQC architectures: transversal STAR and a T-state cultivation architecture. Under the evaluated hardware and latency model, FT-Weave achieves a speedup of up to 3X over a baseline compilation flow for simulations of the two-dimensional transverse-field Ising model. In the case study, we further find that maximizing exposed concurrency does not necessarily minimize execution time. Although fine-grained asynchronous execution can reduce local idle time, its smaller optimization windows and increased routing contention can outweigh these gains. Together, these results show that effective runtime coordination, rather then exposed parallelism alone, determines how efficiently FTQC resources translate into application throughput:FT-Weave provides a blueprint for solving this real-time orchestration problem across resource protocols and architectures.

High-harmonic generation (HHG) is a prototypical strong-field process in which intense light drives matter to emit radiation at integer multiples of the driving frequency. Extending HHG into the quantum-optical regime offers new opportunities to probe and control strongly nonlinear light-matter interactions using nonclassical states of light. Yet describing this regime requires a fully quantum treatment of the correlated electron-photon dynamics, which becomes computationally challenging for broadband, strongly squeezed fields. Here we solve the quantum-electrodynamical dynamics of a two-level system driven by bright squeezed vacuum in a converged multimode Hilbert space. Both the driving field and emitted harmonics are fully quantized, with the light-matter interaction treated nonperturbatively. This enables direct access to the multimode quantum state and its higher-order correlations beyond semiclassical sampling or perturbative descriptions. We show that squeezed-vacuum driving produces harmonic emission with qualitatively distinct second- and third-order photon correlations compared with coherent excitation. Moreover, back-action from the driven emitter strongly reshapes the incident squeezed field, generating pronounced Wigner-function negativities that evolve on attosecond timescales. Our results establish a fully quantum framework for broadband strong-field dynamics with squeezed light and provide a route to predicting and interpreting quantum-HHG experiments and their extension to more complex emitters.

We present a variational quantum-circuit model for fragmentation functions (FFs). Isospin and charge-conjugation symmetries are imposed to construct an independent six-flavor basis describing charged and neutral pion production, while physics-inspired Ansätze, including logarithmic feature maps and mass thresholds, encode the relevant kinematics. This quantum architecture substantially reduces the quantum circuit redundancies and improve optimization convergence. Using the DSS14 pion FF set as a benchmark, we first develop a one-dimensional variational representation (FF-VQR) in the momentum fraction at fixed energy scale, and show how entanglement between quark and gluon FFs yields a significant improvement, with accurate results already obtained using just two variational layers. A spectral analysis further demonstrates that the quantum model achieves high expressivity with a limited number of Fourier modes, supporting its use as a compact non-perturbative parametrization suitable for DGLAP evolution. We then extend the FF-VQR to two dimensions by incorporating the energy-scale dependence. By encoding all flavor channels within a single entangled quantum circuit, the quantum model provides a unified representation with higher accuracy than an independent encoding for each partonic species.

Utility-scale quantum computing will require executing long, complex algorithms with end-to-end error rates far below what physical qubits can support directly. Error-corrected logical qubits are needed to achieve this goal. To make the progress on logical qubits measurable and comparable we introduce the definition of scalable logical qubits: logical qubits preserved for long computations by repeated quantum error correction, capable of fault-tolerant universal operations with low-latency real-time decoding and feedback, and replicable to the hundreds or thousands, as required by applications. We characterize these scalable logical qubits along four coupled dimensions: reliability, scale, capability, and performance, and discuss trade-offs among these dimensions.

The feasibility of cost-effective simultaneous quantum and classical communication (SQCC) transmitting both the quantum key and classical information via a superimposed coherent state is investigated both in optical and Terahertz (THz) bands. Since the existing THz SQCC schemes assume single-carrier (SC) transmission over flat fading channels, we embark on investigating SQCC in realistic frequency-selective multipath THz fading channels. We then propose an orthogonal frequency division multiplexing (OFDM) based SQCC system for time-invariant frequency-selective THz scenarios, supported by low-density parity-check coded (LDPC) multidimensional QKD reconciliation schemes. Our simulation results demonstrate that the OFDM-based SQCC scheme is capable of achieving a practical secret key rate (SKR) over a wide range of power sharing scenarios between the classical and quantum signals. By contrast its single-carrier counterpart requires the classical signal to be at least 100 times stronger than the quantum signal in THz SQCC.

A key appeal of quantum low-density parity check (qLDPC) codes is their ability to suppress stochastic Pauli noise below nonzero thresholds. Coherent errors are fundamentally different: they produce superpositions of error patterns whose amplitudes can interfere even after syndrome measurement. Rigorous understanding of coherent errors remains limited. Here we show that general qLDPC codes admit a nonzero code capacity threshold against local coherent noise and more generally local channel noise. For any family of qLDPC codes with distance $d=Ω(\log n)$, we show that there is a constant noise strength below which the logical recovery error in diamond distance decays exponentially with the code distance. The result is established for optimal recovery as well as the minimum-weight decoder. The key technical ingredient is what we call a \emph{cluster resummation}: rather than bounding superposed error configurations one by one, we isolate a large connected error cluster in the channel expansion and exactly resum all errors disconnected from it before taking norms. Standard cluster counting then yields exponential suppression. This work resolves a longstanding challenge in fault tolerance theory, providing general robustness guarantees for qLDPC codes against coherent noise and laying a rigorous foundation for future studies of fault-tolerant quantum technologies.

Quantum communication underpins secure information processing and scalable quantum networks. In particular, remote state preparation (RSP) enables efficient quantum state transfer, but accurately estimating target states under complex noise remains challenging. Here, we propose a Transformer-based Quantum State Characterizer (TQSC) model for noisy RSP experiments. Our model reconstructs experimentally prepared pure and mixed photonic polarization states from noisy measurements in complex scattering environments, while its attention patterns provide physically grounded insights into correlations among the measured observables. The method achieves a mean estimator-target fidelity exceeding 99.999% under complex scattering and dynamic Gaussian noise, while its robustness and generalization are further examined using Qiskit-simulated Bloch-ball states.Furthermore, in a practical MNIST image transmission task with held-out states, the decoded bit error rate is reduced from 50.34% to zero after TQSC post-processing. The TQSC model enables accurate tomographic characterization under dynamic noise and provides physically grounded post-hoc insights, holding promise for intelligent quantum information processing applications.

We review recent advances in particle physics enabled and motivated by the rapid progress of quantum technologies. The continued development of quantum computing toward large-scale, fault-tolerant systems has the potential to address dynamical problems that remain extremely challenging for classical computational approaches, opening new avenues for studying nonperturbative dynamical processes. Tabletop detectors and quantum-enhanced technologies have reached unprecedented sensitivities, enabling novel searches for ultralight particles, gravitational waves, and other physics beyond the Standard Model in parameter regimes previously inaccessible to conventional instrumentation. Taken together, these developments highlight a rapidly evolving landscape in which quantum technologies are beginning to reshape fundamental physics. We aim to synthesize recent progress and illuminate the opportunities they present for advancing particle physics in the coming years.

Neutral atom arrays have emerged as versatile platforms for performing both digital and analogue quantum computing and simulation, with demonstrations ranging from large-scale programmable Hamiltonians realising topological phases or weighted graph optimisation to error-corrected logical qubits with transverse gate operations. This paper provides a broad overview to the neutral atom platform, and the potential applications relevant to materials science and quantum chemistry.

Validating variational quantum eigensolver (VQE) pipelines on realistic chemical systems is a critical stepping stone toward tackling classically intractable molecules. In this work, we report emulator-based validation of the VQE workflow proposed for the copper active site, executed on the LRZ Eviden Qaptiva emulator. A problem-tailored ADAPT-VQE with a full singles-doubles-triples (S+D+T) pool removes over 99% of the correlation error, reaching a stable plateau at 4.03 mEh relative to exact diagonalisation (148 selected operators). This establishes a >40x improvement over the hardware-efficient ansatz (HEA). Finally, we frame these emulator results as a robust baseline for upcoming physical quantum hardware runs on Euro-Q-Exa.

Quantum $p$-local spin glass Hamiltonians are natural quantum analogues of the classical spin glass models. We provide an asymptotic characterization of the maximal energy achievable by the product states. We prove that for every $p \ge 2$, the limit of ground state energy exists and is given by a Parisi-type variational formula. This settles a question left open by Anschuetz et. al. (2025). The variational formula also recovers the known large-$p$ asymptotics as a consequence. Finally, we prove that the limiting product state energy is universal for a broad class of non-Gaussian interactions.

In order to understand which initial states retain memory under periodic driving, it is necessary to depart from the ideal limit giving rise to invariant structures and work inside near-degenerate manifolds. We show that degeneracy itself is not conclusive and what actually matters is how perturbations, such as structural and driving imperfections, acts on the projected multiplet. For systems decoupling into the local clusters in the ideal limit, the projections can be computed within degenerate perturbation theory. There the stability is decided by two criteria: the coupling can not connect the state with other degenerate partners in the manifold, either by kinetic blocking, or more generally, by diagonalizing the projected coupling, and the drive's local selection rule must admit only transfer energies detuned from Floquet sidebands, in which case the projected drive generator exactly vanishes. We formalize these understandings in a periodically driven clean, short-ranged alternating XXZ chain and demonstrate a set of results that include, long-lived states, both of product form and entangled across the clusters, a periodic family of sideband resonances, and an explicit example showing opposite fates for states with identical energy and charges.

Recent advances in the field of quantum computing hardware motivate the search for applications which demonstrate so-called quantum advantage. One promising use case that has been identified is the simulation of quantum many-body systems. The computational resources required for performing such a simulation on a classical computer generally grow exponentially with the size of the system being modeled, which is ultimately due to the exponential growth of the Hilbert space in which the dynamics of such a system take place. While digital quantum computers natively evolve quantum states directly in such a Hilbert space, thus naively avoiding this problem, the result of such a computation is typically not obtained as a deterministic output. Rather, it requires projective measurements which are fundamentally affected by shot noise. Any desired expectation values must therefore be reconstructed from repeated measurements, making the number of those measurements a relevant computational resource, and thus an important consideration for any potential claims of quantum advantage. In this work, we study how this resource scales with system size (a scaling which itself depends on the desired accuracy of the final result), using the simulation of nuclear magnetic resonance (NMR) spectra as a test case. We study this scaling for both real-world molecules, as well as a class of model NMR Hamiltonians which allow for efficient large-scale simulations with one-dimensional, two-dimensional, and all-to-all interactions. We find that the required resources increase only weakly with molecular size, far below the exponential growth of the underlying Hilbert space. This result suggests that shot noise should not pose a fundamental barrier to achieving quantum advantage in the simulation of NMR systems, and perhaps for many-body systems more broadly.

We investigate the entanglement dynamics of quantum states defined on graphs with non-local Ising interactions governed by the Katz kernel of the underlying network. The interaction pattern is physically motivated by a gapped fermionic mediator propagating on the same graph, whose perturbative elimination yields an effective Katz-weighted Ising Hamiltonian. Using the Entanglement Distance, we derive an exact analytical expression for the entanglement generated from an initially separable state and apply it to representative deterministic graph families. We then characterize the dynamics in different propagation regimes. In the weak-Katz regime, the dynamics admits a systematic motif expansion with triangles entering at first order order and four-cycles, local degree structure, and overlappin triangles appearing at second order. In the strong-propagation regime, the interaction is instead dominated by the principal adjacency mode and by the localization properties of its eigenvector. For Erdős--Rényi graphs, the weak-propagation expansion can be averaged analytically, revealing a locally tree-like contribution in the sparse regime and saturation of the Entanglement Distance density in the dense regime. Our results connect entanglement dynamics with both the walk-based and spectral structure of complex networks.

Enhanced performance of quantum reservoir computing has been associated with dynamical phase transitions, but whether this connection extends to dissipative systems and which relaxation mechanisms underlie it remain insufficiently understood. We systematically compare driven-dissipative Kerr reservoirs across first-order and continuous dissipative phase transitions and find enhanced memory and nonlinear processing near both phase boundaries. Although the closure of the Liouvillian gap marks the transitions in the thermodynamic limit, computational performance does not generally follow gap suppression. An exact post-training Liouvillian-mode decomposition quantitatively attributes the trained memory to intrinsic relaxation channels. It shows that the gap mode contributes only weakly, while finite-rate modes and their cross-contributions dominate the enhanced capacity. These results go beyond phenomenological correlations by directly linking memory capacity to the intrinsic Liouvillian relaxation spectrum. Moreover, these findings provide a physical basis for designing dissipative quantum reservoirs and testing memory-enhancement mechanisms in experimentally accessible Kerr platforms.

Many signal processing tasks require intensive computations. Quantum computing promises to accelerate certain tasks, but algorithms must be designed around the limitations of quantum mechanics. This paper provides a quantum implementation of finite impulse response (FIR) filters, which are a widely used tool in classical signal processing. The filter can be parallelized and composed as part of larger quantum algorithms, with potential for speedups using quantum amplitude estimation and future fault-tolerant quantum hardware. To accomplish these properties, we introduce a state-space framework wherein sample-based signal processing is performed with unitary quantum circuits. We present the quantum delay gate as the quantum analog of the delay line in discrete-time signal processing. Unitary circuits intrinsically describe lossless systems, but we also implement lowpass and other bounded filters by emulating a projection operator. The FIR filter implementation is tested and demonstrated with a quantum circuit simulator.

Exceptional-point signatures in first-passage observables are governed by two independent survival mechanisms: nonlinear spectral defectivity must pass from the one-record or transfer description to the physical one-level first-passage ladder, and the resulting ladder Jordan mode must have nonzero overlap with the chosen preparation and terminal observation. For finite reset-form monitored quantum systems with upward-skip-free counting, we prove the exact threshold factorization $H_N(s)=R_s^N$, identify the physical Perron branch, and derive the transfer factorization $Q_s(r)=B_s(r)(R_s-rI)$. Invertibility of the cofactor gives local equality of Smith data, whereas a singular cofactor can contribute transfer multiplicity absent from the ladder. An order-two Keldysh formula yields an independent observation gate. We then prove a fixed-reset no-go theorem: even a defective full tilted generator cannot generate a cumulative-count Jordan polynomial when the post-count ladder is scalar. Finally, we construct a three-reset monitored-Lindblad witness, minimal within irreducible nonnegative ladders, with a genuine subleading $Nλ^N$ threshold term and a coherence-tuned model in which a binary terminal effect retains the exact polynomial signature at a transversal transform-domain exceptional point. The analysis is formulated at the level of exact transform-domain structure; time-domain asymptotics and perturbative robustness remain separate questions.

Control of charge-state stability in near-surface quantum defects is critical for nanoscale sensing, yet remains particularly challenging under ultra-high vacuum (UHV), where surface-induced band bending destabilizes the metrologically relevant charge-state. Here, we present a robust and reproducible approach for stabilizing shallowly implanted (< 10 nm deep) nitrogen-vacancy (NV) centers in near-UHV conditions (P = $3 \times 10^{-9}$ mbar) based on dielectric interface engineering. Through measurements on individually addressable NV centers, we demonstrate that a TiO2 coating on the diamond suppresses surface-induced electrostatic fields, yielding a 79% increase n NV- population and a 45% enhancement in NV-spin resonance contrast at room temperature. Coherent control measurements further reveal suppressed charge-state conversion dynamics. These results establish dielectric screening as a powerful and reproducible strategy to engineer charge transition energetics of NV centers in scanning-probe-compatible geometries under extreme conditions.

A channel capacity quantifies the communication capability of a noisy physical process. In contrast to communication channels in the classical world, quantum theory makes this capability contextual. We show that two Pauli two-qubit channels, each with zero private classical capacity, can be used to transmit private information when used together. One is a two-qubit Pauli channel whose environment can reconstruct the receiver output up to matrix transposition; the other is an antidegradable channel. We obtain a similar result when the second channel is the 50% qubit erasure channel. A simple binary code built from rank-three mixtures of Bell states activates private communication. The main ingredient in our construction is a transpose-antidegradable channel that is not antidegradable.

We study the off-diagonal matrix elements of real-space observables in time-reversal-invariant single-particle chaotic systems. By analyzing the semiclassical expression for the off-diagonal variance derived from Berry's conjecture, we show that the banded structure of the observable matrix emerges naturally. For local observables, we identify a characteristic bandwidth associated with a late-time timescale inversely proportional to the particle velocity. We further show that, for systems with steep-wall confinement, the predicted magnitude follows the entropy scaling of the eigenstate thermalization hypothesis (ETH), multiplied by an additional kinetic-energy-dependent factor that is independent of spatial dimension and is not captured by conventional many-body ETH. We illustrate these results through a case study of quantum billiards and verify the semiclassical scaling numerically in a generalized quarter-Sinai billiard. Our results elucidate the dynamical implications of Berry's conjecture and provide a comparison between single-particle eigenstate thermalization and many-body ETH.

We report progress toward the development of a quantum silicon-on-insulator (QSOI(R)) technology compatible with 300mm CMOS fabrication and adapted from the 28nm Fully-Depleted SOI (28nm FD-SOI) platform for scalable quantum computing. We compare quantum devices fabricated with standard 28nm FD-SOI and QSOI(R) technologies, and show striking improvements of room temperature electrostatic properties of the individual device. Moreover, the QSOI(R) technology has significantly reduced the device variability and the dispersion of device properties at the wafer level. Transistor metrics are reproduced by TCAD simulations showing that the electrostatics of the devices behave as expected for QSOI(R) technology. Wafer-scale measurements at sub-2K show reproducible quantum dots down to the few-electron regime with 69\% yield for successful charge detection of the first electron and a dispersion of the first electron position of $\mathrm{\pm 35 mV}$ over 377 quantum dots. These results establish QSOI(R) as a promising platform for CMOS-compatible quantum device co-integration.

Many-body localization is remarkable in that localization persists despite the presence of dynamical interactions. Here we demonstrate the converse phenomenon: enhanced many-body delocalization induced solely by exchange statistics. We study a Aubry-André quasiperiodic system of anyons in one dimension in the absence of density-density interactions. In terms of anyon operators, the system is described by a quadratic Hamiltonian. By analyzing the finite-size scaling of its spectral properties and the inverse participation ratio of many-body eigenstates, we find that increasing the anyonic statistical phase systematically shifts the many-body localization crossover toward larger quasiperdiodic potentials. We further confirm these findings using a dynamical probe, namely the persistence of an initial density imbalance following quenches. Our results establish exchange statistics as an independent mechanism capable of altering many-body localization, revealing a fundamentally distinct route to delocalization in one-dimensional quantum systems.

Entanglement scaling provides a powerful probe of universal properties at quantum critical points. In two dimensions, contributions originating from a corner-shaped bipartition exhibit a universal scaling, which is determined by the underlying conformal field theory. We develop a method to extract this corner entanglement entropy from projected entangled pair states directly in the thermodynamic limit. When applied to models at a quantum critical point, we show that the corner contribution exhibits scaling with the effective correlation length, in agreement with the hypothesis of finite-entanglement scaling. Our results for the corner coefficients are consistent with other methods, demonstrating the efficiency of our method for diagnosing strongly-correlated quantum critical points in two dimensions.

Graph Neural Networks (GNNs) achieve state-of-the-art performance on graph-structured data, but training and inference on large graphs are often bottlenecked by memory constraints and sparse linear-algebra workloads. Quantum computing offers an alternative set of primitives that may improve scalability for graph learning. Building on the quantum graph neural network (QGNN) framework of Liao \textit{et al.}, this work implements two representative architectures --- the Simplified Graph Convolution (SGC) and Linear Graph Convolution (LGC) models --- and evaluates them on open benchmark graph datasets and semi-supervised learning tasks using quantum simulation. We compare predictive performance and optimization behavior against classical baselines, showing that the quantum models achieve competitive performance with fewer parameters. Finally, we present a cost gradient analysis that identifies the tasks for which the models showcased are trainable. This is followed by a classical simulability study to find regimes in which the proposed circuits remain robust during training.

Recent advances in quantum computing hardware toward fault-tolerance have increased interest in evaluating near-term quantum platforms on application-relevant quantum algorithms. In this work, we introduce Quantum WalkScore (QWS), a scalable application-oriented benchmark designed to assess the performance of NISQ and future fault-tolerant quantum computers in executing essential quantum routines --discrete-time quantum walks and quantum amplitude amplification-- to solve the graph nodefinding problem (marked-vertex search). QWS quantifies performance by scoring the largest problem size for which a designated target node can be found with success probability above a defined threshold. In addition to the complete protocol description, we provide example parameter-selection scenarios designed from noiseless simulation results and demonstrate QWS evaluation through experimental runs on multiple generations of IBM real quantum processors.

Magic state cultivation prepares high-fidelity magic states at low expected space-time costs; however, the exact performance of some schemes is unsettled due to the difficulty in simulating non-Clifford circuits. Here, we use matrix-product states (MPS) based methods to compute the exact performance of two types of fold-transversal cultivation schemes: (i) the Sahay et al method based on the regular surface code S gate, and (ii) a method we propose based on a partially fault-tolerant fold-transversal S gate. We show that for the former protocol at $d=5$, the $|T\rangle$ output reaches similar logical error rates to the $|S\rangle$ output, traditionally used as a cheap full Clifford proxy. This contrasts with the $\sim10\times$ discrepancy reported for the $d=5$ colour-code scheme of Gidney et al. We also find that our new $d=5$ scheme has $\sim1.3\times$ lower expected space-time cost while still reaching $10^{-9}$ logical error rate. We show that MPS and Clifford-augmented MPS (CAMPS) perform on par with or even better than the recently introduced near-Clifford simulator Clifft on the hardest $d=5$ regular surface code scheme. Additionally, to speed up simulation, we propose a new pre-screening method based on simple Pauli propagation, lowering by up to three orders of magnitude the required number of exact simulations, and use several simulator-agnostic sampling methods such as subset sampling.

Distributed quantum sensing is an emerging application of quantum networking, where entangled probe states are employed to sense combinations of delocalized parameters with enhanced precision relative to using separable states. Squeezed states of light are a prime resource for experimental demonstrations of entanglement-enhanced sensing, because they can be generated and entangled deterministically. Existing distributed quantum sensing experiments have been fundamentally limited in scalability due to their bulk-optic architectures. Meanwhile, integrated photonics provides a scalable and compact platform for quantum sensors. Here we demonstrate entanglement-enhanced sensing of linear functions of four phase shifts in an integrated photonic circuit. We find an entanglement-enhanced precision of 0.199(16) dB below the shot noise limit compared to 0.041(18) dB for separable states. A four-mode entangled state is generated on-chip with entanglement verification and phase sensing also performed on-chip with an array of four integrated homodyne detectors.

Can an attacker turn influence over an artificial intelligence (AI) adviser into a harmful quantum error-correction update? We identify an ambiguity in passive syndrome records that obstructs recovery selection, then show how additional calibration measurements support certified recovery updates under uncertainty and drift. In an odd-distance square toric code with error-free preparation, syndrome measurements, and recovery operations, opposite coherent $X$ rotations produce identical passive syndrome-history distributions. Yet a fixed phase correction can help at one sign and harm at the other. A terminal logical measurement on known encoded calibration states supplies the missing sign information. A separate evaluator accepts an update only when calibration uncertainty and a justified drift bound certify improvement over the current recovery, without assuming that the adviser recommends correctly. In simulated advice attacks, calibration-confidence checks reject harmful proposals while retaining beneficial updates under honest advice. We derive sufficient limits on calibration age that require improvement through deployment. In matched simulations, a validated channel-specific bound retains more beneficial updates than the general bound after accounting for evaluation time, while preventing the tested harmful activations under the stated drift assumption. A separate surface-code experiment includes stochastic circuit faults and noise changing during acquisition. Deterministic controllers achieve at least as many beneficial updates with the same observations. Violating the drift assumption permits harmful acceptance in the toric experiment. The results identify information required for recovery selection, establish conditional guarantees against harmful updates, and quantify the recovery improvements forgone through conservative acceptance.

We compute exactly the acceptance and logical error rates for the distance $d=3$ and $d=5$ magic state cultivation circuits from Clifft [arXiv:2604.27058] and SOFT [arXiv:2512.23037] using Pauli propagation and binary tensor contraction. Actual $T$ gates are studied, not the $S$-gate proxy used for sampling. The calculation includes every fault order at several circuit-level noise strengths ($p$). We provide a series expansion form to the logical error rates, through order $(p/(1-p))^{10}$. The analytical results recover the numerical values from Clifft and SOFT at both $d=3$ and $d=5$ to within their sampling uncertainty. Then, we show that the $d=3$ and $d=5$ circuits actually have fault distances of $d_{\text{fault}}=2$ and $d_{\text{fault}}=3$ respectively, explaining the similar distance degrading effects from the companion code of [Quantum 10, 2134 (2026)].

Taming the exponential increase of the Hilbert space dimension with system size in the simulation of gapped quantum lattice models is of the highest relevance for understanding and designing exotic quantum materials, where nonlocal interactions are of particular interest. High-order linked-cluster expansions provide access the solution of the eigenvalue problem for the infinite system, yet rely on the computation of high-dimensional oscillatory lattice sums with a graph structure, only approachable with Monte Carlo methods so far. This work resolves this issue, rendering all required graph lattice sums, referred to as graph zeta functions for kernels involving power-laws, computable. The resulting method reduces the evaluation time for state-of-the art series expansions from tenthousands of core-hours to minutes. After factorizing the lattice sum over blocks, each block is evaluated by the cheapest available strategy depending on its treewidth $\mathrm{tw}$. Basic blocks admit analytic forms in terms of generalized zeta functions. Series-parallel blocks with $\mathrm{tw}\le 2$ can be computed at linear cost in the number of graph nodes and in the size of the momentum grid using a semi-analytical algebra based on Epstein zeta functions and rapidly decaying Fourier series. Finally, for $\mathrm{tw}>2$, the method is combined with tensor-network bucket elimination yielding polynomial scaling of numerical work and memory in momentum grid size with exponents only growing with $\mathrm{tw}$ rather than with the number of vertices. Through use of FFT, the full momentum grid is recovered at the cost of a single momentum evaluation. We provide a detailed analysis of the precision and runtime of our method against analytic and numerical benchmarks. We further reproduce published Monte Carlo data for the transverse-field Ising model on different 1D, 2D, and 3D lattices, obtaining full agreement.

We develop a geometric framework for Hamiltonian engineering in finite-dimensional quantum systems using ideal control pulses. Starting from a bilinear Schrödinger equation with unbounded control amplitudes, we construct the closed pulse group and use extensions of control systems and Filippov's relaxation theorem to obtain a family of effective Hamiltonians given by the convex hull of the drift's adjoint orbit plus the Lie algebra of the pulse group. The geometry of this orbitope describes possibilities beyond group averaging. Using the isotypic decomposition of the adjoint representation, we characterize its affine hull and show that the group average lies in its interior. This yields locally accessible families of effective Hamiltonians around the invariant part of the drift. We apply the framework to recover the necessary and sufficient condition for dynamical decoupling from arbitrary interactions with a finite-dimensional bath. For connected abelian pulse groups, we describe the relevant representation decomposition through restricted roots. Finally, for qubit networks with identical pairwise couplings, we give a qualitative characterization and quantitative estimation of effective Hamiltonians that can be generated using our framework.

We show that boson sampling with an arbitrary $m$-mode interferometer and $n\le m$ single-photon inputs can be simulated to inverse-polynomial total-variation error by a logarithmic-depth qubit circuit with polynomially many qubits. The circuit uses Clifford+$T$ gates, arbitrary qubit connectivity, and a single final measurement, and its family is logspace uniform. The key idea is to enlarge the optical system, decompose the resulting transformation into six quadratic shears, and distribute each mode over many submodes. This redistribution permits a fixed local occupation cutoff, after which local basis changes and parallel phase gates give the qubit circuit. Consequently, our result places boson sampling within shallow quantum computation.

Quantum networks are resources for scaling quantum computers and distributed sensing technologies while offering post-quantum security benefits. Teleporting non-classical resources like entanglement, via so called entanglement swapping, is essential for networks in particular overcoming rate-loss limits via quantum repeaters. Deploying these systems on real infrastructure will likely require multiplexing photonic qubits into fibers carrying 'classical' light encoding standard Internet communications and control plane signals for multi-node quantum protocols. Here, we report the first demonstration of entanglement swapping and conventional communications operating over the same fibers. Entanglement is swapped across a five-node quantum relay topology connected by four long-distance fibers, each populated with classical data signals. Time-bin entangled photons in the C-band are multiplexed alongside C-band classical signals using dense-wavelength division multiplexing, introducing noise photons generated by high-power classical light. We experimentally and theoretically characterize the trade-off between quantum fidelity and Raman noise photons. Entanglement swapping is demonstrated over a maximum fiber length of 40 km (four 10-km fibers) while simultaneously transmitting 10-Gbps classical data through all fibers. These results represent a significant advancement in the demonstrated complexity of coexisting quantum and classical networks and provide a roadmap for achieving the widespread deployment of advanced quantum technologies.

Nitrogen-vacancy (NV) centers in diamond are a leading platform for vector magnetometry, offering intrinsic sensitivity to both the magnitude and direction of magnetic fields. NV magnetometers typically rely on an external bias field to lift the degeneracy of the ground-state spin sublevels, enabling spectral discrimination of different NV orientations and spin transitions. At high accuracy, however, such a bias field systematically introduces errors through thermal, mechanical, and hysteretic drifts, thus hindering the accurate measurement of the magnetic field of interest. Several strategies have been proposed to address this limitation, including optical polarization-based orientation labeling, optical anisotropy, strong coupling to nearby nuclear spins, circular microwave polarization, and tailored pulse sequences. In this work, we introduce an optimization-based pulse-shaping control framework that enables selective and robust manipulation of NV ensembles without relying on a static bias field. Our method achieves both orientation-selective and subspace-selective control through optimal temporal modulation of the driving fields, providing a route to resolving spectral overlaps in degenerate NV systems.

The coupling between self-sustained oscillators, such as lasers or polariton condensates, leads to different steady-states in different regimes. Weak coupling allows the oscillators to behave independently, with different frequencies and uncorrelated phases, while stronger coupling can produce synchronization. In classical or semiclassical theories transitions between these steady-states correspond to changes in the topology of the phase space attractors and occur at generalized exceptional points. We investigate the corresponding changes in a quantum theory of coupled lasers or condensates. We show how the different steady-state regimes of the classical limit give rise to distinct forms for the spectra and eigenmatrices of the slow modes of the Liouvillian. By following the spectral flow between the different regimes we show that the synchronization transition is controlled by cascades of exceptional points in these slow modes, protected by a generalized PT symmetry. Our results show how singularities of the quantum Liouvillian control the different dynamical regimes, and give rise to experimental signatures of the synchronization transition which remain well-defined in the few-particle regime dominated by quantum effects.

The conditional probabilities achievable by local measurements on a shared quantum state in a Bell scenario form the set of quantum behaviors, whose structure was studied by Tsirelson. In 1993, Tsirelson asked whether this set is semialgebraic, that is, describable by finite Boolean combinations of polynomial equations and inequalities. This question has remained open. We answer it in the negative: with four binary measurements per party, the set of finite-dimensional quantum behaviors, its closure, and the commuting-operator set are all nonsemialgebraic. More strongly, none admits a finite real-analytic description even locally near a particular classical behavior. These results rule out exact finite semidefinite representations and show that no finite level of the Navascués-Pironio-Acín hierarchy characterizes these sets exactly.

In this introductory review, we present and compare four algorithms for the numerical integration of the Lindblad equation for one-dimensional quantum lattice systems. All four methods are based on Matrix Product State representations and can be viewed as extensions of the Time-Evolving Block Decimation (TEBD) algorithm to open quantum systems. Two approaches directly integrate the vectorized Lindblad equation, one of them explicitly enforcing the positivity of the density matrix. The other two rely on stochastic unravelings of the Lindblad equation, namely the quantum trajectory and quantum state diffusion approaches. We discuss the principles, numerical implementation, accuracy, and computational efficiency of the different methods, and benchmark them against an exactly solvable free fermion model.

Direct quadrature of the Hadamard-reduced sixth-order time-convolutionless (TCL6) generator at all $N_t$ sampled times requires $O(N_t^3)$ operations at fixed system dimension. We derive an exact reduction for a finite-dimensional system coupled through one Hermitian operator to a stationary centered Gaussian bath. By separating fixed operator coefficients from scalar bath kernels, the complete TCL6 time series is reduced to cumulative sums and first-order recurrences, one-dimensional causal convolutions, and an exact dyadic recursion for interlocked histories. With the algorithm, evaluating the complete TCL6 time series requires $O(N_t\log^2 N_t)$ operations at fixed system dimension. In addition, we show that TCL$2n$ can be evaluated with $O(N_t\log^{n-1} N_t)$ complexity. A fixed finite Matsubara expansion of the bath correlation function permits $O(N_t\log N_t)$ evaluation at any fixed TCL order. These reductions enable fast long-time simulations of non-Markovian open quantum systems within the regime of validity of the TCL expansion.

This work studies the placement of an entanglement source along a communication line formed by two noisy qubit channels. Recent work argued, on analytical and numerical grounds, that midpoint placement should be at least as favorable as endpoint placement. Here it is shown that, for arbitrary qubit channels, if a sequential composition can preserve entanglement, then the corresponding parallel action cannot annihilate all entanglement. The proof uses the transpose-factorization criterion introduced in that recent work. Quantum Sinkhorn scaling converts every strictly positive qubit channel into a unital representative, and the special normal form of unital qubit channels then yields the required factorization of the transposed map through the original channel. Depolarizing regularization and the closedness of the set of entanglement-breaking channels extend the result to arbitrary channels. Consequently, $Λ_1 \otimes Λ_2 \in \mathrm{EA}$ implies $Λ_2 \circ Λ_1 \in \mathrm{EB}$, and, by exchanging the two channels, the same holds for the opposite composition order. This proves the recent conjecture that midpoint placement is optimal for all qubit channels, in the feasibility sense in which that optimality was originally defined.

Recent quantum gas cavity-QED experiments demonstrated simultaneous coupling of photons to single atom transitions as well as correlated pairs of ultracold fermions trapped inside optical cavities. This enables simultaneous control over density ordering and pairing. Using extensive numerical simulations, we show that in a transversely driven, two-component degenerate Fermi gas, the interplay of cavity-induced and bare atom--atom interactions controls not only the power threshold for self-organization, but also the type of spatial ordering in the $\mathbb Z_2$-symmetry-broken superradiant state. In the repulsive interaction regime, unpaired or weakly paired fermions first self-organize through a charge-density-wave instability, and finite-momentum pairing only occurs at much stronger pump strengths. In contrast, an attractive superfluid undergoes a joint density--pairing instability, directly entering into intertwined phase with charge-density-wave and pair-density-wave orders. At strong pumping the photon-enhanced pair interaction generates localized density and pairing order even when the bare contact interaction is repulsive. In this cavity-dominated regime strong spatial localization suppresses the long range superfluid coherence. Our results identify the role of cavity-induced atomic interactions in supporting intertwined fermionic orders and pave the way for exploring exotic states with multiple orders in highly controlled hybrid light-matter systems.

Over the past decade, high-order series expansions based on linked-cluster methods have become an important tool for studying low-energy properties of gapped quantum systems with long-range interactions. We introduce a deterministic framework that removes a central computational bottleneck of this method. Our graph zeta method replaces the costly and statistically noisy Monte Carlo (MC) evaluation of high-dimensional lattice sums by a systematic, high-precision computation that delivers series coefficients within minutes on standard desktop hardware. The full momentum-dependent series is obtained in a single calculation, enabling high-resolution excitation spectra throughout the Brillouin zone. Building on the companion paper [1], the method reformulates graph-embedding sums as graph zeta functions and decomposes them into blocks classified by their treewidth tw. Low-treewidth blocks (tw$\leq2$) admit closed expressions based on Epstein zeta functions, while higher-treewidth blocks (tw$>2$) are evaluated using tensor-network bucket elimination. We benchmark the approach for transverse-field Ising models with power-law interactions in 1d, 2d, and 3d, reproducing previous MC results at a fraction of the computational cost while enabling substantially denser parameter sampling. An open-source implementation makes the method directly applicable to general interactions and large parameter scans. As an application, we compare microscopic interaction models for the stacked quasi-2d transverse-field Ising triangular-lattice antiferromagnet KTmSe$_2$ and find that a model including dipolar interactions best describes existing experimental data. The graph zeta method thus turns high-order linked-cluster expansions into a practical and deterministic tool for fast quantitative momentum-resolved modeling of short- and long-range quantum matter.

We give a quantum algorithm for Lindbladian simulation given a block encoding of the Hamiltonian $H$ and a projected unitary encoding of the stacked jump operator $B=\sum_{k=1}^m \lvert k\rangle\otimes L_k$, with normalization factors $α_H$ and $α_B$, respectively. For evolution time $t$, set $τ=(α_H+α_B^2)t$. The algorithm approximates the evolution channel to diamond-norm error $\varepsilon$ using $O\!\left(τ+\frac{\log(1/\varepsilon)}{\log\!\left(e+\log(1/\varepsilon)/τ\right)}\right)$ oracle queries, matching the query lower bound for Hamiltonian simulation. The number of additional one- and two-qubit gates is linear in the query complexity up to polylogarithmic factors. The query- and gate-complexity bounds extend to Lipschitz-continuous time-dependent Lindbladians under coherent time-indexed oracle access. Our construction uses a one-query transducer that implements a product of rational approximations to short-time evolution when supplied with a catalyst. We bound the error from omitting the catalyst by exploiting orthogonality between different sequences of Kraus labels. The gate implementation combines a compressed Kraus-label representation, which stores only the positions and values of the nonzero labels, with the rotation factorization of Chen et al.

We prove that minimum-output Rényi-entropy additivity can fail by almost one bit simultaneously at every nonnegative order. For every $\varepsilon\in(0,\log2)$, there exists a finite-dimensional quantum channel with a real Stinespring isometry such that the same maximally entangled input witnesses a tensor-square entropy gap of at least $\log2-\varepsilon$ for all $p\in[0,\infty]$. The output dimension can be chosen to be $O(\varepsilon^{-3})$ as $\varepsilon\downarrow0$. The construction uses direct products of free groups: tensorized Haagerup estimates control the one-copy outputs, while commutation between distinct factors forces exact Bell-branch collisions at two copies. Strong convergence gives both an existential realization through finite-dimensional representations of right-angled Artin groups followed by realification, and a Haar-orthogonal model whose success probability tends to one as the matrix dimension grows. We also determine the exact Bell quotient, prove asymptotically sharp regular-radius bounds, and show that the cubic output-dimension scale is optimal within the present purity--rank certificate.

The use of quantum resources in the work extraction from a quantum system is an emerging research topic. Recently, [arXiv:2602.22893] established the necessity of measurement coherence for obtaining advantage in work extraction from an unknown isolated quantum system. However, a quantitative relation between the magnitude of this advantage and established measures of measurement coherence is missing. Here, we establish such a connection by introducing a faithful operational quantifier of the work advantage provided by a measurement. We show that measurement coherence is necessary and sufficient for a positive advantage, and derive upper and lower bounds in terms of the robustness of measurement coherence and an $l_{\infty}$ norm based coherence measure respectively. Finally, we examine this quantifier of advantage from the resource theoretic perspective. Our results provide an operational characterisation of measurement coherence as a resource for work extraction and reveal a nontrivial relation between its resource content and thermodynamic value.

In a frustrated spin system, highly entangled eigenstates can form a separable thermal mixture. We study this distinction for four spin-$1/2$ moments on a tetrahedron, the elementary unit of the pyrochlore lattice, with the general four-parameter exchange Hamiltonian. Tetrahedral symmetry allows a restricted search over thermal-state decompositions to be carried out by linear optimization, yielding an upper bound on multipartite concurrence and explicit separable decompositions where this bound vanishes. At low temperature, the concurrence maps show extended separable regions near the all-in--all-out limit, whereas suppression near the spin-ice point is narrowly localized. Heating broadens the latter region as nearby multiplets are repopulated. The optimization identifies fully separable thermal states even when the eigenstate-averaged concurrence remains large. Negativity independently confirms finite-temperature entanglement in selected coupling regions. A mixed-state stabilizer Rényi diagnostic, used to explore quantum magic, favours different couplings and can increase locally with temperature. These results connect thermal entanglement to the splitting and population of symmetry multiplets, and provide a practical basis for identifying frustrated spin configurations for studies of quantum resources beyond the ground-state limit.

We show that, starting from a product state, local unitary quantum evolutions generate intermediate states which exhibit a multiscale entanglement-spectrum structure required for universal entanglement embezzlement. This facilitates entanglement extraction from a catalyst many-body state while leaving it asymptotically unchanged. Remarkably, these atypical structures emerge generically at intermediate stages, well before reaching maximum entropy where thermalization has flattened out the spectral hierarchy. The resulting state is accompanied by nonlocal nonstabilizerness that diverges with the system size, consistent with a recently established equivalence between universal embezzlement and divergent nonlocal magic. Thus, without any fine tuning, a chaotic quantum evolution generates intermediate states which form a universal family of catalytic reservoirs.

Certifying nonclassicality without assuming any particular underlying physical theory constitutes both a foundational challenge and a requirement for device-independent protocols. Realizing such theory-independent certification in scalable architectures is essential for connecting fundamental tests with emerging quantum technologies. Integrated photonic circuits are a leading platform for scalable quantum information processing, motivating the development of rigorous methods to certify the nonclassical resources underpinning quantum advantage. In this paper, we report a theory-independent certification of generalized contextuality on a three-mode integrated photonic circuit. Our approach combines theory-agnostic tomography with simplex-embeddability certification---a framework that requires no assumptions about the underlying physical theory---and applies it to experimental data from a three-mode photonic circuit seeded by single photons. An independently constructed quantum model of the experiment provides a consistency check on the observed nonclassicality, without entering the certification as a theoretical assumption. The method rules out simplex-embeddability for our experimental data, providing robust, theory-independent evidence that our photonic circuit exhibits nonclassicality.

Quantum key distribution (QKD) enables secure underwater communications essential for maritime infrastructure. Underwater optical channels introduce substantial photon loss (erasures) and ambient noise that degrade QKD performance. This paper investigates whether two four-qubit Calderbank-Shor-Steane (CSS) quantum error correction codes (QECC) mitigate these impairments in vertical underwater communication BB84 QKD protocol. After developing a comprehensive stochastic channel model incorporating photon loss, geometric spreading, and solar noise, we assess the viability of QECC through the analytical study of the quantum bit error rate (QBER) and the secure key rate (SKR) with and without security depending on the signal-to-noise ratio (SNR) validated against Monte Carlo simulations. The standard four-qubit CSS code achieves a 3 dB SNR gain at the QBER 11% security threshold; the discard code variant achieves 4.5 dB. However, QECC includes an encoding overhead that reduces the SKR. We demonstrate a crucial relationship between the SKR and the probability of arrival of the sent photon. Analysis shows that QECC is beneficial exclusively in marginal SNR regimes; at high SNR, raw BB84 dominates. For an ocean Type III Jerlov water scenario with sunlight coming from the sun located at the top of the atmosphere, we identify operational depth-range windows where QECC enables communication otherwise infeasible. This analysis establishes that error correction deployment must be scenario-dependent: extend operational range at the cost of throughput when SNR is marginal, or prioritize key generation rates at high SNR.

Quantum neural networks (QNNs) are typically built from variational quantum circuits (VQCs), which are limited by local measurements. Adaptive non-local observables (ANO) address this by jointly optimizing circuit parameters and multi-qubit measurements. However, existing ANO-based VQCs learn only a single static observable that remains invariant across all inputs. We propose QFWP-ANO, a novel architecture which employs a classical hypernetwork to dynamically program VQC parameters and/or non-local observables conditioned on each input. On multivariate time-series forecasting across four ETT datasets, QFWP-ANO achieves the lowest MSE in 16 of 20 settings and second-lowest in the remaining four, surpassing ANO-based and other strong baselines. On reinforcement learning tasks, QFWP-ANO consistently surpasses ANO-VQCs. Our results establish input-conditioned ANO as an effective approach for enhancing QNNs.

In this manuscript, we analyze the dynamics of a model in which two spin-1/2 systems are each coupled noncommutingly to a static environmental field and to a self-Hamiltonian, while also being mutually coupled through a $σ_y^{(1)}σ_y^{(2)}$ interaction. By constructing an exact solution that exploits parity symmetry, and by applying the stationary-phase approximation (the saddle-point method) in the continuum limit of the environmental field, we show that coherence associated with the ordinary isolated stationary point decays as $t^{-1}$, whereas, under the resonance condition at which the local effective fields of the two spins cancel each other, only the coherence between a pair of maximally entangled, Bell-type states- the eigenbasis of the inter-system coupling-survives, decaying via the anomalously slow power law $t^{-1/2}$. Through a comparison with the pointer-basis theory of W. H. Zurek and coworkers (the 1981 and 2005 models), we further reveal a mechanism not reducible to local coupling: in this system, the pointer observable is determined not by the individual system-environment couplings but by a statistical resonance condition between the two environments.

Hilbert's sixth problem placed probability and mechanics at the center of the axiomatization of physics. It asks how irreversible statistical probability and thermodynamics can produce from the reversible, deterministic dynamics of a system. Building on an exact open quantum system theory developed in the past two decades, we construct a dynamical route from the reversible quantum dynamics to reduced statistics. For quadratic bosonic and fermionic systems bilinearly coupled to arbitrary environments, we derive the exact reduced density operator determined completely by a dissipative propagator u and a fluctuation correlation function v of the system. For continuous spectral densities with no bound-state pole, u vanishes in the long-time limit, information about the system initial states is lost completely, and the reduced density operator of systems approaches a thermal Gibbs state. Gapped spectral densities with localized bound states instead preserve long-time memory and prevent thermalization. We then remove the usual assumption of an initially thermal, mixed environment, start from a product of pure states for the system and environment, unitary evolution first generates system-environment entanglement and a periodic quasi-Gibbs reduced state for a finite environment. When the number of environmental degrees of freedom tends to infinity, the spectrum becomes continuous, the recurrence disappears, the exact reduced density operator converges to a thermal Gibbs state. The total entropy remains zero, whereas the system entropy becomes entanglement entropy and reaches its maximum. Probability is therefore not an additional random postulate imposed on unitary dynamics, it is the objective statistical structure of an open system in a composite. These results provide an exact, testable dynamical solution of the determinism to statistics.

Quantum networks require scalable photon sources combining narrow linewidth, high efficiency, and high indistinguishability. Microresonator photon-pair sources are promising candidates, yet a source-only description based on the joint spectral amplitude (JSA) predicts near-zero Hong-Ou-Mandel (HOM) interference visibility between photons generated by independent, CW-driven microresonators. In this work, we show that the observed HOM interference is not determined by the JSA alone. By combining finite-time detection with cavity-enhanced spontaneous four-wave mixing, we characterize a detector-conditioned heralded state governed by the idler-photon detection window. We further demonstrate that independently optimizing the idler and signal detection windows allows both heralded-photon indistinguishability and intrinsic heralding efficiency to approach unity, without spectral filtering or complex source engineering. Utilizing integrated high-$Q$ silicon nitride microresonators, we achieve HOM visibilities of 0.992(8) and 0.942(12), without background subtraction, at fourfold count rates of 4.5(3) and 12.2(6) Hz, respectively. Our work establishes CW-driven high-$Q$ microresonators as a robust and scalable platform for quantum-network primitives.

We demonstrate the possibility to activate genuine multipartite entanglement (GME), the strongest form of entanglement for multipartite states, within the framework of quantum catalysis. Specifically, we show that any biseparable state (i.e. not GME) that is not partition separable can be deterministically transformed into a GME state via the help of a catalyst and local operations, without any classical communication. In turn, we construct a catalytic protocol tailored to the multipartite case. The protocol is termed "sum-to-product", as it transforms a mixture of states into their tensor product in a heralded manner. We apply this protocol to random network entangled states, which are biseparable by construction, and demonstrate catalytic activation of both GME and genuine multipartite Bell nonlocality.

We study maximum purity and minimum von Neumann entropy of absolutely positive partial transpose (APPT) states, together with the relative volume of their spectral sets. A consequence of Hildebrand's criterion gives an explicit outer spectral polytope, whose vertices we classify. Optimizing purity over this polytope, together with the Song--Chen result for the $2\otimes3$ system, yields, for every $mn\ge6$, an explicit upper bound on the purity of APPT states that is asymptotic to $4/(3mn)$. This improves the previous $2/(mn)$ upper bound for absolutely separable states. The new bound applies to every APPT state, a class containing all absolutely separable states, and is sharp for every $2\otimes n$ system with $n\ge3$. For every $3\otimes n$ system with $n\ge3$, however, the unique outer-polytope maximizer is not APPT, so the bound is strict and disproves the Dũng--Khôi qutrit--qudit conjecture. The polytope also gives an explicit entropy lower bound in arbitrary bipartite dimensions and, together with the Song--Chen extreme-point classification, the exact minimum entropy for every $2\otimes n$ system. Finally, exact formulas for the relative volumes of an inner polytope and the outer spectral polytope give explicit two-sided bounds on the qubit--qudit relative spectral volume $a_n$ whose ratio is less than $4$ and tends to $3$. Consequently, $a_n=Θ\!\left(\sqrt n(4/27)^n\right)$, and the relative volume of the qubit--qudit APPT spectral set (equivalently, the absolutely separable spectral set) has exact exponential decay rate $\ln(27/4)$.

We propose a compact NISQ-compatible quantum transformer architecture for synthetic QNLP sequence modelling. The model preserves the autoregressive next-token interface of a classical transformer, but replaces attention and feed-forward sublayers with variational quantum encoder blocks, connector circuits, decoder blocks and a direct two-qubit measurement readout. Token contexts are angle-encoded into small quantum registers, processed by parallel variational heads and encoder integration circuits and conditioned through decoder ancillae to produce a distribution over a four-token vocabulary. We evaluate several architecture variants on deterministic and lexicographic grammar-generation tasks against a compact classical transformer baseline. The quantum models are trainable end-to-end and learn nontrivial grammar structure, including perfect deterministic generation in individual runs and high lexicographic validity in the strongest variant. The classical baseline remains more accurate and stable and the quantum models are sensitive to initialization. The contribution is therefore not a claim of quantum advantage, but a concrete architecture and evaluation of transformer-inspired QNLP sequence modelling under near-term quantum constraints.

Indefinite causal order extends the conventional circuit paradigm by allowing local quantum operations to be connected without a predetermined global order. Within the process-matrix framework, it is characterized by causal nonseparability, whereas extensible causal separability (ECS) requires that, under arbitrary input-ancilla extensions, a process admit a recursive decomposition into components, each compatible with a particular operation acting first. Quantum circuits with classical control of causal order (QC-CC), in which previous outcomes dynamically determine which operation acts next, are known to generate ECS processes, but whether every ECS process admits such a realization has remained a longstanding open problem. We settle it through a generalized teleportation construction that realizes every multipartite ECS process as a QC-CC. We further establish consistency between ECS definitions for trivial and nontrivial global past and future systems. These results provide ECS with an exact operational interpretation and identify QC-CC as the complete circuit structure underlying this class of processes.

The gap between the classical and quantum Fisher information matrices (CFIM and QFIM) separates what is operationally accessible through measurements from what is intrinsic to a quantum state. In the multiparameter setting, this quantum obstruction is generically not saturable. Motivated by the recently introduced semiclassical geometric tensor (SCGT), we perform an explicit information-geometric study for a class of pure four-parameter single-qutrit states (FPSQSs). These states are probed by a one-parameter family of measurements that interpolates between an uninformative POVM and a sharp projective measurement. We derive closed-form expressions for the CFIM, the quantum geometric tensor (QGT), and the SCGT. We show that the SCGT reproduces the QGT in the projective limit and vanishes in the trivial limit. The real part of the SCGT splits into two terms: the CFIM and an additional nonnegative measurement-transmitted metric in the phase sector. Its imaginary part provides a semiclassical Berry curvature. Its loss relative to the QGT is quantified by a measurement-dependent gap. Our results provide an exactly solvable four-parameter platform for the semiclassical geometric framework. They also clarify how realistic measurements read out the geometric content of quantum states, and how they partially degrade it.

Photon blockade is a phenomenon where the presence of system nonlinearity causes the output to consist of single photons, which has been extensively studied in point atom systems, but it is barely explored in giant atom ones. In this paper, we propose giant atom-mediated photon blockade scheme based on two cavities and three cavities systems with driving field applied to the first cavity. We show that simultaneous unconventional photon blockades (UPBs) can not occur in the point atom system (the atom coupling only to the leftmost cavity) due to there always existing a cavity to have a single path. In contrast, the spatially extended nature of giant atom enables coupling to multiple cavities and allows for the introduction of a phase and coupling strength. Consequently, simultaneous UPBs in multiple cavities can be obtained due to the multipath destructive interference. Moreover, by manipulating the detuning, we observe simultaneous conventional photon blockades (CPBs) in multiple cavities. Finally, we study simultaneous two-photon blockades (2PBs) in point atom multiple cavities system.

The Hong--Ou--Mandel (HOM) effect is a hallmark of two-photon quantum interference, in which two indistinguishable photons impinging on a balanced beam splitter bunch into the same output port. Here, we show that a giant atom (GA), coupled to two waveguides through two coupling points each, can function as a programmable HOM interferometer, enabling continuous control over single-photon beam splitting and two-photon interference. This programmability arises from coupling-phase differences in the GA, which tune its self-interference and directionality, and thereby its scattering response. To characterize the two-photon interference, we analyze the scattering of two Gaussian single-photon wave packets injected through different waveguides and evaluate the bunching and antibunching (coincidence) probabilities of the resulting four output ports. At the operating point where the GA acts as an effective 50:50 beam splitter for single photons, we observe a pronounced HOM dip as the relative input delay between the two wave packets is varied. Away from this point, adjusting the coupling phases continuously tunes the two-photon output statistics between bunching into the same output port and antibunching across distinct output ports. In addition, we explore an application to quantum parameter estimation, showing that small deviations of coupling phases can be estimated from the two-photon output statistics, with the achievable sensitivity quantified by the classical Fisher information associated with a binary coincidence measurement. Our giant-atom beam splitter thus provides a programmable platform for two-photon interference in waveguide quantum electrodynamics, with potential applications in quantum information processing, quantum communication, and quantum sensing.

We investigate the connection between classical and quantum chaos in a dissipative system of two coupled collective spins. Although the classical dynamics possesses a stable fixed-point attractor, we find pronounced signatures of chaos in the transient dynamics preceding relaxation. In the quantum model, such transient chaos is accompanied by a transition to random-matrix statistics in the relevant part of the Liouvillian spectrum and by a qualitative increase in the number of Liouvillian modes contributing to expectation values of physical observables. The transition occurs before the bifurcation at which the stable fixed point disappears and a chaotic attractor emerges. Our results show that Liouvillian quantum chaos can be associated with transient classical chaos, rather than requiring a chaotic asymptotic attractor, and provide a refinement of the Grobe-Haake-Sommers conjecture.

Continuous-time quantum walks (CTQWs) on dynamic graphs realize quantum gates as sequences of time-evolving graph Hamiltonians, but naive constructions produce long sequences with redundancy. Simplification rules, which are graph rewrite rules that shorten a dynamic graph sequence while preserving the unitary it implements, are the CTQW analogue of circuit identities in the gate model. In this work, we give CTQW realizations of the standard single-qubit gates and introduce new graph rewrite rules. We demonstrate the simplification rules through worked circuit reductions and outline their use as transpilation primitives for converting between the circuit model and the dynamic graph framework.

Scalable quantum networks require processing nodes with flexible internal connectivity, yet neutral-atom architectures remain constrained by the strong spatial dependence of native Rydberg interactions. Here we show that a Rydberg atom chain can act as a coherent quantum bus, converting a locally connected one-dimensional architecture into an effectively nonlocal interaction network. Virtual excitations in the dispersive regime mediate controllable interactions between spatially separated data units, which we derive analytically using a Green's-function continued-fraction method. The resulting mechanism is not restricted to single-excitation dynamics and supports several distinct functionalities, including Floquet-engineered chiral transport, remote entanglement of mechanical oscillators, and destructive interference for selectively suppressing unwanted dipole exchange. Simulations incorporating full long-range Rydberg interactions, atomic position fluctuations, and finite Rydberg-state lifetimes show that the mediated dynamics remain robust under experimentally relevant conditions. These results establish Rydberg chains as programmable coherent mediators for extending the internal connectivity of neutral-atom quantum nodes toward quasi-all-to-all coupling, providing a hardware-level route toward scalable and reconfigurable quantum-network architectures.

The survey discusses the problem of measuring correlations in composite quantum and statistical systems. After briefly recalling the standard methods of describing correlations, the emphasis is on the method of correlation indices. The latter method for quantifying the strength of correlations in composite physical systems is sufficiently general allowing for measuring in a unique way the correlation strength in both quantum and statistical systems, for static as well as for dynamic processes. The correlation indices, can be defined for correlation operators, reduced density matrices, and other operators containing information on correlations in the studied composite systems. The correlation indices measure all types of correlations, quantum correlations, such as entanglement, as well as classical correlations. They are applicable for characterizing static as well as dynamical processes. Examples are given of correlation indices for several quantum states and for spin and pseudospin systems. The quantification of correlations in a nonequilibrium system is exemplified by calculating the correlation index for a trapped Bose-Einstein condensate subject to the action of an alternating field.

Indirect quantum control aims to manipulate a target system through interventions on an auxiliary controller with which it interacts. We formulate finite-step indirect-control protocols using the language of higher-order quantum operations, representing admissible controller manipulations as deterministic superinstruments. This representation separates the uncontrolled but fixed dynamics from the controllable operations and allows the optimal control problem to be written as a semidefinite program for a chosen figure of merit. The resulting optimum gives an operational benchmark by providing the best performance achievable by a finite sequence of control operations, including protocols with classical or quantum feed-forward. More restricted and experimentally motivated control classes, such as independent unitary controls or memoryless quantum channels, can then be compared against this benchmark. We illustrate the framework with a two-step qubit-purification task, in which an initially mixed target qubit is steered toward a pure state through a fixed interaction with a controller qubit. The example shows regimes where simple unitary strategies saturate the higher-order benchmark, as well as regimes where they are provably suboptimal. This approach provides a systematic way to study the value of control resources in indirect quantum-control schemes.

We demonstrate the emergence of quantum-chaotic dynamics in a quasiperiodically driven impact oscillator near the grazing condition. While previous studies of the quantum impact oscillator under periodic driving reported strange nonchaotic dynamics, we show that quasiperiodic driving produces robust signatures of chaos. The corresponding classical system undergoes a sharp grazing-induced transition from quasiperiodic motion to chaos, as established by bifurcation analysis, Lyapunov exponents, Fourier spectra, and the 0-1 test. In the quantum system, Shannon-entropy time series exhibit broadband spectra, 0-1 test values close to unity, and predominantly positive finite-time Lyapunov exponents for both rational and irrational driving-frequency ratios. Independent quantum diagnostics reinforce this result: the out-of-time-order correlator (OTOC) displays early-time exponential growth with nearly identical rates, while the golden-ratio drive leads to a substantially faster saturation of the OTOC. Fidelity exhibits an exponential decay regime that is approximately independent of perturbation strength. These results establish quasiperiodic driving near grazing as a mechanism for generating quantum-chaotic behavior and reveal that, although the initial onset of scrambling is largely insensitive to frequency-ratio rationality, the subsequent development of global scrambling is strongly influenced by the degree of irrationality of the drive.

Under the label of optical quantum computing, there are a variety of protocols and experiments that use the quantum properties of light to achieve a computational advantage over classical computing machines. In this review, we describe some of the main implementations, which differ in the type of encoding and in how the computation is performed, whether using gates or cluster states. For each protocol, we describe advantages and challenges with an overview of the experimental results obtained, summarized in tables. Because of the great relevance achieved in this field, there is a section dedicated to non-universal quantum computation with photons, where boson sampling, variational quantum eigensolvers, and quantum machine learning applications are described. The aim is to give the reader the broadest overview of the applications where photons and their quantum properties play a key role in computation.

A framework for quantum electrodynamics of equilibrium systems is proposed that takes the Maxwell equations as foundational and links them to the structure of density-functional theory for the quantum system. By switching from purely internal observables like the one-particle density to combined internal and external quantities, the external sources and their energy are taken into account. A fully regularized functional theory emerges that avoids the usual representability problems. With the Kohn-Sham construction that links to an auxiliary uncoupled system, the ultra-violet cutoff can be removed and one arrives at a fully renormalized and non-perturbative light-matter description. Regularized forms of density-functional theory with and without magnetic fields appear as boundary cases, while the emergent physical picture reproduces the macroscopic Maxwell equations.

We characterize the bath resources needed to supply repeated uses of a fixed finite-dimensional quantum channel in a closed device. For each horizon $T$, one bath, one initial state and one repeated unitary are fixed before the user. Each output is returned before the next input arrives; no reset, discard, fresh ancilla or uncounted controller is available. Approximation error must vanish against arbitrary adaptive users with quantum memory and references. Writing $r=\lim \log_2(R_T)/T$ for the bath dimension rate and $s=\lim S(ω_T)/T$ for the actual initial entropy rate, we prove that the achievable region is exactly $s\ge 0$, $r+s\ge h$ and $r-s\geκ$. Here $h$ is maximum entropy exchange and $κ$ is a smoothed independent-reference extension cost, with the zero-error limit taken before the supremum over full-rank inputs. Its exact fixed-input form is an affine transform of the zero-leakage quantum privacy funnel. The minimum dimension rate is $(h+κ)/2$. The proof combines entropy converses, a bath-dimension-independent support repair, and a closed adaptive implementation of encoder-only fully quantum Slepian--Wolf recycling. All seeds, clocks, workspace and retained residues are counted. Worked examples include dephasing, pure replacement and a qubit channel with $0<κ<h$. No computability of $κ$ or efficient circuit synthesis is claimed.

Time-dependent coherent control can enhance excitation transport in open quantum networks, but independently controlling every inter-site coupling creates a control space of high dimension and leads to difficult optimization problems. We introduce an edge-ranking strategy based on the control-induced change in the gradient component of the time-integrated quantum probability current, which is obtained via a graph Hodge decomposition. When our strategy is applied to the seven-site Fenna-Matthews-Olson (FMO) model, the six-edge set retains $99.83\%$ of the enhancement achieved by full control, and the four-edge set retains $97.60\%$ while reducing the pulse fluence---used here as a proxy for control effort---by $41.55\%$ relative to full control. Dephasing scans and comparisons with random edge sets and random networks provide numerical support for the relevance and potential broader utility of the ranking. These results show that edge selection guided by the quantum probability current can substantially reduce the control space while preserving high transport performance with lower control effort.

Computing dynamical expectation values typically relies on approximations optimized for the state or observable separately, without accounting for how their errors combine in the final expression.This work explores an alternative approach in which each approximation is guided by both the state and the observable, accounting for how they jointly determine the target expectation value. This idea is implemented through a sweep algorithm with coupled loss functions for forward state and backward observable updates. Exact error relations provide an analytical rationale for how the proposed losses can improve the accuracy. Numerical tests on 30-qubit random circuits show errors two to three orders of magnitude smaller than those of variational state compression at equal bond dimensions. These results motivate further exploration of joint state and observable approximation for dynamical expectation value estimation.

We investigate the purity dynamics of a quantum system coupled to a continuous-variable pointer through a von Neumann-type interaction Hamiltonian of the form $\hat H_{\mathrm{int}}=g\,\hat H\otimes\hat p$. For an initially Gaussian pointer state, the interaction generates energy-dependent conditional translations whose mutual overlaps are determined explicitly by the populated spectral separations of the system Hamiltonian. After tracing out the pointer degrees of freedom, we obtain the reduced density operator and derive an exact analytical expression for the time-dependent purity. Using this expression, we establish two-sided purity bounds governed by the minimum and maximum nonzero energy gaps on the populated spectral support. These bounds provide a state-dependent spectral characterization of the loss of purity and become exact for two-level systems. We further show that the short-time decrease of purity is controlled by the Hamiltonian variance of the initial state, with $\mathcal P''(0)=-(g^2/σ^2) \operatorname{Var}_{ψ_S}(\hat H)$. In addition, an explicit sufficient timescale is derived for the purity to approach its asymptotic value within a prescribed tolerance, revealing the scaling $t_{\varepsilon}\proptoσ/(|g|Δ_{\min})$. Finally, the general results are illustrated for an equally weighted $N$-level system with an equally spaced spectrum, for which the asymptotic purity is $1/N$. The analysis clarifies the distinct roles of spectral separation, energy variance, coupling strength, and pointer width in Hamiltonian-conditioned purity loss.

Can quantum entanglement continue to grow even after the entanglement entropies of subsystems have saturated? We address this question using genuine multi-entropy, which probes multi-partite entanglement structure beyond bipartite entanglement. In a two-sided BTZ black hole, this quantity grows linearly with time after every subsystem entropy of a fixed tripartition has saturated, extending the interval in which entanglement detects Einstein-Rosen bridge growth. The result refines the ER=EPR relation by identifying multi-partite structure invisible to ordinary entanglement entropies. Some spin-chain models and the spatially partitioned Sachdev-Ye-Kitaev (SYK) model exhibit distinct transients, while the late-time plateau values in holography, the SYK model, and Haar-random states share a universal behaviour.

We establish unbounded two-use Holevo additivity gaps in finite dimensions. For each sufficiently large fixed integer $K$ and all sufficiently large $n$, we construct channels $T_n$ with output dimension $K^n$, input dimension $\exp(Θ_K(n^2))$, and \[ χ(T_n^{\otimes2})-2χ(T_n) \ge n\left[\frac{\log_2K}{K}-2\log_2(1+9/K)\right]-O(1/n). \] The gap is linear in output qubits, with an explicit quadratic input-qubit cost and an explicit threshold on $n$. We also obtain channels whose single-use Holevo quantity tends to zero while their two-use Holevo information, and hence classical capacity, diverges. The channels arise from structured tensor products of the complementary mixed-unitary channels used in Collins's free-probabilistic proof. We establish minimum-output-entropy gaps by combining Collins--Youn's product-group Haagerup inequality with Bordenave--Collins's quantitative strong-convergence estimates

Heisenberg originally envisioned the error-disturbance relation under the premise that the state after measurement must remain consistent with the Kennard-Robertson uncertainty relation. This implies that the measurement error must be formulated via a posterior observable $\hat{x}_t$, rather than a prior observable $\hat{x}_0$, because the posterior measurement error determines the post-measurement uncertainty of the electron. Building upon the preliminary conceptual foundation reported in arXiv:1504.03779, this paper presents a rigorous derivation of the error-disturbance principle formulated from the unitary transformation equations of observables. Each readout $X$ of a posterior probe observable $\hat{X}_t$ completes a single measurement event, producing a specific conditional object state. The Kennard-Robertson uncertainty relation must hold for these states. Specifically, we show that the uncertainty relation between the error $ε_{X}(\hat{x}_t)$ and the disturbance $η_{X}(\hat{p}_0)$ holds strictly at the level of individual measurements, characterized by the specific readout $X$. We also verify that conventional error-disturbance relations, where the errors are evaluated by averaging over the unconditioned state, hold true. Our results provide a refined theoretical basis for understanding the fundamental trade-off in individual measurement outcomes.

Feasibility-preserving mixer Hamiltonians offer an attractive alternative to penalty encodings for constrained quantum optimization, yet how enforcing constraints alters the state space reachable by the Quantum Approximate Optimization Algorithm (QAOA) remains largely unexplored. We address this question within the context of the Maximum Independent Set (MIS) problem. Alongside the standard controlled bit-flip mixer, we analyze the alternative $\mathit{Flip\text{-}or\text{-}Stay}$ mixer, whose restriction to the feasible subspace $W_{\mathcal{F}}$ corresponds precisely to the shifted negative Laplacian of the independent-set reconfiguration graph. Although both mixers induce identical transitions between independent sets, the diagonal modification changes the spectral structure and can substantially enlarge the set of reachable quantum states. For every connected input graph with at least two vertices, we prove that independently parameterized local controls associated with either mixer generate the full unitary Lie algebra on the feasible subspace. Standard QAOA exhibits a more nuanced algebraic structure. We prove that the dynamical Lie algebra associated with MIS-QAOA employing the conventional mixer embeds into its Flip-or-Stay counterpart. Furthermore, we construct an infinite family of graphs for which the corresponding vacuum-state dynamical group orbits exhibit strictly distinct dimensions, establishing a qualitative expressivity separation between the two architectures. For either mixer, we show that standard QAOA initialized in the empty set can prepare a state supported entirely on maximum independent sets at finite depth. For the free architectures, we also derive an exact loss-variance formula in the unitary-design limit, expressed through the number of feasible independent sets and the variance of their cardinalities.

Barycentric Rényi divergences were introduced in [Mosonyi, Bunth, Vrana, Linear Algebra and its Applications, 2024] as an alternative to standard Kubo-Ando constructions to define multivariate quantum Rényi divergences. They are defined via a variational expression and depend on a finite collection of quantum relative entropies $D^{q_x}$. When all the relative entropies are monotone under CPTP maps then so are the corresponding barycentric Rényi divergences, and when all the relative entropies are additive then the corresponding barycentric Rényi divergences are subadditive under tensor product. Additivity has only been established before for the case where all $D^{q_x}$ are chosen to be the Umegaki relative entropy, which is also the only case where the barycentric Rényi divergence (called the minimal one) admits an explicit expression. Here we settle the problem of additivity by showing that for any choice of additive and monotone quantum relative entropies, the regularized barycentric Rényi divergence coincides with the minimal barycentric Rényi divergence on strictly positive inputs. This in turn implies that the only additive barycentric Rényi divergence is the minimal one.

Hardware noise has been shown to significantly impact the accuracy of ADAPT-VQE, a ground state preparation algorithm. While previous work has studied the impact of noise on its parameter optimization step, its impact on the critical operator selection step remains comparatively unexplored. In this work, we examine the impact of a variety of noise channels on this step, using a linear H$_3$ molecule as a test case. We show that, despite the selection criterion's natural resilience to some noise, both coherent and incoherent noise can prevent convergence for sufficiently high noise rates. We employ quantum error mitigation techniques--dynamical decoupling, zero noise extrapolation, and Pauli twirling--and show that when combined appropriately, these techniques are capable of restoring a successful convergence profile. Our results highlight how error mitigation can improve the performance of ADAPT-VQE and enable convergence in the presence of hardware noise, offering valuable insights into the implementation of the algorithm on near-term quantum hardware.

We investigate antidistinguishability of states within the framework of general probabilistic theories (GPTs). We formulate antidistinguishability, strong and equal antidistinguishability as refined notions that imposed additional constraint on the measurement effects. We establish general results relating these notions of antidistinguishability and derive an upper bound on the cardinality of equally antidistinguishable sets in terms of the affine dimension of the state space. We then study antidistinguishability in polygonal theories, obtaining conditions for antidistinguishability of a set of states. In consequence, we show that the set of all pure states in a polygon model is antidistinguishable. Additionally, we identify broad families of strongly and equally antidistinguishable states. Finally, using Random Exclusion Codes, whose success probability is governed by the antidistinguishability of different sets of encoding states, we probe the nonclassicality of polygon theories. We find that certain polygon models can outperform the optimal quantum value, while their optimal performance converges to the quantum limit in the large-polygon limit.

Recent advances in quantum computing have been driven primarily by improvements in hardware. Here we show that substantial gains can instead arise from how finite computational resources are allocated throughout a quantum computation. We introduce Adaptive Algorithmic Control (A2C), a software paradigm founded on a State-Proxy Equalization theorem, which proves that the optimal allocation for a state-derived proxy-error functional equalizes cumulative computational hardness rather than physical time. The required computational hardness is inferred directly from the evolving quantum state, avoiding explicit reconstruction of the exponentially large many-body spectrum. Across quantum optimization problems containing up to 156 qubits, combining exact simulations, large-scale supercomputer computations and IBM quantum hardware experiments, A2C improves the low-energy sampling probabilities by $22\%$ to over $100,000\%$ under matched circuit depths and measurement budgets. These results demonstrate that quantum computational performance depends not only on hardware capabilities, but also on how finite computational resources are organized, establishing adaptive algorithmic control as a complementary software pathway for advancing quantum computation.

For the problem of simulating Lindblad evolution for time $t$ to precision $ε$, Hamiltonian simulation provides an additive query lower bound, informally, $Ω(t + \mathrm{polylog}(1/ε))$. However, the best previously known algorithms for general Lindblad simulation achieve a multiplicative upper bound, informally, $\mathcal{O}(t\,\mathrm{polylog}(1/ε))$, in gate complexity. It has remained open whether this multiplicative dependence is necessary. In this paper, we close the gap in query complexity by giving an algorithm with optimal additive dependence on evolution time and precision in the block-encoding model. Our approach uses the transducer framework to reduce the query cost of composing first-order approximations to the evolution channel, together with linear combinations of reuse circuits of different lengths to suppress catalyst-removal error. Although our additional gate complexity is higher than that of existing algorithms, our optimal query complexity resolves the question of how much oracle access is fundamentally necessary and identifies the remaining challenge to achieve the optimal gate complexity.

Rare outputs of random quantum circuits are usually treated as terminal statistics. We ask whether they reveal intermediate organization that remains useful beyond the selecting future. Comparing unconditioned random-normal (RN) and peak-selected random-peaked (RP) circuits from the same local generator, we find stronger pairwise correlations and probability redistribution but reduced bipartite and output spreading in RP across n=8-16. Exact full-suffix decomposition reveals stronger peak-directed interference. The structural separation and fresh-future advantage persist across four nominal depths at n=8-14, with 2.01-7.15 fold RP enrichment in the depth extensions at fixed, independently calibrated thresholds. Within the unconditioned ensemble, a structural prefix score predicts fresh-event probability without using the evaluated circuits' terminal outcomes. Population-preserving phase scrambling identifies a functional contribution from relative-phase organization across the tested settings, including primary-depth held-out confirmation. RP trajectory-guided initialization improves high-peak yield over Haar initialization under common local refinement. Intermediate multivariate guidance also improves the fresh-continuation susceptibility of constructed states beyond peak-only guidance across the same size-depth grid. Rare outputs thus reveal intermediate physical organization that remains useful under new dynamics and can guide circuit construction.

Scalable quantum computation is expected to rely on fault-tolerant quantum computation (FTQC), in which quantum error correction (QEC) suppresses physical errors sufficiently to support reliable logical operations. This requires quantum compilation to move beyond general-purpose circuit optimization toward encoding-aware and protocol-structured compilation across the full stack of fault-tolerant quantum computers. Beyond circuit synthesis and hardware mapping, an FTQC compiler must lower algorithm-level operations into the logical gate set supported by the chosen code, coordinate encoded data and ancilla resources, realize logical operations together with repeated syndrome extraction under hardware constraints, and provide the resulting measurement stream to real-time decoding. This survey presents a full-stack view of compiler design for QEC-protected quantum computation. We organize existing work into three interacting layers: logical-level QEC compilation, physical-level QEC realization, and decoder runtime integration. At the logical level, we review surface-code lattice-surgery compilers, beyond-surface-code code-surgery frameworks including emerging qLDPC approaches, and compilation support for non-Clifford operations such as magic-state distillation and code switching. At the physical level, we survey hardware-aware QEC realization on superconducting, trapped-ion, and neutral-atom platforms. We further examine decoder models, real-time decoding systems, and frame-management mechanisms that close the feedback loop during fault-tolerant execution. Finally, we identify open challenges in cross-layer optimization, qLDPC compilation, compiler-decoder co-design, runtime adaptivity, and the development of integrated and benchmarkable FTQC compilation stacks. An actively maintained paper list is available at: github.com/chenghongz/QEC-compiler-design.

A random unitary quantum circuit is expected to be incompressible for exponentially long times. We show that the constant-error circuit complexity of a random unitary circuit grows almost linearly with time as $Ω(T/\log T)$. The bound holds for all $2\leq T\leq 4^n$ where $n$ is the system size, and involves no other $n$-dependence. This improves previous lower bounds derived from spectral gaps and unitary designs by a factor of $\mathrm{poly}(n)$. Drawing on insights from stochastic calculus, geometric functional analysis, and randomized linear algebra, our approach exploits the circuit's response to variations of individual gates and requires no control over convergence to high-order unitary designs.

We investigate the relaxation of an approximately conserved charge in interacting quantum systems close to local equilibrium. To this end, we provide a pedagogical review of Zubarev's non-equilibrium statistical operator approach in the minimal setting of a single non-conserved charge and apply it to the problem at hand. We explicitly highlight the physical assumptions that lead to a local relaxation law: weak charge violation, a separation between the short timescale of microscopic correlations and the much longer timescale of charge relaxation, and the resulting loss of microscopic memory. Under these conditions, the leading relaxation rate is determined by an equilibrium correlation function of the charge-violating operator. We show that the same result follows from a simpler local-equilibrium construction based on the system's evolution over an intermediate timescale, providing a direct alternative for practical calculations and making the common physical ingredients of the two approaches explicit. Beyond the decay law itself, we relate the relaxation rate to the equilibrium diffusion of the same charge. We then allow the charge density to vary in space, which leads to a diffusion-relaxation equation. Finally, we illustrate the formalism through electroweak $\mathrm{B+L}$ washout and a perturbative scalar model, where agreement with the linearized Boltzmann equation establishes a direct connection between equilibrium-correlator and kinetic descriptions.

Reliable quantum engineering is essential for turning quantum phenomena into practical technologies. As quantum platforms grow in scale and complexity, their characterization and operation require increasing human effort and coordination. Scientific artificial intelligence agents, which can plan experiments, operate instruments, and analyze observations, offer a promising route towards autonomous quantum engineering. Yet whether current agents can perform reliably in this setting has not been systematically established. To fill this gap, we developed Quantum-Harbor, a virtual laboratory that provides a controlled execution environment for agents to interact with quantum systems. This design enables direct verification of both the actions taken and the conclusions drawn. Building on this framework, we introduce QIQCBench, a benchmark of $49$ expert-authored tasks spanning multiple layers including calibration and control, error correction and compilation, sensing and networking. Across $17$ frontier agentic systems, QIQCBench reveals wide variation in verified performance. These results expose a substantial gap between demonstrating capability and achieving reliable operation, and establish Quantum-Harbor as a foundation for measuring progress towards verified autonomy in quantum engineering.

Electron-phonon interactions underpin a variety of phenomena, ranging from transport and superconductivity to polarons and ultrafast carrier dynamics. Despite being one of the most intensely studied subjects in condensed matter physics, research on electron-phonon physics mostly focused on linear, first-order couplings. Second- and higher-order nonlinear couplings are commonly ignored because their calculations are too demanding and we lack computational frameworks that can provide both diagonal and off-diagonal coupling matrix elements. In this work, we report a theory and computational method for computing nonlinear electron-phonon interactions of any order in real materials. Our approach combines the advantages of unit-cell calculations of electron wavefunctions and supercell calculations of phonon perturbations, is systematically improvable, can be used with either semilocal or nonlocal exchange-correlation functionals, and is amenable to Wannier-Fourier interpolation. As a first proof of concept, we illustrate this method by computing second-order electron-phonon coupling matrix elements in diamond, lithium fluoride, and graphite as representative nonpolar semiconductors, polar semiconductors, and metals, respectively. Furthermore, we generalize the ab initio polaron equations to second-order electron-phonon couplings, and we show that second-order couplings are essential to achieve quantitative accuracy in polaron formation energies and hopping barriers. The present methodology will find application in the study of all properties and phenomena that are currently being investigated within the linear electron-phonon coupling approximation, from phonon-mediated superconductivity to excited-states dynamics, both in harmonic and anharmonic systems.

A multiset of pure quantum states is said to be k-learnable if there is a measurement strategy that always narrows an unknown sample drawn from the list down to one of at most k candidates. The parameter k interpolates between distinguishability and antidistinguishability, and provides a unified framework for partial state identification. We prove two universal, and optimal, Gram-matrix criteria for k-learnability: a Frobenius-norm sufficient condition and an entrywise-$\ell_1$ necessary condition. We apply them to derive explicit learnability and copy-complexity guarantees for several well-known sets of states including SIC-POVMs, mutually unbiased bases, and stabilizer states. We further apply our results to zero-error mutation detection problems such as anomaly detection and changepoint detection.

$\mathsf{QAC}^0$ is the class of constant-depth $\mathrm{poly}(n)$-ancilla circuits obtained by extending $\mathsf{QNC}^0$, the class of local circuits, to include nonlocal interactions via arbitrary width Toffoli gates. It is believed to be weaker than its counterpart, $\mathsf{QNC}^0_f$, obtained by including arbitrary-width FANOUT gates instead ($\mathsf{QAC}^0 \subseteq \mathsf{QNC}^0_f$ [Moo99]). In this note, we show that every $O(\log n)$-qubit state can be exactly and cleanly prepared by a $\mathrm{poly}(n)$-ancilla $\mathsf{QAC}^0$ circuit. Previous known $\mathrm{poly}(n)$-ancilla circuits for arbitrary such states are only known via additional access to either FANOUT or QRAM (indexing) gates [Ros21b, GGJ26b], neither of which are known to be in $\mathsf{QAC}^0$. Equivalently, prior constructions of arbitrary $n$-qubit states in $\mathsf{QAC}^0$ require doubly exponential size and we obtain an exponential factor improvement.

We investigate domain-wall physics in a non-Hermitian Su-Schrieffer-Heeger model featuring the non-Hermitian skin effect and its higher-dimensional extensions, focusing on analytical eigenstate solutions under open boundary conditions. By gluing two Su-Schrieffer-Heeger chains with inverted coupling ratios together, we identify two distinct interface geometries, and derive closed-form quantization conditions for the complex wave number and wave functions using symmetry-based ansatzes. Besides conventional skin modes and topological zero modes, the domain walls generate additional localized states at finite energy that detach from the bulk open-boundary-condition continuum. We validate the analytical results by exact diagonalization, and further generalize the interface construction to a two-dimensional Lieb lattice, where competing nonreciprocities produce tunable funneling regimes towards codimension-one and codimension-two interfaces.

Loading multiple quantum states in parallel into a quantum machine learning (QML) model can unlock learning tasks where key information resides in the \emph{relations} between states rather than in individual states. We introduce an adaptive relational learning framework for such multi-instance quantum data that accesses pairwise and higher-order relations. Our model combines global measurements via SWAP or CYCLE tests for evaluating an $n$-state Bargmann invariant with shallow trainable transformations applied locally to each input state. We demonstrate the approach for continuous-variable (CV) photonic systems, which naturally provide access to quantum data and necessary computing operations. We solve tasks involving hidden relationship detection, geometric phase classification, and sensing in the presence of an unknown shared nuisance interaction. We benchmark the adaptive model against a non-adaptive ``measure-first'' approach based on continuous-variable classical shadows, and show that the cost of shadow estimation grows rapidly with $n$, while our model avoids this dependence. Already for $n=2$, we achieve perfect test accuracy $A=1.0$ with $500$ inference shots, improving average test accuracy over the shadow-based method by $ΔA=0.15$ while using $100$ times fewer shots per data point. Our work opens routes to sensing and quantum-data applications where adaptive photonic QML can access relational features that are costly to recover with non-adaptive, measure-first models.

Quantum imaginarity, as a critical resource metric for quantifying intrinsic nonreal coherence encoded in quantum states, exhibits nontrivial evolutionary behaviors in curved spacetime backgrounds. This work focuses on bipartite Dirac field reduced states in the quantum atmosphere of a static Schwarzschild black hole, aiming to explore the modulation of three mainstream imaginarity measures by Hawking thermal radiation. We reveal that the relative-entropy imaginarity, the geometric imaginarity and robustness of imaginarity, the fully accessible state presents a valley-shaped radial profile with a local minimum inside the quantum atmosphere, while the cross-coupling and fully inaccessible states follow opposite peak-shaped trends. Further analysis demonstrates that the Hartle-Hawking constant significantly strengthens the redistribution effect of imaginarity across both regions, whereas an increase in the event horizon radius weakens such redistribution and flattens the extremum features. These findings offer a new perspective for decoding the information structure of black hole quantum atmospheres and the intrinsic quantum nature of Hawking radiation.

Exceptional points are topological defects of complex band structures that are stable against weak perturbations, yet in bounded two-band systems they are ultimately removed by a sufficiently strong Hermitian field. Here we demonstrate a striking exception in a two-dimensional subwavelength atomic array. Along a continuous square-to-triangular deformation at fixed magnetic field, the bulk passes between line-gapped topological regions with band Chern numbers (C_1,C_2)=(2,-2) through a gapless exceptional region. Within a finite interval of lattice deformation, increasing the magnetic field merely drives the exceptional points toward the light cone because of the singular radiative dipolar couplings. We further show that skin localization toward open boundaries responds non-monotonically to the same field. An intermediate field drives a bipolar skin localization, with bulk modes accumulating at opposite edges, whereas stronger fields suppress boundary localization. Our results establish the interplay of lattice geometry, light-cone singularity, and Hermitian magnetic field as a route to engineering Chern and exceptional topology beyond the conventional strong-field limit.

By consuming multiple copies of an unknown qubit state, one can modify its purity while preserving the direction of its Bloch vector. We determine the maximum linear rate at which qubit states of different purities can be interconverted, allowing a nonzero error, quantified, for instance, by the trace distance, provided that it vanishes in the limit of infinitely many copies. Interestingly, the optimal conversion rate is determined by the two eigenvalues of the complex right-logarithmic-derivative (RLD) Fisher information matrix associated with $\mathrm{SU}(2)$ rotations of the qubit state. When the output qubits have higher purity, corresponding to concentration, the optimal rate is given by the ratio of the maximum eigenvalues of the input and output RLD matrices. In contrast, when the output qubits have lower purity, corresponding to dilution, the optimal rate is given by the ratio of their minimum eigenvalues. Remarkably, both concentration and dilution can be implemented using SWAP tests as the only nontrivial two-qubit measurement primitive, together with ancillary qubits initially prepared in maximally mixed states, without requiring any additional two-qubit gates. Our work thus provides a novel operational interpretation of the full complex RLD Fisher information matrix. Crucially, its antisymmetric, purely imaginary part encodes geometric information beyond the statistical distance between density operators and plays an essential role in determining the optimal state-conversion rates.

The generalised quantum Stein's lemma is a key result in quantum hypothesis testing, and connects this fundamental primitive of quantum information processing with quantum resource manipulation, a task that is central for technological applications. Prior works have proved this statement in the idealised setting of independent and identically distributed (i.i.d.) sequences of quantum states, and recent extensions consider also sources that are 'close' to i.i.d., according to the strict notion put forth by Mazzola, Sutter, and Renner. For several applications, however, one would need to consider yet more general sources. We establish a version of the generalised quantum Stein's lemma that is conceptually much simpler and general, as it applies to any source that is asymptotically close to an i.i.d. state with respect to the normalised quantum Wasserstein distance of order 1. As an immediate consequence, we solve the Stein exponent of a scenario where the null hypothesis is arbitrarily varying, expressing it in terms of i.i.d. Stein exponents corresponding to arbitrary states in the convex hull of the null hypothesis base set.

A system between a preparation and a post-selection has had no agreed state since 1964. With positivity as the criterion, a post-selection admits an interval of orderings around the symmetric one exactly when the subspace it forbids is spanned by eigenvectors of a full-rank filtered state. Otherwise it certifies contextuality, testable on a qubit. The averaged filtered state carries the entanglement spectrum of the record, so the smallest forbidden subspaces a symmetry allows are even-dimensional in the Haldane class and odd in the trivial one. That parity is the record's topological class.

We present an open source Python package, ConteXtuAlity, for computing various quantities related to contextuality. This package features an interface to the sheaf-theoretic framework for contextuality, providing an implementation of measurement scenarios and empirical models as well as linear programs to compute the contextual fraction and the signalling fraction. In this work, we demonstrate the package's features and give examples of its use. We also provide benchmarks, demonstrating how performances scale with the size of measurement scenarios. The package is designed for both experienced theorists and newcomers to the field of contextuality alike, with an emphasis on flexibility and extensibility.

Standards bodies report cryptographic security as a single number of bits, but this value depends on the adversary cost model used to price time, memory, and quantum resources. Different conventions can therefore produce different rankings of cryptographic schemes. GAUGE represents security as a function over admissible cost models, called a security profile. Comparisons then become comparisons between profiles, and ranking reversals become an explicit structural property rather than a measurement error. We formalize price functionals over a cone of adversary cost models, show that security profiles are piecewise-linear and concave, and prove a rating trilemma: when two profiles cross, no rating can simultaneously be faithful to underlying costs, total over comparable pairs, and independent of the chosen cost model. We provide a polynomial-time linear-programming procedure that certifies whether the ranking of two schemes is robust, reverses under admissible models, or is genuinely incomparable. We extend GAUGE with a two-layer risk measure combining stochastic cryptanalytic decay with uncertainty over the appropriate cost model. We evaluate the framework on NIST post-quantum standards, classical anchors, and a 25-year chronology of cryptanalytic breaks. The analysis certifies a ranking reversal for ML-KEM-512 versus AES-128 from a 4-5% shift in memory pricing, and measures a lattice-sieving cost drift of 9.79 bits per year over eight years. A hybrid X25519 + ML-KEM-768 handshake reduces combined-break probability twenty-fold at a 2.3 kilobyte cost. The artifact reproduces all tables and figures in under seven seconds. GAUGE provides an explicit and auditable framework for reporting cryptographic security under competing cost models.

Entanglement in indistinguishable particle systems can be characterized by the impossibility of unambiguously attributing a complete set of physical properties to the individual constituent particles. In this work, we introduce a geometric quantifier of the incompatibility of such simultaneous property attribution for pure states of $N$ indistinguishable bosons. Using the Majorana stellar representation, any symmetric multi-qubit state can be expressed as the symmetrization of constituent single-particle states, allowing the associated single-particle properties to be directly linked with the corresponding Majorana stars. This establishes a direct connection between the geometry of the Majorana representation on the Bloch sphere and the entanglement criterion based on the attribution of single-particle properties in systems of identical two-level bosons. We then generalize this geometric approach to higher-dimensional bosons, extending the quantifier from qubits to qudits, while retaining a geometric interpretation of property-attribution incompatibility in terms of Fubini-Study angles.

When a classical Brownian particle is subjected to a temperature gradient it can undergo thermophoresis, i.e., the particle gets transported towards the colder regions of the environment, which bears relevant consequences to nonequilibrium self-organization. Here, we investigate how the quantum Brownian motion is affected by a temperature gradient. We employ a recently proposed generalized system-plus-reservoir model, where one assumes a continuum field of thermal baths. As our main result, we obtain the quantum influence functional, within the Feynmann-Vernon path integral approach. To test convergence, we derive an effective Langevin equation for the center of mass of the quantum wavepacket, and show that it coincides with the classical Langevin equation at high temperatures. Both the fully quantum (low temperatures) and the semiclassical (high temperature) limits show signatures of quantum thermophoresis in the quantum Brownian motion, a so far unexplored effect.

Stabilizer states constitute an important class of quantum states that can be generated from computational-basis states using Pauli operators and Clifford gates. Although they may exhibit substantial multipartite entanglement, quantum circuits restricted to stabilizer operations can be efficiently simulated classically and therefore cannot, by themselves, provide a quantum computational advantage. Such an advantage requires non-stabilizer resources, commonly referred to as quantum magic. In this paper, we investigate the non-stabilizerness of quantum states arising in a class of spin Hamiltonians by computing their stabilizer Rényi entropies. Using real-space renormalization-group techniques, we obtain a closed-form expression valid in the low-energy, large-distance regime. We analyze how quantum magic evolves under coarse-graining and explore its behavior across different parameter regimes and quantum phases.

We investigate the quantum Mpemba effect in a graphene nanotorus qubit and show that its strength depends strongly on how the initial state is prepared. We compare two protocols that share the same final Hamiltonian, thermal bath, and Markovian Liouvillian: bare Gibbs preparation, in which the coherent drive is switched on only at the final quench, and driven steady-state preparation, in which the initial states are stationary states of the driven dynamics. Using the distance to the final stationary state and an integrated Mpemba parameter, we find broad regions of strong anomalous relaxation for bare Gibbs preparation, with $M_B$ approaching unity, whereas the driven steady-state protocol almost completely suppresses the effect. A Liouvillian-mode analysis reveals the mechanism: the bare Gibbs protocol typically yields a smaller hot-state weight in the slow active sector than the cold state, $R_s<1$, while the driven steady-state protocol predominantly gives $R_s>1$. Since the final Liouvillian spectrum is identical for both protocols at corresponding parameter points, the contrast originates from preparation-dependent modal weights rather than from changes in the decay-rate hierarchy. These results identify state preparation as a control parameter for anomalous quantum relaxation in a curved graphene qubit.

Parametric interactions are foundational to superconducting quantum technologies, yet conventional microwave-driven pumping introduces parasitic Kerr nonlinearities and higher-order harmonics that limit device performance. Josephson Photonics (JP) avoids these parasitics by utilizing dc-biased junctions but has remained constrained by high phase noise and the absence of a stable phase reference. Here, we overcome this limitation by integrating a Josephson voltage standard (JVS) to establish a noise-tolerant phase reference, and demonstrate that this reference is coherently transferred to an inelastic Cooper-pair tunneling amplifier (ICTA) via the superconducting order parameter.The resulting low-phase-noise architecture yields a 14-dB enhancement in averaged gain and better quantum-limited noise performance. Critically, the phase reference enables the first observation of phase-sensitive gain and sqeezing in a dc-biased amplifier. By reconciling clean, Kerr-free nonlinearities with phase-coherent drive, our architecture establishes a robust platform for high-purity parametric processes in superconducting circuits.

We present a claim-relative evidence/reference framework for hybrid quantum-classical workflow integrity. Observational indistinguishability yields structural blind regions, distinct from finite-batch statistical misses. Within the declared lattice, a trusted same-batch scalar $R_0$ suffices for conclusion integrity, aggregate $M_0$ for aggregate plus conclusion integrity, and item-aligned binding for item identity. In 3,600 label interventions, feature/prediction views realize exact label-path invariance; all 764 geometry-aligned aggregate-blind rows equal their paired-clean responses, giving zero attack-only increment. For statistical response, the geometry-aligned construction detects 343/2,700 conclusion-changing ($τ\to 0^+$) label interventions with the conformal rule and 1,183/2,700 with the uncorrected union; the original frozen same-item geometry yields 11/2,617 and 43/2,617, respectively. The executed conformal clean false-action rates are 0.048--0.059 descriptively; its finite-sample guarantee requires exchangeability, which the overlapping-draw design violates. The cluster-preserving adaptive stress test (Gate A) reduces response versus matched controls in 25--40 of 40 environment/split cells while retaining conclusion changes. A bounded 165-design-cell ideal-statevector and finite-shot-emulation branch directly instantiates semantic, estimated and observed kernel transitions. The fixed equal-weight design estimates neither deployment prevalence nor QPU, provider or deployed-service assurance.

An accurate theoretical treatment of periodically driven quantum systems is crucial for various fields in the exact sciences, for instance Nuclear Magnetic Resonance (NMR) spectroscopy. Conventionally, either average Hamiltonian theory or Floquet theory is used to predict or describe experimental outcomes, such as the time evolution or the spectra yielding the information of the sample under study. A detailed analysis of the equivalence of these two approaches with an emphasis on applications in NMR will help to improve the theoretical understanding of NMR experiments. In this work, we identify the Floquet-Magnus expansion as essential to prove the mathematical equivalence of Floquet theory and average Hamiltonian theory. We advocate a calculation scheme which is less prone to algebraic mistakes because explicit integration is avoided. On this basis, we provide the first four orders of both theories. We further examine their applicability to some experiments in NMR. As examples, we investigate the Bloch-Siegert shift and dipolar coupled spin systems under magic-angle spinning. Based on our analysis, we recommend the use of the Floquet-Van Vleck approach including both the effective Hamiltonian and the kick operator. The consistent separation of secular and non-secular contributions appears to be especially advantageous for numerical robustness. Its accuracy is about three times better than the one provided by average Hamiltonian theory despite their formal equivalence. Our findings provide important insights into the theoretical background of Floquet theory and average Hamiltonian theory. This includes the extent of their algebraic and perturbative equivalence, with an emphasis on how these findings are of relevance in the analysis of solid-state NMR experiments.

Thouless pumping is a celebrated topological effect that enables quantized particle transport and holds promise for applications in quantum technologies. However, the standard adiabatic pumping theory dictate that the Hamiltonian must be varied continuously and slowly throughout the whole pumping process. In this work, we show that Thouless pumping can be realized by using only discrete sampling of the Hamiltonian, removing the conventional constraint of continuous and slow change of control. Specifically, we select particular parameter points of the Hamiltonian for conventional continuous quantum adiabatic evolution, and then apply the Hamiltonian at these parameter points which induces a geodesic evolution for the pseudospin with a given quasimomentum. This realizes an adiabatic evolution for the Thouless pumping according to a necessary and sufficient condition for quantum adiabatic evolution.

Simulating nuclear magnetic resonance (NMR) spectra is a promising application of quantum simulation. Using Quantinuum's System Model H2, a trapped-ion quantum computer, we demonstrate an end-to-end, large-scale digital NMR simulation of a classically challenging benchmark molecule, 1,2-di-tert-butyl-diphosphane. We implement a hardware-efficient reduction of the nuclear-spin Hamiltonian, enabling Trotterized real-time evolution of an effective 21-spin model with tailored error suppression to reduce the effects of device noise. The reconstructed liquid-state proton NMR spectrum agrees with classical reference calculations and reproduces key spectroscopic features that previous quantum hardware demonstrations did not capture. Given the widespread use of NMR in chemical analysis and industrial research, these results advance digital quantum simulation of NMR spectra towards practical quantum utility.

This course on two-dimensional quantum gases, prepared for the S{ã}o Paulo ICTP-SAIFR IVth School on Light and Cold Atoms, is organized into three lectures. The first introductory lecture addresses Bose-Einstein condensation in an ideal gas, the effect of interactions in the weakly interacting limit, Gross-Pitaevskii equation and its hydrodynamic formulation, as well as superfluidity. The second lecture is devoted to the main features of two-dimensional quantum gases: importance of the interactions, enhanced phase fluctuations and the emergence of a quasi long-range order, superfluidity through the Berezinskii-Kosterlitz-Thouless mechanism, scaling symmetry. The third lecture has taken the form of a seminar on fast rotating quasi two-dimensional Bose gases and thermal melting of the vortex lattice. The slides accompanying these notes can be found on the school website: https://www.ictp-saifr.org/slca2025/.

In order to solve practical problems on a quantum computer, it is necessary to use fault-tolerant quantum error correction schemes to overcome noise: the errors arising from imperfections in physical components. The Gottesman-Kitaev-Preskill (GKP) code aims at achieving this in a hardware efficient manner by encoding finite-dimensional logical subspaces in the Hilbert space of one or more continuous variable modes. In near term implementations, however, it is not feasible to eliminate errors entirely, so it is natural to also employ alternative error mitigation techniques together with error correction. In this work, we study a quantum error mitigation method known as probabilistic error cancellation in the context of the GKP code. We compare Steane-type and teleportation-based GKP error correction, and calculate the sampling overheads associated with the technique for square and hexagonal GKP codes. We employ the stabilizer subsystem decomposition for GKP codes to obtain an effective logical channel for noisy operations that is used to express the ideal one of a target logical unitary. We consider noise from finite squeezing on the data and the two ancilla modes, needed for error correction, and examine the relationship between the sampling overhead and the noise for different decoding methods. Our results are calculated for single- and two-qubit GKP Clifford gates and one round of error correction, and show the nontrivial combination of error correction and mitigation in continuous variable codes.

Muon-spin rotation/relaxation is one of the most powerful microscopic probes for understanding magnetic order, spin dynamics, superconductivity, and complex magnetic phases in emerging quantum materials. Quantitative interpretation depends critically on the accurate identification of the muon stopping site, a problem traditionally addressed using density functional theory-based structural relaxation. However, conventional DFT approaches are computationally demanding, time-consuming, and require extensive calculations. Here, we develop MEOWN (Muon Engine for Optimized Weighted Networks), a machine-learning-based, physics-informed computational framework that combines a Polarizable Unperturbed Electrostatic Potential (P-UEP) model with machine-learning-guided optimization and symmetry-driven relaxation to predict energetically favorable muon stopping sites in crystalline solids. MEOWN explicitly incorporates electrostatic interactions, electronic screening, polarization effects, and zero-point motion into the learning workflow, providing physically interpretable predictions with substantially reduced computational cost while maintaining physical consistency and scientific rigor. To validate the framework, we investigated several well-established benchmark materials, including MnSi, CoF2, CaF2, LiF, and NaF. The predicted muon stopping sites and dipolar fields are in close agreement with previously reported DFT+mu results, demonstrating the reliability and transferability of the approach across chemically diverse systems. Notably, MEOWN predicts the equilibrium muon stopping site within a few minutes, offering a significant speedup over conventional DFT-based calculations. This manuscript presents the theoretical foundations, computational methodology, and validation of MEOWN as a general-purpose software for rapid and reliable muon stopping-site prediction in crystalline materials.

In order to circumvent that no universal set of gates can be achieved on a given quantum error-correcting codes, additional gates can be performed through magic state injection. This however requires to have access to high fidelity magic state, which can be obtained by the distillation of low quality states to fewer higher quality ones. In this paper, we provide a family of distillation protocols able to produce diagonal states at every level of the Clifford hierarchy. This family is obtained recursively using code doubling techniques and leveraging qubit recycling, the fact that some idle qubits of the protocols can be measured and re-used. At a given level of the Clifford hierarchy, we show that the protocols we derive can be performed at arbitrary high distance on a fix number of logical qubits. This family recovers many known efficient protocols, and uncovers new ones, such as a $111 \to 1$ protocol for $|T\rangle$ state distillation at distance $7$, which are the most compact in term of volume. Finally, we discuss possible extension of this framework for distillation protocols producing more than one output state.

Eigenstate thermalization constrains the smooth dependence of observables on energy, but it does not by itself fix the microscopic statistics of the overlaps between many-body eigenstates and a chosen basis: the smooth envelope is a one-point statement, and the fluctuation field it leaves undetermined carries a structured two-point covariance. We establish this distinction, and solve that fluctuation field exactly, in random free fermions---an ensemble of Slater-determinant eigenstates built from a Gaussian orthogonal single-particle Hamiltonian, whose eigenstate thermalization was established by Magán. In this ensemble every channel overlap is a minor of a Haar-distributed orthogonal matrix, so its statistics follow from classical random-matrix theory. The one-point law is exactly flat for every channel, with an exact moment hierarchy that is not Porter--Thomas: small intensities are enhanced algebraically rather than by the exponential Porter--Thomas form, and the mean sector carries a negative, order-one correlation correction of purely normalization origin. The two-point covariance closes exactly at the Gaussian fixed point: it is organized by the number of one-body modes shared by two eigenstates and by the number of modes shared by two channels, and its energy-resolved form factorizes into this geometry times the classical convolution of the single-particle semicircle, from which the two-resolvent covariance follows by an integral transform. Exact finite-size computations confirm all closed forms, and the structural identities of the dictionary hold at machine precision. The results provide an exactly solvable microscopic realization of the two-point fluctuation sector underlying multi-resolvent descriptions of eigenstate thermalization: a smooth envelope does not determine fine-grained fluctuations.

We derive a thermodynamic uncertainty relation for work in an open quantum system driven by a time-dependent protocol and subject to repeated projective energy measurements. The protocol is represented by a sequence of protocol quenches separated by finite-time Lindblad evolution, so that work is accumulated at the quenches while dissipation occurs between them. The resulting work statistics obey the Gallavotti-Cohen symmetry to give rise to the Crooks and Jarzynski fluctuation relations. By perturbing the dissipative dynamics and combining the Cramér--Rao inequality with the quantum Fisher information, we obtain $\mathrm{Var}\,{\cal W}/[τ\partial_τ\langle{\cal W}\rangle]^2\ge 1/{\cal F}\ge\max(1/{\cal A},2/{\cal E})$, where $\langle{\cal W}\rangle$ is the work expectation value, $\mathrm{Var}\,{\cal W}$ is the variance of work, ${\cal F}$ is the Fisher information, ${\cal A}$ is the dynamical activity, ${\cal E}$ is the dimensionless entropy production, and $τ$ is the switching time interval between quenches. The two thermodynamic bounds follow from two independent perturbations that generate the same response of the work statistics. We illustrate the relation for a dissipative two-level system under square-wave and sinusoidal driving and show that the tighter thermodynamic bound can depend on the driving protocol and switching time scale.

We study strictly localized mixed states in quantum field theory: states that are indistinguishable from vacuum outside some spacetime region. Such states are generated from the vacuum by so-called Licht maps. While the states associated with individual outcomes of local, projective measurements on the vacuum are not strictly localized, the corresponding non-selective states are strictly localized and even admit decompositions into strictly localized pure states. Remarkably, however, there are strictly localized mixed states that cannot be written as mixtures of pure states strictly localized to the same region. Such states can arise from unsharp local measurements. Finally, we extend Knight's theorem to mixed states, showing that strictly localized bosonic mixed states contain terms with arbitrarily high particle numbers.

We theoretically investigate the indistinguishability of single photons generated from single trapped $^{40}$Ca$^+$ ions in a Raman scattering process driven by few-nanosecond excitation pulses. Of particular interest is how spontaneous decay back to the initial state affects Hong-Ou-Mandel (HOM) photon interference. Numerical simulations identify the mean number of back-decays as a measurable quantity that correlates with achievable HOM visibility. Optimization of the excitation pulse with respect to a trade-off between photon yield and indistinguishability is analyzed. Finally, we compare the performance of different trapped-ion species for long-range dual-rail entanglement swapping via HOM photon interference.

Low-dimensional Dirac systems offer a versatile platform for quantum-geometric non-linear transport. Hexagonal warping in topological insulator (TI) surface states generates rich momentum-space geometric textures. However, mirror and time-reversal symmetries strictly constrain both the Berry curvature and quantum metric dipoles to zero. Here, we show that proximity-coupling a hexagonally warped TI to a d-wave altermagnet lifts spatial mirror symmetry via the interplay of C_{3v} warping and d-wave spin-splitting. This symmetry breaking enables finite Berry curvature dipole components, which, however, remain heavily suppressed near charge neutrality, establishing the intrinsic quantum metric dipole as the sole driver of the non-linear Hall response. This scattering-independent response vanishes at μ= 0 and exhibits odd parity under chemical potential inversion. Importantly, rotating the altermagnetic orientation angle φcontinuously tunes quantum metric dipole and induces a sign reversal, peaking near φ=0 and vanishing at φ= π/4. Our findings highlight TI-altermagnet interfaces as ideal candidates for gate- and orientation-tunable quantum metric spintronics.

Entanglement can enhance precision in phase estimation and in frequency estimation with atomic clocks, but it remains a central challenge to identify useful states and measurements under realistic noise processes. Here, we study quantum metrology with an ensemble of atoms subject to spontaneous emission, which limits frequency estimation by constraining the useful interrogation time. We identify spin grid states (SGSs) as the relevant near-optimal probes beyond a crossover at an ensemble size of 51, where GHZ-like states cease to be optimal. SGSs display a periodic grid on the Bloch sphere and can be generated with two one-axis-twisting (OAT) operations separated by a collective rotation. By optimizing the quantum Fisher information over permutationally symmetric states, we find that SGSs perform close to the globally optimal probes for intermediate and large ensembles, which turn out to be spin GKP states. We further present a sequential readout strategy that nearly saturates the corresponding quantum Fisher information. This strategy uses an OAT echo to map spontaneous-emission events onto collective rotations, making the corresponding jump sectors distinguishable and allowing the measurement basis to be conditioned on the number of decay events. Together, these results show that SGSs provide a practical route to quantum-enhanced phase and frequency metrology in atomic ensembles limited by spontaneous emission.

We introduce a robust quantum communication protocol that integrates classical error-control coding, entanglement distribution, and superdense coding. Classical error-correcting codes are used to mitigate dark counts and photon losses by determining the positions of qubit transmissions and protecting the data embedded through superdense coding. We derive conditions on the employed codes that guarantee successful error correction under a bounded error-frequency model. Moreover, upper bounds are derived on the performance of conventional superdense coding protected by classical error correction. It is shown that, under the same constraints on error frequency, suitable code configurations of the proposed protocol can exceed those upper bounds both in terms of data rate and energy efficiency. Finally, we develop a physical error model based on fiber attenuation, detector efficiency, dark counts, and time-slot duration, and use it to evaluate the effective performance of different configurations of error-correcting codes. The proposed approach is primarily suited for short-distance quantum links, as in Quantum Local Area Network (QLAN) where it can provide high communication throughput while integrating entanglement distribution directly into the communication process.

Nonlocal magic quantifies the minimum nonstabilizerness attainable under independent local unitary transformations on the two subsystems. Here, we use min-relative nonlocal magic (NLM) to characterize the crossover from ergodicity to many-body localization (MBL) in the random-field XXZ chain. Unlike entanglement entropy, NLM probes how entanglement is organized through the distance of the Schmidt spectrum from dyadic-flat stabilizer spectra. From weak to intermediate disorder, NLM evolves from an $O(1)$ Haar-like value into a size-enhanced dome, while entanglement remains volume-law, revealing a spectral reorganization not visible in the entropy. Deep in the MBL regime, a two-level cut-hybridization model captures the nearly binary Schmidt spectrum and explains why the mean and median NLM decay approximately as $W^{-1}$ and $W^{-2}$, respectively. Following a product-state quench, NLM overshoots and relaxes in the ergodic regime, whereas at strong disorder it grows slowly and approximately logarithmically. These results show that NLM resolves Schmidt-spectrum structure not visible in the entanglement entropy and provides a complementary probe of ergodicity breaking.

The preparation of high-fidelity logical magic states is a crucial subroutine for universal fault-tolerant quantum computation (FTQC). Predicting the performance of FTQC and developing improved protocols rely on numerical methods to classically simulate logical magic state preparation in the presence of noise. Clifford logic on Pauli-stabilizer codes with circuit-level Pauli errors can be efficiently simulated using Pauli-stabilizer formalism, but the non-Clifford operations required to prepare logical magic states render generic simulation inefficient. We introduce Clifford-stabilizer simulation, an exact and efficient algorithm based on updating a Clifford-stabilizer group to simulate noisy preparation protocols for a broad class of logical magic states used to implement non-Clifford gates in the third level of the Clifford hierarchy under circuit-level Pauli errors. Clifford-stabilizer simulation applies to a range of operations that commonly appear in preparation protocols for such logical magic states, including Pauli-stabilizer measurements, logical Clifford measurements, and transversal non-Clifford gates. Our algorithm for Clifford-stabilizer simulation maps a non-Clifford circuit with sampled circuit-level Pauli errors to a Clifford circuit that exactly reproduces its measurement outcome distribution, achieving time and space complexities polynomial in relevant protocol parameters. We perform exact simulation of magic state cultivation up to fault distance 7 by Clifford-stabilizer simulation. Our method provides a route to perform exact benchmarking of large-scale logical magic state preparation protocols required for useful FTQC.

Ensemble nitrogen-vacancy (NV) diamond magnetometers combine high sensitivity with vector-field reconstruction, but practical deployment is limited by errors arising from high-frequency laser noise during short-duration operations and slow-varying gain fluctuations and offset drift during long-term operation. Here, we present an integrated digital architecture for achieving NV magnetometry stability across distinct timescales. A dynamic differential readout continuously balances fluorescence and reference channels to suppress correlated laser noise. Second-derivative Lorentzian lineshape tracking enables in-situ correction of slope variations arising from slow changes in gain and optical excitation. We further identify temperature-induced bias-magnet fluctuations as a dominant source of long-term drift and introduce a magnetic eigenvector transformation that uses the intrinsic response of NV resonances to eliminate these variations. We show, under unshielded ambient conditions, that this architecture achieves an off-resonance noise factor of 1.0 $\pm$ 0.1, matching the fundamental limit with ten-fold suppression of long-term drift, enabling stable, field-ready quantum magnetometry.

Optically readable molecular spins are attractive as quantum sensors due to their nanoscale modularity, synthetic tunability, and scope for sensitive readout. In particular, photoexcited spin-triplet states in organic molecules are appealing in supporting high optical-spin contrast at room temperature. Their utility is underpinned by their coherence, which warrants a detailed understanding of it. Here, from first principles, we systematically explore the Hahn-echo decoherence of the benchmark molecular system for room-temperature optically detected spin coherence---pentacene guest molecules coupled to a para-terphenyl host. Using generalized cluster-correlation expansion methods, we investigate the mechanisms of nuclear-spin-induced decoherence from zero to high magnetic field, exploring the role of guest vs host molecules, specific nuclei, zero-field splitting interactions, and hyperfine parameters. We describe how zero-field decoherence is driven by ~6 nuclei on the guest, while high-field decoherence is driven by ~600 nuclei in the host; how the longitudinal zero-field splitting parameter, $D$, can prolong $T_2$; and the magnetic-field-dependent processes which drive decoherence. These results advance our understanding of decoherence in optically readable molecular spins, providing insight for their synthetic enhancement and deployment as quantum probes.

Understanding how optical orbital angular momentum (OAM) is transferred to matter requires treating recoil and translational motion alongside the internal electronic dynamics. We develop a center-of-mass-resolved theory of one-photon ionization of hydrogen by a monochromatic Laguerre--Gaussian beam and show that the Bessel-vortex photoelectron predicted in fixed-target models is a preparation-dependent limit. For a sharply defined atomic center-of-mass momentum, the recoil records the photon-cone azimuth, and tracing over it generally destroys the coherence required for a pure electron vortex. In the small-transverse-retardation regime, the optical OAM is transferred predominantly to the center-of-mass motion and hence, in the laboratory frame, to the proton. Finite-retardation corrections redistribute angular momentum between center-of-mass and relative motion, while an additional correlation contribution to the electron and proton angular momenta can be tuned through the spatial uncertainty of the atomic center of mass. These results reveal atomic recoil as a key element of OAM transfer in photoionization.

In this study, quantum spin pumping in an antiferromagnetic chain driven by time-dependent potential is investigated. The aim is to explore the possibility of generating and controlling spin currents in the absence of external bias and to examine the role of exchange field and periodic driving in the separation of spin-up and spin-down currents. The system is described using a tight-binding model, and spin-resolved currents are calculated employing the Keldysh non-equilibrium Green's function formalism. Two time-dependent potentials with a specific phase difference are applied to the two ends of the chain, while the chemical potentials of both electrodes are set equal. The results demonstrate that in the adiabatic regime (low frequencies), the response of the two spin channels is nearly identical. However, as the driving frequency increases and the system enters the nonadiabatic regime, absorption and emission processes of energy quanta become activated, leading to significant differences between spin-up and spin-down currents. The pumped current exhibits strong dependence on the chemical potential, allowing for the control of both magnitude and direction of the spin current through its adjustment. With increasing frequency, the spin current enhances, and parameters can be tuned such that the charge current nearly vanishes while a considerable spin current persists. This finding indicates the feasibility of achieving nearly pure spin pumping without net charge transfer in the antiferromagnetic chain. The results provide a promising perspective for designing spin-pumping devices based on antiferromagnetic systems.

We have observed that Hadamard matrices whether real or complex lead to a dense output of identical probabilities for any given single input state. Complex Hadamard matrices have unusual orders and introduce phase which prove useful when controlled phase transformation gates are used. By taking a superposed combinations of input states, we discovered that the Hadamards generate non-uniform probabilities which is practically significant towards amplitude amplification without the need for manual parameterization like Grover's operator~\cite{grover1996}. A variety of graph theoretic properties are applied to TSS graphs and their trends were explored. Additionally, graphs turn out to be nearly isomorphic for the same set of input states which has potential applications for developing Quantum Algorithms. Keywords: Quantum Algorithms, Hadamard Matrices, Unitary Matrix Approach, Topological Structure of Superpositions (TSS), Graph Theory

We investigate the quantum Mpemba effect, whereby a system initially farther from equilibrium relaxes faster than one initially closer to equilibrium, emerging in a quantum harmonic oscillator linearly coupled to a bosonic environment. Starting from factorized thermal states at different temperatures, we derive exact analytical criteria for the occurrence of the quantum Mpemba effect valid also beyond the typically considered weak-coupling and Markovian approximations. Most importantly, we show that the effect is enabled by the initial-slip dynamics generated by the sudden switch-on of the system-bath interaction. Neglecting this contribution completely suppresses the anomalous relaxation, identifying transient system-bath correlations as the key ingredient underlying the quantum Mpemba effect.

Coherent and efficient light-matter interfaces between an atom and a single mode of the electromagnetic field are essential for quantum technologies. Traditionally, these systems employ optical cavities or waveguides to isolate a specific mode of light, but a more recent approach is to engineer antennas from ordered configurations of trapped ultracold atoms that exhibit controllable and directed scattering. In this work, we propose a method to engineer an antenna from the center-of-mass wavefunction of a single atom, which can produce directed emission and thereby exhibit strong coupling to a target mode of light in free space. We predict that the resulting single-atom cooperativity can be comparable to the current state of the art in optical cavity and waveguide QED experiments. Building on this approach, we show that a wavepacket antenna becomes a single-atom mirror in the linear response regime. We study the modified dipole-dipole interactions and band structure of chains of such emitters, which can exhibit sub- and superradiance at spacings much larger than the wavelength of the light. Extending our approach to multi-level atoms, we propose a method to achieve arbitrary spatial scattering from a single atom, including uni-directional spontaneous emission. Finally, we elucidate how our approach can enhance cooperative scattering in conventional arrays of tightly trapped atoms.

While quantum interactive proof systems using at least three messages can achieve perfect completeness, as shown by Kitaev and Watrous (STOC 2000), whether perfect completeness is achievable for one- and two-message quantum proof systems has remained open. For the one-message case, whether $\sf QMA$ can achieve perfect completeness was posed as an open problem in Watrous (FOCS 2000) and Aharonov and Naveh (2002); for the two-message case, the corresponding problems were (implicitly) posed in Jain, Upadhyay, and Watrous~(FOCS 2009) and Kobayashi, Le Gall, and Nishimura (SICOMP, 2019). In this work, we establish that ${\sf QIP}(2)$, ${\rm qq}\text{-}{\sf QAM}$, $\sf QAM$, and $\sf QMA$ can achieve perfect completeness. Here ${\rm qq}\text{-}{\sf QAM}$ denotes the class of promise problems admitting two-message quantum-public-coin quantum interactive proof systems in which the verifier's only message consists of half-EPR pairs. Our main technical contributions are the follows: 1. For $\sf QMA$ (and directly for $\sf QAM$), an exactly constructible block-encoded matrix whose kernel certifies yes instances, constructed from the acceptance operator induced by the verification circuit. 2. For ${\sf QIP}(2)$ (and implicitly ${\rm qq}\text{-}{\sf QAM}$), a new turn-halving transformation that preserves completeness and ensures that the resulting proof system retains at least two messages, provided that the terminal state before the final measurement is efficiently preparable.

Quantum error correcting (QEC) plays a crucial role in protecting quantum information against decoherence and enabling scalable, reliable quantum computing. One of the most realistic and ubiquitous sources of noise affecting quantum hardware today is generalized amplitude-damping (GAD) noise. Conventional, deterministic QEC codes struggle to correct for GAD noise because of their inherent structure, leading to fidelity losses that scale linearly with the damping strength. In this work, we introduce the framework of probabilistic approximate quantum error correction (PAQEC), that combines the flexibility of approximate QEC with the potential of post-selected recovery, enabling high-fidelity, resource-efficient error correction. We construct a five-qubit permutation-invariant code that, under probabilistic recovery, achieves a fidelity loss quadratic in the damping strength, thus outperforming existing QEC codes. Formulating PAQEC as an optimization problem, we present a numerical technique based on Charnes-Cooper and semidefinite programming to identify the optimal recovery map for any PAQEC code. Our results establish PAQEC as a powerful tool for developing resource-efficient, high-fidelity quantum codes tailored to realistic noise, with promising implications for near-term quantum devices and future fault-tolerant architectures.

We introduce the notion of the BKM coercivity constant and show that the positivity of this constant governs the exponential relative entropy decay of the semigroup. Indeed, we prove that the modified log-Sobolev constant is equivalent to the BKM coercivity constant up to a constant depending on the asymptotic conditional expectation. We also discover that the BKM coercivity constants for matrix amplifications are already attained with a qubit auxiliary system, which also coincides with the GNS spectral gap of the generating Lindbladian. As a corollary, we establish a criterion that the complete modified log-Sobolev inequality holds if and only if the GNS gap of the semigroup is strictly positive. All the discussion above applies to quantum Markov semigroups that admit a faithful asymptotic conditional expectation as long-time equilibration, with no detailed balance condition assumed. As an application, we show the finite-dimensional Chen-Kastoryano-Gilyén Gibbs samplers always satisfy the complete modified log-Sobolev inequality.

Continuous weak measurements of quantum systems are of great relevance in quantum foundations and applications. They can be achieved by probing the quantum system of interest by repeatedly measuring an auxiliary system weakly coupled to it. Here we study two qubits coupled in different points to a common one-dimensional electromagnetic field and simultaneously monitored in the right- and left-propagating output channels by homodyne detection. Using a collision-model description, we derive an analytical Stochastic Master Equation (SME) governing the resulting diffusive quantum trajectories, including the interference between the two measurement channels. For nonlinear functions of the quantum state, such as entropies, averages over quantum trajectories generally differ from the corresponding quantities evaluated on the unconditional state. Through this mechanism, we show that continuous monitoring generates entanglement, absent in the unconditional dynamics, and enhances quantum magic in the qubit pair during the decay. Both resources can be tuned through the optical phase accumulated between the qubits and the phases of homodyne local oscillators. Our results establish continuous homodyne monitoring of multiple emitters as a tunable mechanism for generating quantum resources.

In $^{28}$Si/SiGe spin qubits with micromagnets, the longitudinal stray field gradient transduces charge noise into qubit frequency noise and limits coherence. We compare two neighboring qubits in the same device with 800 ppm residual $^{29}$Si, one near a decoherence sweet spot where the gradient is locally minimized and the other at a position with a larger gradient. At the sweet spot, $T_2^*$ reaches 67 $μ\mathrm{s}$ and the Carr-Purcell-Meiboom-Gill coherence time reaches 4.6 ms, whereas $T_2^*$ is 5.2 $μ\mathrm{s}$ at the neighboring qubit. Near 1 Hz, the frequency noise power spectral density at the sweet spot is nearly two orders of magnitude lower than at the neighboring qubit. The magnitude and low-frequency decay of the residual spectrum are compatible with the prediction for $^{29}$Si nuclear spin noise, and the weak interqubit correlation indicates that local noise becomes important for dephasing at the sweet spot. Despite a finite correlation with the charge sensor, sweet-spot operation strongly reduced the transduction of charge noise, bringing the residual frequency noise close to the level predicted for $^{29}$Si nuclear spin fluctuations.

We report the absolute frequency measurement of the $4s$ $ ^{2}S_{1/2}\leftrightarrow 3d$ $^{2}D_{5/2}$ $^{40}$Ca$^{+}$ clock transition with respect to the SI second. To perform this measurement, a link between our laboratory in Innsbruck and the clocks realizing the Coordinated Universal Time at the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig was installed and characterized using the Global Navigation Satellite System GNSS. The comparison between our clock and the ones at PTB was done using the Precise Point Positioning technique. After the evaluation of the systematic shifts, the measured transition frequency is 411 042 129 776 401.2$\pm$0.6 Hz with a fractional uncertainty of 1.5 $\times$ 10$^{-15}$. The stability of the clock measurements was also corroborated by comparing two different calcium ion clock experiments, which share the clock laser source at our institute. Furthermore, after careful evaluation of the trap-drive induced ac magnetic fields, we estimate ac Zeeman shifts on the $D_{5/2}$ sublevels and reevaluate the Landé g-factor of the $3d$ $^{2}D_{5/2}$ level to be g$_{5/2}= 1.200329(1)$.

The limits of the well-established single-atom model for describing photon-pair generation via four-wave mixing in a diamond configuration in atomic ensembles are experimentally tested. Using a cold-atom source, biphotons are generated and detected through polarization analyzers that resolve the emitted light into horizontal and vertical components in the laboratory frame. The pump lasers driving the first and second excitation transitions are horizontally and vertically polarized, respectively. To predict single-photon counts and coincidence rates in all polarization channels, the first- and second-order correlation functions are calculated directly using a comprehensive model that accounts for all Zeeman sublevels of the relevant hyperfine states. Furthermore, the population dynamics with and without the re-pump laser of the magneto-optical trap are compared, revealing substantial differences in the populations of the Zeeman sublevels. This motivates the inclusion of two additional hyperfine levels and their corresponding Zeeman sublevels in the final model. The resulting density matrix is used to calculate expectation values of the far-field electric-field operators and compare them with experimental measurements over a range of pump-laser powers. Excellent agreement with the measured photon counts is obtained over most of this range. For the coincidence measurements, good agreement is found when the polarization of the photon generated by the first (second) decay is parallel to that of the first (second) pump beam. In contrast, the model consistently underestimates the experimental coincidence rates for the opposite polarization configuration. These findings indicate that effects beyond the internal level dynamics of individual atoms, most notably collective phenomena, are required to fully account for photon coincidences generated by four-wave mixing in atomic ensembles.

Recent work has introduced the Hamiltonian phase state (HPS) assumptions, which postulate that Hamiltonian phase states can be used to instantiate pseudorandom and one-way state generators. Additionally, it has been conjectured that these assumptions can be true, even if one-way functions do not exist. This is exciting, because if true, then the HPS assumptions provide a route to the instantiation of Microcrypt. In this work we falsify this conjecture, by proving that if the HPS assumptions are true, then one-way functions exist. While this removes the possibility of instantiating genuine Microcrypt cryptography with Hamiltonian phase states, it shows that the HPS assumptions provide novel inherently quantum assumptions for the construction of classical cryptography. Technically we achieve this via a method for the construction of one-way puzzles from one-way state generators and tailored "measure first, ask later" state certification protocols. This generalizes prior constructions of one-way puzzles from one-way state generators via classical shadows and allows us to relate properties of the one-way puzzle to properties of the state certification protocol used in the construction. Specifically, if the state certification protocol admits efficient classical post-processing then one obtains an efficiently verifiable one-way puzzle, and if the state certification protocol can be efficiently classically simulated in a certain sense, then one obtains a classical one-way puzzle, which implies one-way functions. The latter observation allows us to prove that the HPS assumptions imply one-way functions, by exploiting properties of state certification protocols for phase states. The former observation provides a new toolbox for the construction of efficiently verifiable one-way puzzles by exploiting tailored state certification protocols for pseudorandom and one-way state generators.

Quantum thermodynamics is traditionally formulated as a theory of equilibrium states and state transformations. Recent advances in higher-order quantum transformations, which describe physical scenarios beyond states and channels and provide a systematic framework for causal order, raise the question of how equilibrium should be defined and preserved in this more general setting. Starting from the Gibbs state as the unique equilibrium state, we identify equilibrium preservation as its natural higher-order extension. We show that, while this principle can in general give rise to distinct classes of transformations, all such distinctions disappear when equilibrium preservation is required completely, namely under arbitrary ancillary extensions. Remarkably, every transformation satisfying this condition is causally ordered, making causal order an emergent consequence of thermodynamic equilibrium. We establish this result for arbitrary higher-order maps and use the resulting framework to introduce free-energy-like quantities for quantum channels. Our findings reveal a fundamental connection between thermodynamic equilibrium and causal structure, providing a foundation for a fully fledged theory of higher-order quantum thermodynamics.

Practical quantum key distribution (QKD) systems inevitably exhibit imperfections in both the source and detector. At the same time, the behavior of these imperfect devices is never exactly known due to characterization uncertainty, parameter fluctuations, and potential influence by an adversary. In this work, we present a security proof for generic prepare-and-measure QKD protocols, including decoy-state BB84, with imperfect and imperfectly characterized sources and detectors using the marginal-constrained entropy accumulation theorem (MEAT). Our approach uses a sequence of proof technique independent source maps and squashing maps, yielding a very modular framework. We show that practical key rates can be achieved even when multiple imperfections are combined. More broadly, our work provides a unified foundation that avoids the need for dedicated protocol-specific arguments and can be readily extended to other protocols and device imperfections.

Quantum algorithms for ground-state energy estimation require initial states with non-negligible fidelity to the ground state. Guided by classical simulations, we design shallow circuits for the two-dimensional half-filled Hubbard model by first preparing an approximate Heisenberg ground state and then applying charge-fluctuation gates derived directly from the Schrieffer-Wolff (SW) generator. For the Heisenberg model, we demonstrate effective parameter transfer from a $4\times4$ lattice to lattices up to $10\times10$ without further optimization. We obtain promising lower bounds on the ground-state fidelity using tensor-network simulations, variational Monte Carlo reference states, and estimates of the ground-state energy and singlet gap. Exact $4\times4$ calculations show that the SW gates substantially improve the Hubbard ground-state fidelity of the embedded Heisenberg state. The successful Heisenberg parameter transfer supports the use of these small-lattice results to design shallow Hubbard circuits on larger lattices beyond the reach of classical simulations. For a $10\times10$ lattice, the estimated preparation cost is on the order of $10^5$ $T$ gates, including Clifford+$T$ synthesis, which is well within the megaquop regime. These results offer a route to low-cost initial-state preparation for ground-starongly correlated systems.

Entanglement can reduce the communication required for coding tasks, but establishing the minimum achievable cost is essential to understanding its limits. We address this question in a zero-error source-coding task where Alice receives a word and Bob knows an unordered pair of candidates containing it. Alice does not know the pair and must enable Bob to identify her word without error using shared entanglement and one classical message. The candidates satisfy a balanced-difference promise: for words in $\mathbb{Z}_q^n$ with $n=q\ell$, each residue modulo $q$ occurs exactly $\ell$ times in their coordinatewise difference. For all integers $q\geq2$ and $\ell\geq1$, we prove that the task requires exactly $n$ messages when $(q-1)\ell$ is even and two messages when it is odd. These minima allow arbitrary finite-dimensional shared states independent of the inputs and arbitrary local measurements. In even parity, this establishes optimality of an existing entanglement-assisted protocol. In odd parity, an explicit deterministic protocol achieves the optimum of one bit without entanglement. Our proof combines Fourier analysis with a combinatorial counting argument to determine the smallest eigenvalue of the associated graphs. In even parity, this resolves the spectral assertion of Cao et al.'s Conjecture 6.3 for balanced cyclic generalized Hadamard graphs. Together with an explicit odd-parity bipartition, this determines the quantum chromatic number as $n$ in even parity and $2$ in odd parity, where the classical chromatic number is also $2$. All lemmas, theorems, and corollaries are formalized and verified in Lean.

Exchange coupling and microwave drives are widely used control mechanisms for spin qubits. However, the influence of exchange coupling on microwave-driven spin dynamics is not fully understood. We report simultaneous drive measurements of two spin qubits as a function of exchange coupling and drive power. When the Rabi frequency exceeds exchange, we observe a beating pattern in the Rabi oscillations. In the opposite limit, two exchange-split patterns emerge in the Rabi chevrons. We find that these exchange-induced effects are suppressed when the difference in the Rabi frequencies exceeds the exchange coupling. A theoretical model is developed that reproduces the main features in our data.

We characterize the magic of random fermionic Gaussian states through their Pauli spectrum and their stabilizer entropies. For the Haar ensemble of Majorana Gaussian states we derive closed finite-$N$ expressions for the average stabilizer purities and reconstruct the Pauli spectrum exactly, as a mixture of products of beta-distributed variables resolved by Majorana weight. The stabilizer entropies, and their filtered versions, freeze at Rényi index $q_c=2$: for $q>2$ the magic density is $1/(q-1)$, controlled by rare weight-two Majorana strings. Resolving these contributions requires exponentially many characteristic samples, making direct sampling estimates of the stabilizer entropies inefficient in this frozen regime. For Haar-random Gaussian states at fixed filling, we express the averaged stabilizer purities at positive integer $q$ as coefficient integrals over $\mathrm{SU}(2q)$, with dimension independent of $N$, and evaluate the $q=2$ case exactly. We establish that the frozen density describes typical states in the Majorana and half-filled number-conserving ensembles and relate these ensembles to the corresponding $\mathrm{SYK}_2$ ground states. Finally, we show that typical fermionic Gaussian states retain certified magic after discarding any fixed fraction $κ<κ_\star^{\rm G}\simeq0.7613$ of their modes in the thermodynamic limit, remaining magical even beyond the $2/3$ threshold for Haar-random states in the full Hilbert space.

The role of entanglement in quantum optimization remains actively debated. To address this question, we focus on the fixed-parameter expanding-depth regime of the quantum approximate optimization algorithm (QAOA), where a compact two-parameter schedule is trained once on small instances and then applied as the problem size and circuit depth increase. To probe this regime beyond full state-vector simulation, we perform approximate matrix product state simulations for up to 50 qubits and 100 layers and quantify entanglement by the bond dimension. We observe an entangle--disentangle profile, with the peak bond dimension decreasing with depth and eventually saturating. This observation motivates an extreme approximation: projecting the state onto the product-state manifold (bond dimension one) after every two-qubit interaction. Based on this approximation, we introduce BOND-1, a quantum-inspired classical solver. Despite the drastic simplification, BOND-1 achieves cut ratios above 0.95 relative to the best known values on standard GSet MaxCut benchmarks with up to 20000 variables, and in some cases it matches those values. It achieves these results without per-instance optimization and has linear memory cost, while per-instance tuning can provide further improvement. These results show that, in this regime, a substantial fraction of the optimization power of QAOA survives even in the complete absence of entanglement. Our conclusions, however, are specific to this setting and do not imply that entanglement is unnecessary for quantum optimization in general.

Distributed quantum computing (DQC) seeks to scale beyond the limits of monolithic processors by interconnecting multiple quantum processing units (QPUs) through entanglement-based links. Realizing this vision requires the co-design of hardware and software across the domains of quantum networking, compilation, and scheduling, yet existing tools remain fragmented between monolithic circuit compilers and long-distance quantum network simulators. We present an open-source, topology-informed framework for the compilation and scheduling of distributed quantum programs. Given an input circuit and a description of the target network, the framework partitions and reconstructs the circuit into a distributed program that respects the specified inter- and intra-QPU topology, covers cross-QPU operations through gate and state teleportation, and schedules the result under either deterministic or stochastic entanglement-generation models. By accepting and emitting standard OpenQASM, the framework interoperates with existing monolithic toolchains, and its standardized module interfaces allow partitioning and scheduling strategies to be interchanged and benchmarked. Using this framework, we show that the best-performing compilation strategy varies across the tested circuits and network configurations, and that both network topology and intra-QPU connectivity substantially affect the entanglement cost of execution. These findings underscore the need for a co-design approach to distributed quantum computing, which our framework is designed to support.

Searches for post-quantum correlations depend on two distinct ingredients: how abundant such correlations are in the underlying correlation space and how efficiently the chosen representation preserves their distinguishability from quantum correlations. We quantify these effects by introducing the popularity rate and the projection acceptance, whose product defines the search performance. We illustrate these concepts in binary-outcome Bell scenarios with symmetry-related sites, using the CHSH and pyramid representations. Particular attention is paid to the distinction between exchange-symmetric synchronous correlations and correlations satisfying only exchange symmetry. In the synchronous quantum sector, the common-vector representation follows automatically from synchrony, whereas exchange symmetry alone defines a substantially larger correlation space. We show that this distinction can qualitatively change the effectiveness of a projected search: the pyramid representation, which retains substantial discriminatory power in the synchronous sector, has no discriminatory power when only exchange symmetry is imposed. Our results provide a simple framework for assessing and comparing searches for post-quantum correlations.

We introduce OpenQARP, the Open Quantum Application Research Package: an open-source Python framework for quantum application research, built on a compiled C++ core. In OpenQARP, an application is assembled from an algorithm library that orchestrates three interchangeable layers: blocks describe circuits, primitives describe what to extract from them, and engines describe how they run. The release spans near-term through fault-tolerant methods, targeting problems from electronic structure to combinatorial optimization, with device-aware compilation, circuit cutting, and resource estimation over a single set of numerical conventions that the code must follow. Every numerical feature is checked against an independent oracle, and every published timing carries a correctness check. Against OpenFermion, Qiskit/Aer, PennyLane/Lightning, Qulacs, qsim, and pytket, OpenQARP is one to two orders of magnitude faster on operator algebra and among the fastest on simulation. It matches mature compilers on two-qubit gate count, and expresses a complete algorithm in the lines a framework needs rather than the plumbing a primitive stack demands.

Multiplexed quantum memories increase the entanglement distribution rate in long-distance quantum repeater architectures by harnessing storage in several degrees of freedom. Here, we report on the distribution of light-matter quantum correlations using an array of time-multiplexed solid-state quantum memories. We store telecom-heralded single photons sequentially in up to ten memory cells using the full atomic frequency comb protocol with on-demand read-out in a Pr$^{3+}$:Y$_2$SiO$_5$ crystal. Leveraging both spatial and temporal multiplexing, we demonstrate quantum correlations between the telecom photon and up to 60 spatio-temporal modes of the quantum memory array. We then transmit the heralding telecom photon over 39.1 km of deployed optical fiber in the Metropolitan Area of Barcelona. In a realistic scenario where the generation rate is limited by the two-way communication time, we show that up to 15 % of the $393 μs$ round-trip communication time is filled with communication trials, leading to a 60-fold enhancement in the rate of detected telecom photons correlated with the quantum memory array, compared to a single-mode memory. With increased storage times and efficiencies, our multiplexed quantum memory array will constitute the backbone of a long-distance quantum network, establishing remote entanglement at high rates.

Spin of a donor bound electron in silicon has been shown to be a very coherent qubit system but lacks a coherent optical interface. There does, however, exist a donor bound exciton transition that can be excited optically but decays dominantly via an Auger recombination producing an electrical signal. This provides an opto-electrical pathway for spin readout. Scaling this readout to single-spin level will require interfacing the spins with silicon photonics for efficient guiding of photons, which in turn will require moving to silicon-on-insulator (SOI) substrates. Here we demonstrate first ensemble opto-electronic measurements of donor bound excitons in SOI material, including isotopically purified 28-Si device layers. The experiments show pronounced shifts in the resonance wavelengths and broadenings of the transition linewidths compared to the bulk experiments.

Quantum state tomography (QST) is of fundamental importance to characterize quantum systems in quantum information processing, but its practical implementation is severely hindered by the exponential scaling of measurement and computational costs. In this paper, we present a novel QST protocol that utilizes Kirkwood-Dirac (KD) quasiprobability to reconstruct quantum states. First, it enables state reconstruction with only two complementary rank-one projective measurements, thus significantly reducing the measurement cost. Then, a complex logistic regression estimator is proposed to process collected KD data, together with a projected gradient algorithm to mitigate numerical instability and to accelerate convergence. The product-operator structure of KD quasiprobability is further exploited to reduce the computational cost. Finally, extensive experiments are implemented to confirm the validity of our protocol. Notably, the full reconstruction of randomly generated 15-qubit mixed-state instances can be accomplished within 20 minutes under the GPU implementation. These results suggest a promising route toward scalable QST and benchmarking large-scale quantum systems.

We present a direct and nonrecursive construction that maps an arbitrary planar polynomial dissipative flow $\dotα=h(α,α^*)$ to an open quantum system in Gorini--Kossakowski--Sudarshan--Lindblad form. Given the homogeneous components of the classical drift, the corresponding Hamiltonian and collapse-operator blocks are obtained algebraically and independently at each degree. No recursive cancellation of lower-order terms is required: in the large-amplitude limit $|α|\sim S\to\infty$, ordering-generated lower-degree terms are parametrically suppressed, while mean-field closure yields the prescribed leading $O(S)$ drift for semiclassically localized states. This provides a simple and systematic route from dissipative classical dynamics to explicit open-quantum-system realizations, without claiming a unique microscopic quantization of the classical flow. We demonstrate the construction for stable fixed points, a Hopf bifurcation, and a bistable-ring flow. The corresponding Liouvillian spectra recover the classical relaxation exponents, the radial Floquet exponent and neutral phase direction of a limit cycle, and the separation between local relaxation and inter-ring switching in the bistable case. These examples show that the construction can be used not only to analyze a given quantum model, but also to design open quantum systems with prescribed classical dynamical structures in the semiclassical limit.

In quantum error correction, fast low-latency decoding is essential for fault-tolerant quantum computation, as delays in processing syndrome data can lead to the backlog problem. Existing decoders, including parallelizable approaches such as Union-Find, begin decoding only after all stabilizer measurement outcomes from an error-correction cycle have been received, inherently introducing a delay before decoding begins. We introduce Cluster-As-You-Go (CAYG), a modification of the Union-Find decoder that processes syndrome information during stabilizer measurements by clustering and correcting errors as they appear. This approach reduces the size of the remaining decoding problem at the end of the quantum error correction cycle and, consequently, the time required to complete the decoding process. While this early start of clustering incurs a modest reduction in decoding accuracy, it preserves the decoder's scalability. Surface-code simulations show that the resulting reduction in post-measurement idling can outweigh the accuracy loss, yielding an improved speed-accuracy trade-off. These results demonstrate that real-time, early-starting decoding during QEC cycles is both feasible and can be advantageous for quantum error correction. Demonstrated here for the surface code, CAYG is broadly applicable to other quantum error-correcting codes, which allow for clustering-based decoding approaches, and is extensible to dedicated real-time decoding hardware.

We propose and demonstrate gates between two superconducting qubits based on quantum interference of consecutive Landau-Zener (LZ) transitions. This gate mechanism bridges between baseband and parametric two-qubit control, enabling in situ tuning of the control frequency across a continuous interval up to hundreds of MHz. Another advantage compared to dispersive couplers is that the speed of the LZ gate is on the order of the full coupling strength. We experimentally demonstrate the gate on two platforms, a modular chiplet architecture of coupled generalized flux qubits, and on a monolithic transmon architecture. The combination of tunability and gate speed establishes the LZ gate as a unique tool for multiplexing control pulses and interconnecting superconducting chiplet architectures.

We introduce information erasure and quantum imprint as two properties that classify quantum instruments. Information erasure is the property that an appropriate postselection can render the distribution of earlier measurement outcomes independent of the initial quantum state while retaining all outcome branches. Quantum imprint is the complementary property that no admissible postselection can eliminate this state dependence. We show that this classification has a nontrivial structure and that the natural intuition that measurements providing more information about the initial quantum state should be less likely to exhibit information erasure does not hold in general. We further show that, under a sufficiently reliable postselection, information erasure enables first-order separation of state-preparation and measurement (SPAM) errors. Specifically, the first-order contribution of state-preparation error vanishes from the posterior distribution, whereas visible first-order contributions of measurement error remain. This result recasts SPAM error separation from the problem of simultaneously characterizing state preparation and measurement into the problem of realizing a reliable postselection.

We show that light transmitted through a disordered ensemble of weakly coupled two-level emitters can violate a Bell inequality in a continuous-wave Franson-type measurement. The Bell signal is determined by two steady-state output-field correlations, the equal-time intensity correlation $g^{(2)}(0)$ and the phase-sensitive two-photon coherence $R$. We compute these quantities for bidirectional propagation through disordered emitter ensembles using a fourth-order cumulant expansion of the many-body master equation. The resulting Bell inequality violation appears in two distinct regimes, an antibunched regime where equal-time coincidences are suppressed and a bunched regime where photon pairs remain phase coherent. Extrapolating the numerics to a representative weak single-emitter coupling $β=0.01$ predicts violation in the antibunched regime for atom numbers $N\simeq75$-$220$, and in the bunched regime for $N\gtrsim250$.

Cat-state qubits, a prominent class of bosonic encodings, offer a promising pathway toward hardware-efficient fault-tolerant quantum computing. In this manuscript, we propose an optimally robust control protocol for the cat-state qubits which are stabilized by engineering two-photon dissipation. By deriving an effective two-level description in the cat-state subspace and applying shortcut-to-adiabaticity via inverse engineering, we design a robust protocol to achieve fast and high-fidelity state transfer in the cat-state qubit. We analyze the sensitivity to systematic control errors and identify an optimal robustness condition that strongly suppresses errors induced by imperfections in the driving fields. Furthermore, we show that dissipative confinement efficiently suppresses leakage out of the cat-state subspace caused by the pure dephasing, highlighting an intrinsic advantage of dissipative-cat qubits. This work establishes a robust and leakage-suppressing framework for high-fidelity bosonic qubit control, offering a promising route toward scalable fault-tolerant quantum computing.

Skyrmions are competitive candidates for information-storage units and have great prospect in quantum information processing. We here study coherent control of a quantum skyrmion via surface acoustic wave (SAW) phonons in a piezoelectric SAW cavity. Exact diagonalization of a finite Dzyaloshinskii-Moriya cluster reveals the eigenstates of quantum skyrmion with robust scalar chirality. The underlying lattice-spin symmetry imposes polarization-dependent selection rules for the electromagnetic transitions between eigenstates states. Considering the small mode volume of the SAW phonon easy to reach strong coupling, we derive the interaction Hamiltonian between the quantum skyrmion as a qubit and a single-mode quantized SAW via the electric field induced by piezoelectric effect, and find that the coupling strength at the single-phonon level increases linearly with skyrmion radius. This enables enhanced spin-acoustic coupling for larger skyrmionic textures and for low magnetic dissipation. Our results establish few-spin quantum skyrmions as compact building blocks for hybrid quantum information processing and suggest a route toward more densely integrated on-chip quantum devices.

Violation of the $N$-partite inequality introduced in Phys. Rev. Lett. 129, 150401 (2022) for genuine multipartite nonlocality under local operations and shared randomness (LOSR) rules out all causal-network models obtained by locally composing arbitrary resources involving at most $N-1$ parties, even when supplemented by shared randomness among all $N$ parties. Here, we demonstrate a device-independent self-test protocol for this. We further establish an analytic noise-robust self-test. For a Bell-score deficit $ε$, we derive explicit $O(\sqrtε)$ vector-norm bounds for the state and the corresponding measurement actions.

We construct exact quantum circuits for a three-spin Heisenberg triangle with Dzyaloshinskii-Moriya (DM) interaction. A change of basis reduces pure DM evolution with arbitrary couplings to two single-qubit rotations, giving a circuit with at most 8 CNOT gates. When $J$ and $D$ are each the same on all bonds, one fixed basis gives a circuit with at most 10 CNOT gates for any real $J,D,t$. Local spin rotations extend the construction to a family with unequal DM couplings and nonzero exchange, requiring at most 14 CNOT gates. All circuits act on the full Hilbert space. An alternative pure DM implementation uses five two-qubit DM gates: analytically retuning the angles of one symmetric Strang step makes it exact. A 12-spin kagome example illustrates the use of these exact local blocks in lattice simulation.

Object detection requires the joint learning of semantic identity and continuous spatial geometry. Existing quantum transfer learning approaches have focused mainly on classification tasks and do not support regression. Here, we introduce a physics informed hybrid classical-quantum architecture for object detection in which a pre-trained MobileNetV2 maps visual features into an eight qubits variationally quantum Hilbert space. The Hilbert space is partitioned into two task specific subspaces for semantic classification and geometric localization. Local quantum expectation values are used to predict continuous bounding box coordinates, while circuit topology regulates the flow of quantum information between the two tasks. We compare linear and circular CNOT topologies and show that periodic boundary conditions suppress bipartite entanglement without degrading detection performance. The circular architecture reaches a bipartite von Neumann entropy of 0.1688 bits and a Meyer-Wallach entanglement measure of 0.0370, while achieving an [email protected] of 0.9448 and an [email protected]:0.95 of 0.6558. A thermodynamic formulation further interprets the total learning loss as a variation in Helmholtz free energy. It interprets geometric localization as an effective internal energy contribution and semantic classification as an entropic contribution. These results indicate that high performance in the proposed object detection model does not require maximal entanglement. Instead, efficient learning can emerge through topology controlled information flow, targeted restriction of entanglement, and information renormalization within the Hilbert space.

We propose a state-dependent diffusion model for strongly driven thermal-atom spectra. Starting from the trajectory-dependent internal-state evolution of individual atoms, we derive a closed spatial equation for the local density-matrix field using a velocity-moment expansion. Measurements of an $^{85}$Rb atomic-filter transmission spectrum agree well with the model up to a maximum Gaussian peak intensity of $1.27\times10^{3}$ W/cm$^2$, approaching six orders of magnitude above the $^{85}$Rb D2-line saturation intensity. Counterintuitively, the model reveals an anomalous optical-pumping pathway in which intense light transfers atoms from nominally dark states into bright states. Hyperfine Paschen--Back splitting selectively enhances this anomalous pathway while suppressing conventional optical pumping, allowing the filter to maintain approximately 97$\%$ transmission at the highest intensity studied. This work provides a framework for controlling strongly driven atomic ensembles and designing saturation-resistant atomic optical devices.

Dissipative phase transitions in the driven-dissipative Kerr parametric oscillator offer a promising route for realizing criticality-enhanced quantum sensing based on continuous measurements. However, achieving such enhancement through realistic measurement schemes remains an outstanding challenge. Here, we extend the backaction-evasion strategy introduced in our earlier work for the Gaussian linear case [arXiv:2511.22248 (2025)] to analyze how the quantum and classical Fisher information scale with the Kerr nonlinearity at dissipative critical points. Our results show that backaction-evading homodyne monitoring achieves enhanced photon-number scaling that surpasses the standard quantum limit, and significantly outperforms alternative protocols such as continuous photon counting. As an additional methodological contribution, we also implement and benchmark time-discrete approximation schemes with improved statistical convergence properties. We use these methods to compute the classical Fisher information for continuous homodyne detection, and demonstrate that they provide efficient access to this quantity near dissipative critical points, thereby extending the reach of existing methods.

Universality relies on combining operators with different algebraic properties, which depend on the physical structure of the Hilbert space encoding the information. Systems of identical symmetric particles---including bosons and symmetric collections of spin-$1/2$ particles---can be mapped to angular-momentum systems, where rotations supplemented by quadratic, spin-squeezing interactions provide universal control. We revisit universality in this framework and confirm that such linear and quadratic operations provide universal control on every fixed-particle-number subspace. At the abstract level, however, we show that the dynamical Lie algebra generated by all degree-at-most-two elements does not exhaust the full universal enveloping algebra of $\mathfrak{su}_{\mathbb{R}}(2)$, contrary to a stronger claim made previously: higher powers of the quadratic Casimir element cannot be generated by commutators and linear combinations. This obstruction does not conflict with fixed-sector universality because, under a fixed irreducible spin-$n/2$ representation, all powers of the Casimir element act as scalar multiples of the identity. We determine the resulting abstract dynamical Lie algebras exactly and show that the central-free and full degree-at-most-two algebras map, respectively, onto $\mathfrak{su}_{\mathbb{R}}(n+1)$ and $\mathfrak{u}_{\mathbb{R}}(n+1)$, establishing special-unitary and full-unitary universality. We further derive a practical degree-two universality criterion and discuss finite-dimensional SSRC universality.

The Lorentz covariance of relativistic Dirac equations serves as a fundamental principle underlying the laws of electromagnetism across different inertial frames. Exploiting the covariance, we obtain the general solutions for Dirac fermions under both the in-plane electric $\boldsymbol{E}$ and perpendicular magnetic $\boldsymbol{B}$ fields, which reduce to either a magnetic or electric field in the inertial frame with drift velocity along the $\boldsymbol{E}\times\boldsymbol{B}$ direction. This dichotomy defines the magnetic and electric regimes, separated by the critical field ratio $E/B=v_\text{F}$ with $v_\text{F}$ denoting the Fermi velocity of Dirac fermions. Using these solutions, we revisit Klein tunneling through a heterojunction with generalized electromagnetic potentials. In the magnetic regime, the transmission exhibits oscillations governed by the Fabry-Pérot interference. In the electric regime, perfect transmission occurs at normal incidence in the drifted frame. The interference phase is further analyzed in terms of the solid angles on the Bloch sphere, providing a geometric interpretation of Klein tunneling. Finally, we briefly discuss the relation between the tilting of Dirac cones and the in-plane electric field, establishing the correspondence of the undertilted and overtilted cases to the magnetic and electric regimes, respectively. Our findings reveal the manipulation of Klein tunneling by electromagnetic fields, offering a theoretical basis for designing novel electronic devices.

Accurate real-time simulation of correlated quantum systems remains challenging for both classical methods and near-term quantum hardware. We introduce operator-projected variational quantum real-time evolution (OVQRTE), which updates a parameterized circuit by enforcing the Ehrenfest equations for a selected set of observables. OVQRTE requires only expectation-value measurements, while the choice of operator set enables a systematic trade-off between accuracy and measurement cost, substantially reducing quantum-resource requirements relative to existing variational real-time-evolution algorithms. After implementing OVQRTE dynamics of Heisenberg model on a simulator, we benchmark the algorithm for the Anderson impurity models on the IQM Emerald superconducting processor using up to 24 qubits. We further use OVQRTE to sample computational-basis states for quantum-selected configuration interaction (QSCI), enabling the calculation of the ground-state energy and density of states within a self-consistent ghost-Gutzwiller Ansatz (gGut) embedding loop. Our results establish OVQRTE as a promising approach for investigating correlated condensed-matter systems on near-term quantum hardware.

Hybrid quantum-classical neural networks provide a promising approach for incorporating quantum circuits into machine learning in the noisy intermediate-scale quantum regime. However, existing hybrid models often rely on fixed or globally shared fusion strategies, which may limit their ability to exploit complementary information carried by quantum branches, especially under distribution shifts. In this work, we propose a Feature-Adaptive Fusion Hybrid Quantum-Classical Neural Network (FAF-HQNN) for biomedical image classification. The model combines a classical deep feature encoder with a variational quantum circuit (VQC) and introduces a feature-adaptive fusion mechanism to dynamically weight classical and quantum predictions. We evaluate FAF-HQNN on two MedMNIST benchmarks, PathMNIST and BloodMNIST, under clean and corrupted test conditions. FAF-HQNN achieves the strongest overall performance on clean data among the compared methods and shows improved robustness under Gaussian, salt-and-pepper, and Poisson corruptions. Further analysis of circuit layout, measurement basis, and depth shows that even shallow variational quantum circuits can provide useful complementary information. These results demonstrate that feature-adaptive fusion is an effective strategy for improving accuracy and robustness in hybrid quantum-classical models for biomedical image classification.

We uncover the quantum geometric structure of graviton Wigner functions and stress-energy tensors via quantum field theory in curved spacetime, revealing the phase-space geometry of spacetime and relativistic quantum-state manifolds. We show that the polarization mode expansion of the underlying graviton field operator is fully captured by quantum geometry, as encoded in the spinor-helicity formalism, thereby establishing the geometric framework from the outset. Applying this to a weak gravitational background, we demonstrate the roles of the quantum metric and connection in describing graviton transport beyond the chiral vortical effect. We also clarify the role of the quantum metric in normalizing the perfect-fluid graviton stress tensor within this approach. This work paves the path for explorations of multistate Hilbert-space geometry in high-energy and gravitational physics. In addition, this framework naturally encompasses lower-spin excitations, allowing for a unified quantum geometric treatment of bosonic and fermionic many-body systems in condensed matter and particle physics.

The papers by Qin et al. [1] and Nielsen et al. [2] report an unconditional quantum metrological advantage based on squeezed-vacuum phase sensing. The principal evidence for this claim is the Quantum Fisher Information (QFI) evaluated per trial or per detected photon, which is subsequently interpreted as a measure of metrological performance. This interpretation is statistically unjustified because it does not account for the total experimental resources required to construct an estimator. Consequently, the reported protocols do not provide an unconditional metrological advantage over classical phase-sensing strategies when resource accounting is performed consistently.

AI for Science aims not only to predict complex physical systems from data, but also to extract mathematical structure and physically testable representations from learned models. Here, a train--prune--readout--rewrite workflow is developed that separates physical-domain grounding from three increasingly stringent analysis claims: algebraically equivalent readout of a trained predictor, compact teacher-faithful symbolic rewriting on the sampled physical domain, and transformation-based tests of learned internal representations. The workflow is implemented with complex-valued Kolmogorov--Arnold networks, whose explicit edge functions enable post-pruning analytic readout of the retained computation. In analytically controlled single-qubit tasks, rewriting recovered the quadratic structure of purity, whereas von Neumann entropy yielded only a domain-bounded symbolic surrogate; physics-aligned variable grouping preserved symbolic fidelity. For two-qubit entanglement-related tasks, shared learning exposed a common internal representation whose physical content was interrogated directly. Local-unitary transformations rejected a direct invariant-coordinate interpretation, while fixed-decoder transfer showed that the shared activation carries Pauli-correlation information in a transformation-consistent form. Task-related invariant spectral features were subsequently recovered through low-order nonlinear readouts. Separate predictive tests retained high accuracy for three-qubit classification and controlled ten-qubit purity regression with over one million complex inputs. These results establish an evidence-resolved framework for distinguishing physical grounding, readable computation, faithful symbolic compression and transformation-tested physical structure in constrained complex-valued scientific learning.

Fast radio bursts (FRBs) are millisecond-duration extragalactic pulses whose discovery requires searches over large signal-parameter spaces and the rejection of candidate sets dominated by radio-frequency interference and noise. Integrating quantum processors into FRB searches requires a workflow connecting telescop data to hardware-compatible models. Here we develop a pipeline that converts raw search-mode PSRFITS data into dynamic-spectrum segments and identifies FRB-like signals using a hybrid Quantum Vision Transformer (QViT). On labelled FAST data, the selected QViT achieves a mean accuracy of 94.00% and recall of 98.30%, with similar performance to a compact classical Vision Transformer. Recall reaches 97.11% on an FRB source excluded from training and model selection. Real-device execution on 82 segments yields a mean simulator-hardware Hellinger fidelity of 0.9161 +/- 0.0074. The workflow connects raw telescope data to quantum-assisted identification and provides an experimental basis for assessing the measurement requirements that must be addressed before survey-scale deployment.

We develop a biorthogonal time-dependent variational principle for real-time dynamics of non-Hermitian quantum many-body systems. Independent left and right matrix-product states obey coupled bivariational tangent-space equations whose cross-Gram matrix defines an oblique projection. A matrix-free scaled Taylor action propagates the resulting non-normal local generators without assembling dense matrices or storing a Krylov basis. We distinguish the fully coupled algorithm, which solves the cross-pairing problem and truncates the two bond bases jointly, from an efficient independently propagated approximation used for large systems. Independent truncation can make the retained left-right pairing nearly singular; overlap drift and the smallest singular value of the bond cross matrix expose this failure, while coupled truncation substantially delays it. Exact benchmarks and convergence tests validate the method. Applied to an interacting long-range non-Hermitian Ising chain, it resolves a biorthogonal dynamical quantum phase transition and shows that a weak imaginary field shifts the leading critical time from $t^{\ast}|J|=1.84$ to $1.04$.

A long-standing open question in query complexity asks whether there is a total Boolean function f with R(f) << C(f), where R(f) and C(f) denote its bounded-error randomized query complexity and certificate complexity, respectively. We construct a function with R(f) = O~(sqrt{C(f)}), which is optimal up to log factors. The same function also has $Q(f) = O~(C(f)^{1/4}), where Q(f) is the bounded-error quantum query complexity of f, which is also nearly optimal.

Fermionic platforms offer compelling architectures for quantum computing, ranging from topologically protected Majorana-based qubits to fermionic cold atoms. To achieve scalability, however, they require quantum error correction. In this work, we prove that any exact and sufficiently accurate approximate fermionic quantum error correction necessarily requires non-Gaussian operations, beyond the free-fermion regime of quadratic dynamics. This is in sharp contrast to the qubit setting, where the efficiently classically simulable stabilizer operations form the standard framework for quantum error correction. Specifically, we show that the logical space of any non-trivial fermionic error-correcting code contains no pure fermionic Gaussian state, utilizing a fundamental incompatibility between fermionic error correction and Wick's theorem. We further show that the required number of bounded-weight non-Gaussian gates for unitary codeword preparation grows at least linearly with both the code distance and the number of encoded modes, revealing an intrinsic resource overhead that increases simultaneously with error-protection strength and logical capacity. Furthermore, we analyze the performance of fermionic Gaussian operations in entanglement distillation, revealing a distinction from their bosonic counterparts. Our results reveal fundamental difficulties for fermionic error correction from the perspectives of both physical implementation and classical simulation, suggesting connections to fermionic phases of matter and state preparation complexity.

Entanglement between two local multi-photon multi-mode systems can be generated by swapping a pair of modes between the two local multi-mode systems. In this presentation, we consider possible strategies for the efficient generation of entanglement between systems with three or more modes. It is shown that the choice of photon number inputs in the local systems adds a new degree of freedom to the non-local interference effects observed in the output photon number statistics.

We investigate the generation and characterization of higher-order harmonics in the probe-laser absorption arising from nonlinear interactions in an electromagnetically induced transparency (EIT) ladder system involving Rydberg states and driven by two microwave fields in the heterodyne configuration. We characterize the amplitude and phase of the generated harmonics as a function of the relative frequency and phase of the applied microwave fields. The phase of the $n^{\mathrm{th}}$ harmonic follows the relation $φ_n=nφ$, demonstrating phase multiplication and suggesting that higher-order harmonics may offer an enhanced phase response for phase-sensitive measurements. We further characterize the harmonic amplitudes and bandwidths and find that the measured bandwidths are significantly larger than the intrinsic Rydberg-state linewidth, consistent with power broadening under the experimental conditions. The experimental observations are supported by density-matrix calculations, which reproduce the key features of the measured harmonic response.