Quantum Physics Paper Analysis

Electrons in two-dimensional electron gases in the presence of an out-of-plane magnetic field propagate along the edge with a high velocity of the order of the Fermi velocity. Under microwave and terahertz radiation, photon absorption by these electrons provides a pathway to realising sensitive radiation detection. Here, we develop a detailed quantum theory of the photocurrent generated in such a system by an incident electromagnetic wave and propose an experimental geometry for observing the predicted phenomenon. By using suitably arranged radiation confinement structures, a strong photocurrent generation efficiency can be obtained. We also demonstrate that the resulting photoresponse in III-V semiconductor structures can be orders of magnitude higher than that measured in graphene.

We study the Néel quench dynamics of a 1D Fermi-Hubbard model which has recently been simulated on quantum hardware. We demonstrate that the set of 7260 observable trajectories measured in the quantum experiment can be obtained more quickly and accurately through classical tensor network simulation using modest computation. Our result relies on transverse tensor network contraction, where a bond dimension of 32 is already sufficient to reproduce the quantum experiment. We further extend the converged observable trajectories to longer times than in the hardware simulation and in other recent classical simulations.

Shao et al. recently showed that the 1+1D staggered fermion Hamiltonian admits a whole algebra of lattice operators that flow to the same axial charge in the thermodynamic limit (TL). On the lattice the principal axial charge does not commute with the vector charge, although their commutator is expected to vanish in the TL, providing a lattice realization of the chiral anomaly. We investigate the effect of this anomaly on the ground state(s) using the entanglement asymmetry. Unexpectedly, the asymmetry remains nonzero in the TL, despite the vanishing of the commutator, and exhibits a novel scaling behavior.

We study quantum processes in which information extracted from a forward simulation is returned as input to an earlier internal time of the simulated dynamics: externally the protocol is an ordinary causally ordered circuit, but internally it is future-referential. Contracting a process tensor with a leakage instrument and a controller induces a completely positive trace-preserving map on a message register, and we classify its fixed points by five operational properties: stability, informativeness, feedability, coherence, and preservation of quantum correlations. Four results separate notions that informal discussions of "information from the future" often conflate. A two-parameter unitary-dilation family yields a closed-form, globally attractive, coherent fixed point (Proposition 1), yet is entanglement breaking whenever future records are perfectly distinguishable (Lemma 1). Releasing that orthogonality, a four-parameter partial-swap family admits a nonempty open non-entanglement-breaking region (Proposition 2), with an explicit Choi partial-transpose neighborhood of half-width $0.0163π$ (Proposition 3). Combining outward-rounded interval enclosures with perturbation bounds tracking the channel and its stationary-state drift, we certify an explicit parameter square of half-width $0.0013π$ on which the feedback channel is simultaneously strictly contractive (margin $\ge 0.237$), coherent ($\ge 0.416$), informative about the designated future variable ($\ge 0.172$ bits), and non-entanglement-breaking (NPT margin $\ge 0.188$) (Proposition 4). Direct evaluation shows all four properties persisting over a region an order of magnitude larger, so the certified square is a proof of principle rather than a phase boundary. All enclosures and margins are confirmed by a machine-verified ball-arithmetic certificate, and the complete code and certificate accompany the paper.

The Choi--Jamiołkowski isomorphism identifies completely positive maps with bipartite states and underlies much of finite-dimensional quantum information theory. For systems with infinitely many degrees of freedom, modelled by von Neumann algebras of type III, neither traces nor density matrices are available, and the isomorphism has to be reformulated. We show that for arbitrary von Neumann algebras $\mathcal{M}$ and $\mathcal{N}$ there is a canonical order isomorphism between the space of normal completely bounded maps from $\mathcal{M}$ into the predual of $\mathcal{N}$ and the predual of the spatial tensor product of $\mathcal{M}$ with the \emph{opposite} algebra of $\mathcal{N}$; under this identification complete positivity corresponds to positivity. Replacing the opposite algebra by $\mathcal{N}$ itself requires an anti-isomorphism of $\mathcal{N}$ with itself, and we prove that this condition is not only sufficient but also necessary, provided the identification is required to be natural in $\mathcal{M}$. Some such requirement is unavoidable, since for every $\mathcal{M}$ anti-isomorphic to itself an isomorphism exists for trivial reasons. Consequently no Choi--Jamiołkowski correspondence exists for the type III factors constructed by Connes. Along the way we show that the space of all normal maps, taken with the operator norm, is strictly too large for this purpose, and that complete positivity does not force complete boundedness in this setting.

Molecular spins represent a versatile platform for quantum information science, with the potential to offer chemically tunable, addressable qubits. However, achieving this requires understanding and mitigating quantum decoherence. This Chapter provides a theoretical overview of current state-of-the-art chemical theory connecting ab initio electronic structure with open quantum system dynamics to guide the rational design of long-lived molecular qubits. Beginning at the electronic level, multi-reference and relativistic electronic structure methods to parameterize effective spin Hamiltonians are discussed, with a primary focus on accurately capturing $g$-tensors, zero-field splitting, and hyperfine interactions. These parameters feed into models of spin-phonon and spin-spin coupling to quantify $T_1$ and $T_2$ relaxation across various environmental regimes. This Chapter evaluates a hierarchy of dynamical methods, ranging from factorization to matrix product state approaches, balancing computational cost against accuracy and generalizability. Ultimately, mapping these theoretical models to molecular architecture can establish design principles, such as isotopic substitution and spatial spin delocalization, to understand and extend coherence lifetimes.

Certifying genuine multipartite entanglement in quantum systems can require a number of measurements that grows exponentially with the system size. Here we introduce a criterion based on correlation-tensor subsector lengths restricted to local measurement planes and show that it can be evaluated using partially randomized measurements without an explicit exponential dependence on the number of qubits. We derive the corresponding bounds for $k$-separable states and illustrate the criterion using representative families of multipartite entangled states. Finally, we demonstrate the practical applicability of the method on an ion-trap quantum computer by certifying genuine five-partite entanglement.

Hamiltonian truncation offers a nonperturbative route to quantum field theory, yet its accuracy is limited by the rapid expansion of the truncated Hilbert space, which drives up computational cost. We tackle this bottleneck with a hybrid strategy that pairs classical and quantum algorithms: 1) we develop an efficient basis-generation scheme built on integer partitions; 2) we speed up the construction of the sparse Hamiltonian matrix using symmetry-aware algorithms; and 3) we explore quantum Krylov diagonalization as a route to the low-lying spectrum. Benchmarking against the free massive scalar and $φ^4$ theories in two spacetime dimensions, we achieve substantial gains in the computational efficiency of Hamiltonian truncation and chart a path toward future quantum implementations.

We extend our recently developed semiclassical strong-field Herman-Kluk (SFHK) propagator method to calculate high-order harmonic generation (HHG) in diatomic molecules driven by few-cycle intense laser fields. On the example of applications to H2 and N2, we show that our method, based on a combination of the Herman-Kluk propagator and the strong-field approximation, can provide very accurate results for both HHG yield and phase, nearly identical to those from the exact numerical solutions of the time-dependent Schrodinger equation. To compare with experimental measurements, averaging over molecular orientations must be performed. Here we demonstrate a distinct and powerful advantage of the SFHK, as its Monte Carlo sampling for the integration over the alignment distribution can be efficiently combined with the integration over the initial momentum distributions of electron wave-packet right after the tunnel exit. Therefore, the total number of trajectories used for the alignment-averaged HHG spectrum does not increase much compared to that for a single fixed alignment. Similar to atomic targets, the main computational task in the SFHK is to solve the classical Hamiltonian equations for the active electron in the combined electron-target ion potential and electron-laser interaction. The motion of the center of each electron wave packet in the continuum, represented by a coherent state, is governed by an independent classical trajectory so that the computation can be parallelized very efficiently.

In quantum physics the order in which different operations occur can be placed in superposition. The resulting processes have an indefinite causal order and are both of fundamental interest and can be viewed as a novel quantum resource that enables a variety of new protocols. Here we report an experimental implementation of one such protocol, where we perform BB84-like quantum cryptography by placing Alice and Bob's measurement-and-preparation operations in a photonic quantum SWITCH. By embedding Alice and Bob within the quantum SWITCH, the protocol achieves an average eavesdropper detection probability of $0.15 \pm 0.02$ per shared qubit, with eavesdropper detection performed through measurements of the control qubit rather than by comparing the key. Unlike the standard BB84 and related schemes, which detect eavesdropping by publicly revealing and discarding a fraction of the raw key, our approach requires no disclosure of key material: every retained qubit can, in principle, be tested for eavesdropping while remaining available for key generation. The experiment relies on a new measurement technique that allows the polarization of a photon to be measured inside the quantum SWITCH without destroying path coherence. Although the present implementation does not yet constitute a secure quantum key distribution protocol, owing to the post-selection required for measurements within the quantum SWITCH, it provides a proof of principle that indefinite causal order can be exploited to detect eavesdropping without sacrificing key bits.

We prove that every PPT linear map has finite entanglement-breaking index, thereby establishing the eventual entanglement-breaking property of PPT channels in full generality. Furthermore, by utilizing completely positive maps with low entanglement dimensionality, we show that a large family of PPT maps, which strictly containing the class of 2-superpositive maps, has entanglement-breaking index bounded above by 3, uniformly in the dimension. In particular, these results provide strong evidence that the PPT-cubed conjecture may hold in full generality.

To achieve large-scale fault-tolerant quantum computation, it may be easier to combine many small sets of qubits than to construct a single large set. For example via quantum error correction with block codes, or distributed quantum processors utilizing shared entanglement. In these regimes, the time or error budget of the overall quantum computation may be dominated by non-local operations. Hence, it is worthwhile to minimize the number of these operations. We consider the case where both non-local and local connectivity may be arbitrarily restricted, and give an asymptotically optimal synthesis method for distributed CNOT and Clifford circuits, based on block-matrix Gaussian elimination. We extend this to all Clifford+RZ circuits by generalizing the Pauli exponential circuit representation; this naturally integrates with existing methods for optimizing T-count. As an application, we show how to implement CNOT circuits in a CSS code encoding n logical qubits in k blocks using O(nk) inter-block transversal CNOTs and intra-block Pauli measurements.

Existing quantum algorithms for simulating dynamical systems -- from Hamiltonian simulation to linear and nonlinear differential equations solvers -- simulate Markovian dynamics, in which the system's future evolution depends solely on its current state. We turn our attention to developing quantum algorithms for non-Markovian dynamical systems where the system's future evolution depends on its past history and thus has memory. Specifically, we develop efficient algorithms for linear Volterra integro-differential equations (VIDEs) with a convolution memory kernel that output a quantum state encoding the state description over a time interval or at a particular time. Given efficient circuits for the problem inputs, our algorithms achieve an exponential speedup in system size over existing classical algorithms. We develop an algorithm for general kernels assuming that $\textsf{M} < 1$, where $\textsf{M}$ characterizes the strength of the memory term relative to the dissipation of the Markovian part of the dynamics. We complement this with lower bounds for general-kernel VIDEs when $\textsf{M} \geq 1$, showing that the problem becomes intractable for a family of systems. However, by specializing to structured kernels which admit concise decompositions over exponentials, we develop efficient quantum algorithms even when $\textsf M \geq 1$ by converting the VIDE into a larger set of ODEs, a procedure which we call Markovianization. As an application of the overall framework, we discuss the Mori-Zwanzig formalism used in open quantum systems and fluid dynamics. Overall, our results expand the range of dynamical systems that quantum computers can simulate efficiently.

The spin of a quasiparticle trapped in a quantum dot Josephson junction forms the basis of an Andreev spin qubit (ASQ): a semiconductor-superconductor device where the interplay between a localized spin degree of freedom and superconductivity leads to a spin-resolved Josephson potential. In this work, we show that shunting an ASQ with a linear inductor enhances its relaxation time by separating the spin-qubit states into distinct potential wells in phase space, nearly eliminating wavefunction overlap. The resulting inductively protected Andreev (IPA) spin qubit is equivalent to two fluxoniums in the heavy regime, one for each spin. Thus, the IPA qubit combines the long coherence times, low-frequency ground-state manifold, and large anharmonicity of a protected superconducting qubit with the operational advantages of a spin degree of freedom.

Characterising the efficiency with which designs over various subsets of the unitary group may be constructed is an important goal of quantum information theory. While it is now known that approximate unitary designs can be realised in depth logarithmic in the system size, it has recently been shown that ensembles of local nearest-neighbour sublinear-depth one-dimensional circuits over the matchgate, orthogonal, and symplectic groups cannot form approximate 2-designs over their parent groups; similarly, sublinear-depth ensembles of Cliffords cannot form a Clifford 4-design. In this note we show that this remarkable exponential separation is not merely an artefact of restricting to ensembles consisting of unitaries from the subgroups themselves, but rather that no ensemble of local nearest-neighbour sublinear-depth unitaries can realise approximate designs in the aforementioned cases, even when employing "ambient" unitaries from beyond the subgroup itself (possibly acting on ancilla qubits). This implies that various natural tomography and benchmarking schemes which involves sampling from these groups suffer from a dramatic circuit depth overhead compared to similar protocols which involve sampling from the full unitary group. We additionally conclude that, in all of the above cases, the known linear-depth design constructions are up to constant factors optimal.

Quantum technology has the potential to transform scientific discovery, but quantum advantages often require processing capabilities well beyond the reach of experimental platforms. We show that coupling a single controllable qubit to an otherwise conventional sensor can exponentially reduce the number of measurements required to learn classical signals. These rigorous quantum advantages apply to fundamental sensing tasks, including learning Fourier coefficients, extracting temporal correlations from time-varying signals, and estimating transformations of physical observables. Using a superconducting cavity--qubit architecture, we experimentally demonstrate $10^7$-fold reductions in the number of measurements required for Fourier-amplitude and time-varying signal learning. Our $\textit{quantum feature sensing}$ algorithms further enable orders-of-magnitude improvements in simulations of weak-signal dark matter detection and wireless communication applications. These quantum advantages are derived from Quantum Phase-Space Inference (Q$Ψ$), a unifying theory of quantum-enhanced experiments that simultaneously converts a set of experimental objectives and constraints into tight lower bounds and optimal quantum-enhanced learning algorithms while producing a certificate of quantum advantage. Q$Ψ$ extends beyond the regimes captured by quantum Fisher information and provides a framework for systematically identifying rigorous quantum advantages in practical experimental tasks. Together, our results establish that near-term quantum technology can exponentially enhance our ability to learn from classical signals.

We study the distribution of quantum correlations and basis-independent coherence in a pair of massive particles confined in a double-well potential and coupled through their mutual Newtonian gravitational interaction. Non-classical correlations are characterized using Bures distance of entanglement and quantum discord, while coherence is quantified through the square root of the quantum Jensen--Shannon divergence (QJSD) from the maximally mixed state, yielding a measure that is invariant under arbitrary unitary transformations and is therefore genuinely basis-independent. The total coherence $C_T$ decomposes into two operationally distinct contributions: the collective coherence $C_C$, which captures quantum correlations between the two subsystems, and the localized coherence $C_L$, which captures the intrinsic quantum coherence of each individual subsystem. We analyze how temperature $T$, the gravitational coupling $Δ$, and the single-particle energy scale $w$ govern the redistribution of coherence between its collective and localized components. Our results show that $C_L$ is more robust against thermal fluctuations than $C_C$, and that increasing $Δ$ preferentially enhances collective coherence by strengthening gravitationally induced inter-particle correlations.

Unitary designs provide finite-moment approximations to Haar-random unitaries, with wide-ranging applications across physics and quantum information, from scrambling and black-hole dynamics to foundational primitives in quantum algorithms. Strong unitary designs capture a more demanding operational notion of approximation, requiring indistinguishability from Haar randomness even for quantum algorithms that may access a unitary not only in the forward direction, but also through its inverse, transpose, and complex conjugate. Motivated by the physical requirement that scrambling arise within the system itself, Schuster, Ma, Lombardi, Brandão, and Huang (arXiv:2509.26310) left open whether strong unitary designs can be generated in logarithmic depth using only the system qubits. For every fixed design order $k$ and measurable-error tolerance, we construct strong approximate unitary $k$-designs in optimal $Θ(\log n)$ all-to-all circuit depth using only the $n$ original system qubits. Our new ingredient is a logarithmic-depth Pauli-mixing bound for the perfect-matching ensemble, whose layers pair the qubits uniformly at random and apply independent random two-qubit gates. This bound controls the mixed forward-reverse two-query case, which we combine with existing design and gluing results to obtain strong unitary designs of arbitrary fixed order.

We identify a general mechanism for the finite-time thermalization of macroscopic observables, such as coarse-grained charge densities, in terms of elementary forms of the quantum dynamics of initial states: (1) aperiodicity, which provides a computable measure of (2) a dynamical partially ergodic exploration of the Hilbert space. Specifically, this mechanism predicts the equilibration of all (concentrated) macroscopic observables, in almost all states in an initial ensemble and almost all times within finite and longer intervals, given only the observable-independent information that the return probability of the ensemble of initial states is small over a finite time range. As a special case, it also accesses standard results on equilibration over infinitely long times in terms of (stronger versions of) the effective dimension of initial state delocalization in the energy eigenbasis. Our results incorporate macroscopic thermalization into the domain of operational quantum statistical mechanics, recently developed to provide finitely computable criteria for microscopic thermalization. We discuss an overall characterization of this approach as establishing connections between (1) the decay of a (theoretically or experimentally) computable probe indicating memorylessness, (2) a fundamental invariant mechanism in terms of the alignment of observables or states in the Hilbert space, and (3) predicting different natural forms of (classical and) quantum thermalization, most of which rigorously recover conventional eigenstate-based descriptions of infinite-time thermalization as a special case but provide stronger accessible predictions over finite observation times in the thermodynamic limit.

We propose a unified physical principle for entanglement harvesting: the entanglement that two localized detectors can extract from a quantum field is determined solely by how localized the field's effective spectral density is. We demonstrate this in an analytically solvable model of two qubits coupled to a leaky single-mode cavity, which in turn couples to a continuous electromagnetic bath, and derive the maximum harvestable concurrence in closed form, $\mathcal{C}_{\max}(Q)=2e^{-π/(2Q)}(1+e^{-π/(2Q)})/(1+3e^{-π/Q})$, where $Q\equiv|Δ|/κ$ is the ratio of the qubit-cavity detuning $Δ$ to the cavity linewidth $κ$. In the high-$Q$ limit, $\mathcal{C}_{\max}\simeq1-π^{2}/(16Q^{2})$, so the entanglement is robust against cavity loss; in the low-$Q$ limit it decays exponentially to zero, consistent with the irreversible-reservoir character of a continuous field, where maximal entanglement is unattainable. Since $Q$ is proportional to the inverse participation ratio (IPR) of the effective spectral density, it is the single dimensionless parameter governing the crossover from deterministic gate-based entanglement ($Q\to\infty$) to vacuum harvesting ($Q\to0$). Our framework operationalizes the Reeh-Schlieder theorem by quantifying the fraction of vacuum correlations accessible to localized detectors. It also reveals a formal correspondence of the maximal concurrence with the IPR, analogous to the conductivity-participation-ratio relation in Anderson localization. The predicted $\mathcal{C}_{\max}(Q)$ curve is, in principle, directly observable in superconducting circuit QED experiments.

Interference of optical signals in free-space channels requires optical receivers to support many spatial modes due to atmospheric turbulence, typically necessitating adaptive optics systems. Field-widened interferometers offer a passive alternative, making them particularly attractive for time-bin encoded signals with delays on the order of one nanosecond. Here, we demonstrate a field-widened, multimode interferometer design that achieves a high interference visibility for spatially multimode beams with large time bin separations. The interference of the multimode beams is enabled using a multi-pass Herriott cell that enables a very long path separation with a small form-factor. The design is tested using both numerical ray-tracing simulations and proof-of-principle demonstrations. We create a prototype interferometer with a path length difference of 12ns and determine that it maintains a high interference visibility with a large field-of-view of $0.4^{\circ}$.

Magic plays a dual role in quantum computation: it promotes stabilizer dynamics from efficient classical simulability to universality, but it presents a central challenge for fault tolerance, since non-stabilizer operations are harder to protect against noise. Magic state distillation addresses this issue; however, existing protocols typically assume prior structure in the input, such as proximity to the target or a specified noise model. Here we introduce universal magic state concentration: a fixed stabilizer protocol that converts a few copies of an unknown pure non-stabilizer qubit state into an exact target magic state. Motivated by the obstruction to exact $T$-state concentration, we show that $\mathrm{CCZ}$ states behave fundamentally differently. Six input copies are necessary and sufficient to distill one exact $\mathrm{CCZ}$ state, with an optimal success probability determined by the linearized order-three stabilizer Rényi entropy $M^{\mathrm{lin}}_3$. Beyond this, we show that $M^{\mathrm{lin}}_3$ governs the optimal state dependence of any protocol up to nine input copies, and we showcase an eight-copy protocol with improved success probability. Furthermore, block repetition of our protocols yields asymptotic distillation rates that achieve optimal scaling up to logarithmic factors. As a corollary, any unknown pure qubit magic state suffices for universal quantum computation via exact $\mathrm{CCZ}$ injection. Together, these results identify the stabilizer Rényi entropy as a fundamental operational quantity in magic state distillation.

Classical image analysis routinely discards structurally meaningful orientation signatures encoded within Fourier phase, which are easily corrupted by local cellular rotation. Although quantum-inspired data processing offers new avenues for complex signal characterization, practical tools for directly extracting gauge-invariant angular correlations without explicit phase reconstruction remain scarce. Here we introduce Quantum Phase Bicoherence (QPBC) spectroscopy, a novel quantum-interferometric framework for capturing gauge-invariant angular order. The method embeds image angular sectors into a nine-qubit entangled state and probes three-body bicoherence via an ancilla, yielding 16 interpretable readout channels. We validate our framework on three independent public multi-modal imaging datasets covering fluorescence (BBBC021), bright-field (BBBC041) and histopathology (PathMNIST). QPBC consistently resolves angular-phase order and discriminates distinct biological phenotypes with high statistical significance. After principal-axis alignment, the optimal probing frequency universally converges, driven by Fourier directional sensitivity; negative-control experiments fully eliminate discriminative capacity, demonstrating frequency tuning acts as an on-off switch. Cross-dataset benchmarks confirm QPBC outperforms conventional Fourier-phase statistics, where inherent inversion symmetry serves as a built-in pipeline self-check. QPBC delivers a universal, classically unachievable quantitative texture observable, establishes interpretable quantum morphometry, and broadens the toolbox for quantum-inspired analysis applicable to diverse multi-modal microscopic measurements.

Discrete-time quantum walks provide a versatile framework for investigating the generation, redistribution, and transport of quantum correlations in composite quantum systems. Here, we study the dynamics of bipartite and genuine multipartite entanglement in a two-walker discrete-time quantum walk on a one-dimensional lattice. By employing logarithmic negativity and the generalized geometric measure (GGM), we systematically characterize the redistribution of bipartite entanglement among different subsystem partitions and the emergence of genuine multipartite entanglement involving the two coin and two position degrees of freedom. We show that the entanglement dynamics are strongly influenced by the lattice topology. The open-boundary regime exhibits a monotonic redistribution of quantum correlations, whereas the closed-boundary regime gives rise to pronounced oscillatory behavior due to boundary-induced interference and recurrent wave-packet overlap. In the open-boundary regime, the GGM rapidly approaches its theoretical maximum value of $1/2$ and remains largely insensitive to the choice of the initial Bell state as well as to continuous variations of the local coin operator over a broad parameter range, except near the Pauli-$X$ coin. These results demonstrate that maximal genuine multipartite entanglement generation is a robust and generic feature of open-boundary two-walker discrete-time quantum walks, establishing them as promising platforms for engineering multipartite quantum correlations in quantum information processing and quantum simulation.

Quantum information transfer between light-matter-type systems is poised to enable important applications, while also serving as a testbed for theoretical investigation. Such systems can be realized with spins coupled to a mechanical oscillator, a platform that has been extensively studied both theoretically and experimentally. Early demonstrations of quantum information transfer have relied mostly on coherent control. However, measurement-induced backaction has emerged as a strong alternative for quantum control. In this work we use post-selection on the spin system as a selective backaction to refocus spin's phase information onto the mechanical oscillator. We identify physical resources and operating regimes that govern conditional phase transfer, including oscillator quantum coherence, the number of spins, the mechanical initial state, coupling strength, oscillator amplitude, and relaxation. We benchmark different scenarios using the variance as the figure of merit, estimated via two complementary approaches: a semiclassical variance estimator and a Pegg-Barnett quantum estimator. The Cramér-Rao bound is also computed for comparison. The analysis provides a framework for understanding phase transfer in high-dimensional hybrid quantum systems and for measurement-induced backaction used in quantum magnetometry.

We provide a comprehensive study of heat transport in periodically driven quantum systems using a combination of master equation and Floquet approach. We give exact results (within the weak coupling Redfield theory, with no Markovian or secular approximations) and compare them with alternative approaches involving further approximations. Numerical and analytical results obtained in their appropriate driving regimes are provided for the driven spin boson-model. The adiabatic regime, which is relevant to thermal machines, is discussed.

Aggregating logical quantum information encoded in continuous-variable phase space is essential for distributed quantum computing. However, passive linear optics fail for non-Gaussian Gottesman-Kitaev-Preskill (GKP) codes due to symplectic lattice compression and entanglement-induced decoherence. We present an active, measurement-based framework for the homomorphic aggregation of multi-node GKP states. Utilizing GKP Bell states and homodyne feed-forward, we construct a completely positive trace-preserving map that computes the logical sum of distributed states while preserving the logical code space geometry up to correctable finite-squeezing deformations. We prove this protocol operates as an approximate quantum non-demolition measurement, bound its cryptographic leakage for continuous one-time pads, and derive analytical logical fidelity limits under finite-squeezing constraints.

High-precision phase measurement of microwave fields underpins a wide range of applications, including wireless communications, distributed radar, plasma diagnostics, and antenna metrology. Existing Rydberg-atom-based approaches, however, often face trade-offs among phase resolution, measurement range, and system complexity. Here we demonstrate a Rydberg-atom-based microwave Mach-Zehnder-type interferometer using a dual-local-oscillator configuration. The two local oscillators establish two coherent interferometric pathways in the Rydberg medium. Their coherent mixing with the signal field produces an interferometric intermediate-frequency output governed by a phase-to-intensity transfer characteristic that enables critical-point enhancement. This scheme supports direct phase retrieval with a resolution exceeding $0.1^\circ$ and unambiguous full $360^\circ$ phase coverage with the reconfigurable dual-LO architecture. Moreover, near the critical interference point, the system exhibits a sharply enhanced phase-to-amplitude transduction, where weak amplitude variations are converted into pronounced phase responses, yielding a sensitivity enhancement exceeding 25 dB. Besides, the same interferometric transfer mechanism enables microwave propagation-distance and polarization metrology, achieving a propagation-distance precision below 20 $μ$m at 5.7 GHz together with a polarization-angle resolution exceeding $0.1^\circ$. This approach eliminates the need for complex optical configurations and lock-in detection, providing a simple, scalable, and reconfigurable Mach-Zehnder-type quantum microwave interferometry framework for multifunctional high-precision microwave metrology.

Squeezed light underpins quantum-enhanced sensing and continuous-variable quantum information processing, and integrated photonics offers a route to producing it at scale. Universal to these applications are squeezed-light generation and measurement. Importantly, quantum measurements serve not only as readout but also as active operations in quantum-state evolution. However, integrating squeezed-light generation and photodetection on the same photonic chip has remained challenging because they impose fundamentally conflicting material requirements: low optical loss to preserve quantum correlations, but efficient photon absorption for photodetection. Here, we demonstrate squeezed-light generation, routing, and balanced homodyne detection integrated on a single photonic chip through heterogeneous integration. A two-mode squeezed quantum microcomb comprising 34 quantum modes is measured with approximately 3 dB squeezing. Our work establishes a scalable architecture for fully integrated squeezed-light quantum photonic systems, unifying quantum-state generation, processing, and detection on a single chip.

We present an ion-trap platform on borosilicate glass with an integrated femtosecond-laser-written waveguide for on-chip light delivery. The optical layer is physically separated from the electrode substrate and bonded atop the trap, remaining compatible with silicon-based integration. We engineer single-mode low-loss guidance at 729 nm with tunable mode-field diameter and achieve low-loss curved waveguides down to a radius of curvature of 6 mm. We also extend single-mode operation to a wavelength of 405 nm. The fabrication process is compatible with the industrial fabrication of a single-metal-layer surface-electrode trap, including active fiber alignment and bonding. We validate the platform in a cryogenic trapped-ion system with $^{40}$Ca$^+$, demonstrating trapping, shuttling the ion to a zone in front of the waveguide, and coherent operations driven by 729 nm light delivered through the integrated waveguide. We characterize the effect of the exposed dielectric on the ion and measure stray electric fields that show slow drift at a timescale of hours. The architecture is compatible with hybrid micro-optics (e.g. pick-and-place lenses) to realize single ion addressing and provides a robust, scalable route to integrated light delivery for trapped-ion devices.

The data processing inequality is a fundamental property that describes the loss of information through noisy channels. A more refined description is characterized by the strong data processing inequality (SDPI). In classical information theory, the tensorization of strong data processing inequality holds for a whole family of $f$-divergences. However, its quantum counterpart is less known. The tensorization of SDPI was shown only for some special cases previously, and the general understanding about the tensorization property of SDPI for quantum divergences remains open. In this work, we report two negative results: the tensorization property fails for certain quantum chi-square divergences, and it also does not hold for the quantum relative entropy.

The trapped-ion optical-metastable-ground ($\textit{omg}$) architecture for quantum processors promises the full functionality of two-species experiments, including sympathetic cooling and non-destructive ancilla readout, without the corresponding hardware overhead. We confirm that we can cool a global motional mode of a mixed metastable-ground state Coulomb crystal to the motional ground state via dissipative operations on the ground ($\textit{g}$) qubit without disturbing coherence of the metastable ($\textit{m}$) qubit. This enables quantum logic spectroscopy to non-destructively readout the state of the $\textit{m}$ qubit using fluorescence detection of the $\textit{g}$ qubit. Extensions of these demonstrations to larger system sizes should enable the mitigation of motional heating after ion shuttling and syndrome extraction for quantum error correction, both crucial primitives for future fault-tolerant quantum computers based on trapped ions.

Entanglement generation between telecommunication photons and matter is central to fibre-based quantum repeaters. Achieving practical communication rates requires multiplexing, which multimode quantum memories can provide. Rare-earth-ion ensembles offer large temporal multimode storage by exploiting the numerous spectral channels within their absorption spectrum. Here, we report on a quantum repeater node comprised of a $^{171}$Yb$^{3+}$:Y$_2$SiO$_5$ multimode quantum memory, featuring a 250 MHz bandwidth and a $76.6~μ\mathrm{s}$ lifetime, and a bandwidth-matched entangled photon-pair source. We introduce and validate a quantitative measure of the effective temporal mode capacity using a Schmidt decomposition. With this platform, we demonstrate entanglement between a telecom photon propagating through a 25.3 km fiber spool and a 979 nm photon stored for $125~μ\mathrm{s}$ across 16340 temporal modes. Finally, we report a field deployment distributing entanglement over 5.66 km through the Geneva metropolitan fibre network while storing 8235 modes for $63~μ\mathrm{s}$.

Determining whether a target unitary can be implemented within a prescribed quantum circuit architecture is a fundamental problem in quantum information, with direct implications for optimisation and compilation of quantum circuits, and hardware-efficient quantum computation. While existing synthesis and compilation methods are primarily constructive, they generally do not provide rigorous certificates that a unitary cannot be realised using given implementation resources. Here we introduce a general framework to define quantum circuit architecture witnesses, which certify the incompatibility of a unitary transformation with a specified quantum circuit architecture. We formulate the witness construction as a semidefinite program by maximising the fidelity between the Choi state of the target unitary and those of tested circuits. The resulting witnesses provide practical and quantitative certificates of incompatibility, implying lower bounds on implementation resources such as the gate count or circuit depth, and can also be used experimentally to benchmark quantum devices by certifying that an implemented unitary channel goes beyond the capabilities of a given circuit architecture. For Clifford unitaries, we exploit the stabiliser formalism to reduce the construction to linear programming, enabling both more efficient numerical certification for circuits containing on the order of seven two-qubit gates, and analytical witnesses for some families of architectures made of an arbitrary number of gates.

We investigate a discrete-time quantum walk of a three-component quantum particle on a one-dimensional lattice. As coin operators, we employ parameterized rotations generated by the Gell-Mann matrices, which enable systematic tuning of the couplings between the internal components. We analyze how these couplings influence and control the dynamics by systematically exploring the position-space probability distribution across a broad region of the parameter space. To quantify the impact of different inter-component couplings, we further examine the ratio of the mean position to the variance in each half of the lattice. Our results indicates that the system supports a rich variety of transport regimes, ranging from nearly symmetric, rapidly spreading walks to strongly anisotropic dynamics with partial localization. This framework thus provides a new avenue for engineering targeted spreading and trapping behavior in multicomponent discrete-time quantum walks.

We classically simulate the IBM doped Clifford random circuit sampling experiment, comprising $70$ qubits, $70$ entangling layers, and $468$ inserted $T$ gates. A deterministic temporal-boundary tensor network contraction approach is specifically designed to tackle such open-boundary one-dimensional brickwork circuits with operator-Schmidt-rank-$2$ entangling gates. For an $n$-qubit circuit of depth $d$, the resulting unsliced path evaluates an exact amplitude with contraction width $\lceil d/2\rceil$; Ratcatcher calculations certify that no smaller width is possible for the tested instances. Because one-qubit gates are absorbed without changing the network topology, the width and dense scheduled contraction cost are independent of their values and of the number and placement of $T$ gates. For the IBM instance, its largest intermediate tensor contains $2^{35}$ complex64 entries (256 times smaller than IBM's estimation), corresponding to a tensor payload of $256$ GiB, and is distributed across eight GPUs within a node. Using 32 nodes, with eight NVIDIA H100 GPUs per node, we completed all 2051 amplitude batches corresponding to IBM's published output bitstrings in 37.3 minutes. The resulting probabilities yield a log-XEB estimate of $0.35034$ with a 95\% interval of $[0.29763,0.40305]$. Under the Porter--Thomas and scrambled-noise assumptions, this is numerically compatible with IBM's fidelity lower bound; separately, fidelity-weighted resource accounting projects a 583-contraction workload with a 10.6-minute makespan on the same 32 nodes. More broadly, the approach provides a practical diagnostic for experimental outputs and a quantitative tool for designing future doped Clifford sampling experiments.

Temporal modulation of the measurement rate provides a powerful mechanism for controlling open-system dynamics through measurement backaction. We demonstrate this mechanism in a minimal exactly solvable model of a continuously monitored quantum particle on a switching lattice. We derive exact analytical expressions for the long-time current under both periodic and stochastic switching, revealing a common slow-switching limit and identifying a measurement-induced crossover between Zeno- and anti-Zeno-dominated transport regimes that controls the direction of the current.

Ensuring ancilla safety is a critical correctness requirement for quantum compilation, since ancilla qubits are routinely introduced to implement complex operations with fewer gates and reduced depth. However, formally verifying this property is computationally hard due to state-space explosion in the number of qubits, particularly for dirty ancillae, which carry unknown initial states and must be restored after use. We propose an end-to-end verification-and-repair framework that rigorously addresses both clean and dirty ancilla safety. Our core contribution is a two-step reduction strategy: we first prove that verifying an $m$-qubit dirty ancilla register decomposes into $2m$ independent clean ancilla safety checks; subsequently, we reduce each clean ancilla safety instance to an algebraic commutativity check against Pauli-$Z$ and Pauli-$X$ operators. This approach yields an efficient and naturally parallel verifier and enables actionable diagnosis by classifying violations into logic errors and phase errors. Leveraging this diagnosis, we further design lightweight repair routines that append local single-qubit rotations to eliminate a broad class of local ancilla faults. We implement the full pipeline in a prototype tool using a dual-backend architecture combining decision diagrams and weighted model counting, and validate it on diverse circuits ranging from arithmetic benchmarks to Grover's algorithm. Our experiments demonstrate scalability to thousands of qubits and show that the proposed repairs effectively improve ancilla safety while preserving circuit functionality.

Memory-assisted quantum networks require photon sources with controllable temporal and correlation properties. The Duan-Lukin-Cirac-Zoller (DLCZ) protocol provides a platform based on spontaneous Raman scattering in atomic ensembles, but a unified predictive theory connecting control parameters to correlations under realistic propagation and noise conditions remains lacking. Here we present a propagation-inclusive open-system quantum theory that retains write-induced population redistribution while combining Heisenberg-Langevin dynamics with Maxwell-Schrödinger propagation. We experimentally validate its key predictions. The theory predicts time-dependent Stokes generation, spin-wave evolution, retrieved anti-Stokes wavepackets, and time-resolved cross-correlations. Experiments confirm robust correlations under retrieval tuning and enhanced correlations for shorter write pulses, consistent with the different scaling of correlated coincidences and accidental backgrounds with the mean spin-wave excitation number. Classically controlled retrieval enables temporal gating and slicing of the anti-Stokes wavepacket, establishing a quantitative framework for correlation engineering in memory-compatible DLCZ photon sources.

We propose a controlled-Z gate scheme for Rydberg atoms based on level-crossing-free echoing rapid adiabatic population transfer. We design antisymmetric Rabi frequency pulses and symmetric detuning pulses, enabling the system to completely avoid level-crossing points throughout the evolution, and the dynamical phase is naturally eliminated by the time-reversal symmetry of the double-pulse sequence. We incorporate dissipative effects through the Lindblad master equation. The numerical simulation yields a two-qubit CZ gate fidelity of 0.9999. When the Rabi-frequency fluctuation is within $\pm 2\%$, and the detuning offset is within $\pm 1\%$, the fidelity can still remain above 0.999. Under the same dissipative model, the three-qubit CCZ gate achieves a fidelity of 0.999. When a single-parameter fluctuation does not exceed $\pm 3\%$, the fidelity is always higher than 0.997. Our scheme requires no laser phase jumps or fast switching operations. The zero-area pulse structure suppresses first-order intensity noise, and the symmetric double-pulse sequence avoids spatially resolved laser switching, making it suitable for parallel gate operations in large-scale neutral-atom arrays.

We introduce an operational measure of nonclassicality for qubit systems based on the violation of Kolmogorov consistency conditions in sequential measurements. In contrast to previous work by Milz et al.~\cite{Milz-2020}, who characterized classicality via NCGD maps, and Sakuldee et al.~\cite{Sakuldee-2022a, Sakuldee-2022b}, who studied quantum correlations under measurement disturbance, our witness explicitly quantifies nonclassicality in terms of the POVM unsharpness parameter $a_z$. For projective measurements on an initially diagonal state, the witness vanishes identically, showing that such measurements cannot reveal nonclassicality. However, by generalizing to positive operator-valued measures (POVMs), we find that non-projective measurements can reveal nonclassicality even for diagonal initial states. We derive explicit expressions for the witness for general initial states, including coherences, and show that its maximum value is $1/4$, which is a new result achieved for unbiased POVMs, maximal dephasing, and equal initial populations. Our results connect Kolmogorov consistency, Leggett-Garg inequalities, and POVMs, providing an experimentally accessible tool for detecting nonclassicality in qubit systems with potential applications in quantum technology certification.

Using patch-matrix-product methods, we study two reversible three-state interaction-round-a-face cellular automata introduced by Klobas and Prosen [J. Phys. A 55, 094003 (2022)] - the species-preserving and species-flipping rules - and a coherent quantum deformation interpolating between them. Within an explicit translationally invariant ansatz, the two classical rules share a one-parameter family of quasi-local conservation laws with an auxiliary-dimension-three realization. Every regular member is also the first centered logarithmic derivative of an analytic auxiliary-dimension-two family passing through the identity observable. On the closed span of this family and the three elementary local charges, the only nonzero Euler velocities are $\pm\sqrt{3/23}$. Consequently, $\sqrt{3/23}$ is a rigorous lower bound on the maximal Euler speed in any larger conserved sector. For the species-flipping rule, this value agrees with the reported extrapolated value $0.361$ of Klobas and Prosen, strongly supporting completeness of the known sound-active charges. The species-preserving rule admits, in addition, a staggered generating family whose logarithmic derivatives form an infinite tower of strictly local charges. In the quantum deformation, the same algebraic structures yield exact low-bond-dimension invariant states (scar candidates), exponentially long-lived quasi-local quasimodes, and diagonal quasi-local charges that produce a nonzero Mazur bound after projection away from the three elementary local charges.

From fluid flow and transport to collective dynamics, numerical simulation of nonlinear partial differential equations underpins modern scientific computing. Extending this capability to quantum computers remains a longstanding challenge because nonlinear and non-Hermitian evolution is fundamentally incompatible with conventional Hamiltonian-based quantum simulation. Here we experimentally realize the time evolution of nonlinear fluid dynamics on a quantum processor using a hybrid variational framework for the viscous and inviscid Burgers equations. Our approach directly encodes the nonlinear dynamics into a variational optimization procedure, avoiding the enlarged linear embeddings and truncation overhead associated with Carleman linearization-based quantum algorithms. We further demonstrate convection-dominated dynamics corresponding to Reynolds numbers of order $10^2$. We encode the governing evolution into parametrized quantum circuits and iteratively reconstruct the time-dependent field through quantum-classical optimization. By introducing a zero-noise extrapolation method without additional circuit-folding overhead, we accurately execute deep error-circuits with entangling-gate counts beyond those typical of Hadamard test circuits. We accurately reconstruct the time evolution across multiple timesteps despite hardware noise and finite device coherence. Our results constitute, to our knowledge, the first experimental realization of nonlinear time propagation on a quantum processor, extending quantum simulation beyond predominantly linear settings and establishing a route toward quantum computation for nonlinear continuum dynamics.

Complete sets of graphical rewrite rules enable fully graphical reasoning about quantum computations and have been an area of active research for more than a decade. Many recent applications of the ZX-calculus have made use of the close correspondence between ZX-diagrams and computations in the one-way model of measurement-based quantum computation. In this model, various kinds of flow properties ensure deterministic implementability; for ZX-diagrams, these same properties allow efficient translation into quantum circuits (a problem that is known to be #P-hard in general). Therefore, flow-preserving ZX-calculus rewrite rules are of strong interest. Here, we extend the set of flow-preserving rules appearing in the literature with a few new rules and extensions of existing rules. We then show that the resulting rule set is complete for all flow-preserving translations between ZX-diagrams of appropriate form. The proof employs a manifestly flow-preserving equivalent of circuit extraction, where a diagram with gflow is transformed, using only flow-preserving rewrite rules, into a diagram with causal flow.

Efficient detection of single microwave photons is a key capability for emerging quantum technologies. Yet, it remains far less developed than its optical domain counterpart. Realizing detectors that simultaneously achieve high efficiency, low dark counts, and continuous operation has proved challenging. Existing detectors operate cyclically, forcing a trade-off between efficiency and duty cycle. Here, we demonstrate a continuously operated microwave single-photon detector based on a superconducting artificial molecule. In our scheme, an incoming photon is captured by a bright state of the molecule and then transferred to a long-lived dark state via a driven-dissipative process. Photon ``clicks'' are revealed as quantum jumps in the continuously monitored dark state. We observe a cyclic detection efficiency of $0.73$, and a continuous detection efficiency of $0.47$ over a $5\,\mathrm{MHz}$ instantaneous bandwidth, with a $1\,μ\mathrm{s}$ temporal resolution and a $15\,μ\mathrm{s}$ dead time. By overcoming the trade-off between efficiency and duty cycle, this approach establishes continuous microwave photon detection for quantum sensing, quantum thermodynamics, and fundamental physics.

We investigate how network geometry and excitation sector separately control pairwise entanglement decay in asymmetric multipartite $W$ states. To disentangle these effects, we introduce an analytically tractable $N$-qubit generalization of the asymmetric Lohmayer geometry and its complementary-excitation partner, yielding inequivalent vertex-base (VB) and base-base (BB) pair classes that can be compared directly with symmetric $W$-state references. We derive closed-form concurrence dynamics under representative one-sided noise models and find that, within either excitation sector, the VB concurrence has exactly the same noise dependence as the corresponding symmetric reference, preserving a noise-independent proportional advantage wherever both remain entangled. The amplitude-damping reordering previously identified for the three-qubit Lohmayer state is therefore a cross-sector effect rather than an intrinsic fragility of the VB geometry. In contrast, the BB pair exhibits a genuine same-sector structural fragility, with lower entanglement-sudden-death thresholds than the VB pair under depolarizing noise and, in the $(N-1)$-excitation sector, under amplitude damping. The results establish network geometry, excitation sector, and noise symmetry as distinct ingredients governing pairwise entanglement robustness in asymmetric quantum networks.

How much work can an agent extract from a temporal sequence of quantum states when it can only operate online under causal constraints---deciding which energy extraction method to use with knowledge of what it has observed before? Here, we study this problem in the context of quantum state sequences that are potentially non-Markovian---generated by some underlying hidden Markov machine that the agent cannot observe. Using techniques from dynamic programming and computational mechanics, we present a method to identify the provably optimal agent strategy, with time complexity that scales linearly with sequence length. This motivates us to introduce the maximum work such agents can extract---time-ordered free energy(TOFE)---as a fundamental measure of free energy available in a temporally correlated quantum system subject to causal considerations.

Rydberg atom arrays natively encode the maximum-weight independent set (MWIS) problem through the blockade mechanism, so the Boolean circuit satisfiability problem (Circuit-SAT) can be brought onto the platform once it is reduced to MWIS. The conventional encoding of Circuit-SAT in the Rydberg atom array proceeds through conjunctive normal form (CNF) and incurs a substantial atom overhead. We introduce CAMERA (Circuit-SAT Atom-efficient MWIS Encoding for Rydberg Arrays), a method that provides MWIS encodings of Circuit-SAT instances on the king subgraph geometry of the array. CAMERA represents each logic gate as a compact weighted gadget and assembles the gadgets with a placement and routing compiler inspired by very large scale integration (VLSI) design. On random multi-gate benchmarks, the direct encoding route lowers the atom cost relative to the CNF route by an average factor of $22.4 \pm 1.8$. To demonstrate that the encoding extends from individual weighted gadgets to multi-gate arithmetic blocks, we compile a full adder and a multiplier, verifying each against its complete truth table by exact classical ground state calculations. We further showcase solving a representative Circuit-SAT instance end-to-end, from gate level compilation through a closed-system tensor-network simulation of a hardware-compatible annealing protocol on the encoded 30-atom instance to readout of a satisfying assignment. These results establish a complete encoding and simulation workflow as a proof of principle, and a concrete route toward solving a broader family of combinatorial problems on Rydberg atom arrays.

As quantum computing progresses from proof-of-principle demonstrations toward practical utility, a significant impediment is the need to augment algorithmic feasibility with system-level optimization across heterogeneous hardware and software stacks. Quantum resource estimation (QRE) plays a central role in this transition, yet existing approaches remain largely compilation-heavy or domain-knowledge-guided symbolic annotations, and tightly coupled to long-term fault-tolerant assumptions, limiting their topical applicability. In this work, we introduce AutoQuREO, an Automated framework for full-stack Quantum Resource Estimation and Optimization. AutoQuREO is built around four core novelties: (i) a flexible, user-defined abstraction of the quantum computing stack; (ii) a modular library of reusable stack components enabling rapid full-stack prototyping; (iii) surrogate modeling of layer-wise resources via algorithmic profiling and neuro-symbolic learning; and (iv) integrated multi-objective optimization that embeds QRE directly into deployment pipelines. Together, these design choices enable AutoQuREO to serve as a digital twin for quantum computing stacks, supporting the tractable exploration of complex design spaces. We demonstrate the capabilities of AutoQuREO through representative co-design case studies, including early-fault-tolerant quantum algorithms, small error correction codes, gate decomposition and variational training of parametric quantum circuits. These examples illustrate how AutoQuREO enables systematic discovery of unexploited resource trade-offs that are computationally intractable or abstruse using existing QRE tools. AutoQuREO is positioned as a general-purpose platform for advancing quantum technology readiness.

Scientific simulations demand methods combining scalability with predictive accuracy. Density Functional Theory (DFT) on High-Performance Computing (HPC) enables large-scale electronic-structure simulations but is limited by approximations affecting strongly correlated systems and band-gap predictions. Quantum computing offers a pathway to address this, though current Noisy Intermediate-Scale Quantum (NISQ) hardware remains constrained by qubit resources, noise, and execution cost. This work presents a hybrid DFT-Quantum Embedding (QDFT) framework integrating classical HPC-based DFT with a quantum electronic-structure solver. Large systems are partitioned to isolate a chemically relevant active space, treated via the Variational Quantum Eigensolver (VQE), while the remaining degrees of freedom are described by DFT. The framework incorporates active-space selection, embedded Hamiltonian construction, symmetry preservation, operator mapping, self-consistent density updating, and modular classical-quantum coupling. We focus on noiseless quantum simulation to systematically evaluate accuracy, convergence, active-space dependence, computational cost, and HPC scalability without hardware noise. Detailed profiling identifies computational bottlenecks and highlights limitations of CPU-based quantum simulation. A QPU runtime-estimation methodology is additionally developed to assess execution requirements on actual quantum hardware. Results demonstrate quantum embedding's potential to improve selected electronic-structure properties while retaining classical HPC's scalability. Noisy quantum simulation and QPU execution remain key future directions, providing a pathway toward practical, scalable HPC-quantum hybrid simulations as hardware matures.

A supersolid combines density order with phase coherence, and doped lattice solids ask whether added defects can become coherent without melting the ordered background. We study a soft-core Bose-Hubbard model with isotropic hopping and an engineered non-axisymmetric dipolar interaction, \(V_{ij}=V_2(x_{ij}^2-y_{ij}^2)/r_{ij}^5+W_6/r_{ij}^6\), where the sign-changing \(d_{x^2-y^2}\) component selects a fixed \((q,0)\) stripe channel and the \(W_6/r^6\) core stabilizes the short-distance attractive branch. Using sign-problem-free quantum Monte Carlo method with worm algorithm, we find that the half-filled stripe parent responds asymmetrically to doping: the hole side forms locked commensurate stripe solids with vanishing superfluid stiffness, whereas the particle side forms a stripe supersolid with finite compressibility \(κ>0\), finite superfluid stiffness \(ρ_s>0\), and enhanced double occupancy \(D\). Keeping the same off-site kernel while increasing \(U/t\) toward the hard-core limit shows that the particle-side supersolid disappears once doublon-like defects are projected out. Thus the engineered dipolar kernel selects the fixed \((q,0)\) stripe channel, while onsite softness selects the phase-coherent defect sector.

Whether neutral-atom quantum optimization protocols exhibit genuine concentration toward low-energy solution structure remains an open question. Here, we introduce a shots-to-approximate-solution metric, STS(r), where r denotes the approximation ratio, and evaluate it using postprocessed outputs modeled by a degeneracy-weighted shell distribution governed by a single effective parameter, $β$, that quantifies concentration toward near-optimal independent sets. To extract the genuine concentration effect in the quantum data, we apply identical postprocessing to both experimental bitstrings and randomly generated bitstrings with matched excitation density, thereby constructing an excitation-matched random baseline. Experiments on programmable Rydberg-atom arrays with system sizes up to 125 sites show that quantum annealing consistently exceeds the random baseline, demonstrating enhanced concentration toward low-energy solution structure beyond what can be attributed solely to excitation density. The results further reveal two distinct target-dependent regimes. For near-exact targets with $r \approx 1$, the required shot count grows exponentially with system size and is reduced at the same exponential level by quantum annealing within the shell-model description. By contrast, for relaxed targets, the shot cost becomes effectively constant, and the corresponding quantum enhancement diminishes, with the classical postprocessing heuristic alone reaching the target in order-unity attempts. Together, these results establish an operational method for quantifying quantum optimization performance and clarify the regimes under which quantum approaches can yield practical benefits.

Quantum subspace diagonalization methods are promising algorithms for quantum chemistry on near-term quantum computers. These methods can estimate low-lying energies of molecular systems using shallow quantum circuits, at the cost of many circuit repetitions to estimate the projected matrix elements. Errors in these matrix elements can be converted into much larger eigenvalue errors by an ill-conditioned overlap matrix. We study this bottleneck for the nonorthogonal quantum eigensolver (NOQE), which constructs a compact multireference subspace from dressed unrestricted Hartree-Fock states. We prove a finite-shot perturbation bound showing that, after overlap thresholding, the eigenvalue sensitivity is controlled by the condition number of the retained overlap matrix rather than by a worst-case dimension factor. With a scalable thresholding scheme, the upper bound on the per-matrix-element shot count required to reach a target accuracy scales as $\mathcal{O}(M)$, improving on the previously known $\mathcal{O}(M^3)$ bound, where $M$ is the number of reference states. Numerical experiments on hydrogen chains and rings suggest that, in practice, the measurement cost of structured NOQE instances can grow even more slowly than this linear bound.

A core characteristic of dissipative non-Hermitian topology is that the relaxation dynamics tracks the non-Bloch bulk-boundary correspondence, rendering an algebraic decay in the gapless regime and an exponential falloff in the gapped phase, so that local observables directly diagnose the topology. We show that this correspondence breaks down in a dissipative topological superconductor, where the local observables turn blind to the very topology they are expected to decipher. Via a bond-dissipative dimerized Kitaev chain in a third-quantized rapidity-matrix formulation, we find that at zero chemical potential the Majorana rapidity matrix decomposes into two independent non-Hermitian sectors, each with its own generalized Brillouin zone and non-Bloch winding number, thereby revealing a sector-resolved non-Bloch bulk-boundary correspondence. The local density is a cross-sector covariance and relaxes at the sum of the two sector rates, so it remains sector-blind even when one sector is gapless and topological. For balanced gain and loss, the finite-time zero events of the entanglement spectrum under purely periodic-boundary Lindblad evolution recover this hidden edge content sector by sector, serving as a dynamical invariant that returns the open-boundary edge rapidities without physically opening the chain.

When quantum information initially stored in a local qubit disappears, it need not be lost: it may have moved into nearby degrees of freedom or become inaccessible to shallow local control. We introduce finite-window recoverability as an operational channel benchmark that separates these possibilities. It compares optimal recovery from the target site, recovery by a bounded-depth decoder on a finite window, and the unrestricted optimum for that window. Its operational component, local variational recovery, uses local state preparation, window-local control, and target-qubit Pauli readout to certify recoverable memory beyond the target and quantify how much of the same-window advantage is accessible to shallow control. In a disordered kicked-Ising Floquet chain, a depth-6 decoder on a five-site window realizes $Q^{\mathrm{opt}}_0<Q^{\mathrm{shallow}}_2<Q^{\mathrm{opt}}_2$ across the crossover regime, with positive certified gain for most disorder realizations and substantial shallow-accessibility fractions. The signal differs from target-site persistence and reconstructed coherent-information increments. Positive radius-2 gain also persists when the task is embedded in longer open chains using an independent tensor-network backend. Guided by this hierarchy, we test a carrier-deletion task in which the original target register is reset after the dynamics. A depth-8 decoder repairs the input from a radius-3 surrounding halo with held-out median $F_{\mathrm{avg}}=0.758$, above the single-qubit classical benchmark $2/3$, and outperforms optimal one-, two-, and three-site halo-subwindow counterfactuals. These results establish finite-window recovery as a local-control benchmark for off-site quantum memory, diagnosing both where local quantum information remains and whether bounded-depth control can refocus it.

It has remained an open question whether a genuinely unextendible product basis (GUPB) exists. We resolve this problem by constructing an explicit three-qutrit GUPB of cardinality fourteen in the smallest tripartite Hilbert space in which a GUPB can exist. Together with the nonexistence of three-qutrit GUPBs of cardinality less than fourteen, our construction proves that fourteen is the minimum cardinality. A padding procedure further extends the construction to all tripartite systems whose local dimensions are at least three. As applications, the normalized projector onto the thirteen-dimensional orthogonal complement of the three-qutrit GUPB is positive under partial transposition and bound entangled across every bipartition, while the GUPB exhibits strong quantum nonlocality without entanglement.

Correlation functions $\langle O_1(x) O_2(0) \rangle$ reveal scaling dimensions through spatial decay. We instead consider static susceptibility, the change in $\langle O_1(x) \rangle$ from perturbing the Hamiltonian by $O_2(0)$, which we term causation for short. In a conformal field theory (CFT), dimensional analysis predicts decay of $|x|^{-2Δ}$ for correlation and $|x|^{-2Δ+1}$ for causation. Yet we find causation can decay up to fifteen additional orders in $x$ through a general mechanism, which we trace to time-derivative fields being unable to contribute to static response. In higher-dimensional CFTs, this mechanism ensures leading causation arises from primaries, even when descendants dominate correlation, which we leverage with DMRG to identify a previously unresolved corner primary of $Δ\approx 8.8$ and a heavy magnetic line defect primary of $Δ\approx 4.6$ in the $(2+1)$D critical Ising model. Moreover, the same mechanism governs edge-mode localization in $(1+1)$D gapless symmetry-protected topological phases, explaining previously observed anomalously small edge-mode splittings and guiding our construction of spin chains with splittings as small as $1/L^{18}$ and $1/L^{25}$.

Magnetic levitation offer passive levitation of massive objects for use in advanced inertia sensors, for the generation of non-classical macroscopic motional states, and towards the table-top testing of low energy gravity with quantum mechanics. Magnons, a quanta of spin wave, couple to many physical quantities and strongly to electromagnetic fields, even at room temperature. In this work we demonstrate the stable trapping of a small YIG sphere using a magnetic Paul trap. We present a classical stability analysis of a magnetic Paul trap and show the stability diagram for all mechanical degrees of freedom. We show that coupling between librational and translational modes changes the stability region. We experimentally levitate the soft magnet yttrium iron garnet at room temperature obtaining Q-factors of $\sim25$ and secular frequencies $15.8$ Hz and $17.2$ Hz. We provide numerical estimates of the achievable enhanced coupling between the center-of-mass motion and excited magnon modes, with a cooperativity above unity despite strong mechanical damping, indicating potential applications in quantum information processing, quantum interconnects and quantum memories.

Fixed quantum feature maps are increasingly inserted into diffusion denoisers, but standard image benchmarks do not reveal which structural constraint limits them. We introduce CoupledPhaseTexture, a torus-diffusion benchmark with analytic heat-kernel noising that separates parity, within-sector approximation, and sample-complexity limitations. For the depth-1 RY+CNOT+Pauli-Z family we prove a containment-free parity floor: all reachable features are even functions of the encoded angles while the sine components of the Bayes denoiser are odd, so the excess risk splits exactly into an inaccessible odd part and a within-sector residual. The first term is an irreducible, noise-scale-resolved lower bound holding for every even feature class, with no containment, linearity, or closedness assumption on the feature class. The obstruction is a property of the noise-conditioned denoising target rather than static representability: the floor is re-derived at each noise scale because the target's parity content changes with noise. The measured excess is dominated by the parity proxy on two distinct priors. Higher-order Z readouts improve the even sector, but entanglement does not lower the floor and re-uploading does not reliably close it. Classical controls confirm the deficit is parity rather than quantumness: a cosine-only bank is floored similarly, while adding the sine sector matches the reference. Among tested constructions, odd readouts and a noise-coupled encoder do not match the sine-carrying classical bank. These results motivate nonclassical data access or feature classes without efficient classical surrogates; they do not establish either as sufficient for quantum advantage.

Entanglement is a defining feature of quantum mechanics, and its relation to quantum criticality is of considerable current interest. Here we show that measurable spin and charge fluctuations provide an entanglement witness of quantum criticality in the two-impurity Kondo model, which has experimental realizations in terms of coupled quantum dots and magnetic impurities added to surfaces. We use density-matrix renormalization group and numerical renormalization group calculations to resolve the non-Fermi-liquid critical point separating two independently Kondo-screened impurities from an inter-impurity singlet and interpret it as a change in the dominant entanglement partner of each local moment: from entanglement of the local moment with an extended set of conduction-electron degrees of freedom to entanglement with the other impurity. This reorganization is accompanied by a singular response of the impurity-bath entanglement and the inter-impurity susceptibility. We show how the same structure is encoded in the quantum Fisher information of collective spin and charge operators at zero and finite temperatures, connecting the entanglement picture to experimentally accessible dynamical response functions. Our results establish impurity systems as controlled settings in which quantum-critical entanglement can be detected through measurable correlations, and provide further insight into the possibility of understanding heavy-fermion physics in terms of entanglement.

We introduce a framework to classify quantum phases, phase transitions, and non-equilibrium dynamics of interfaces separating ordered bulk domains in 2D quantum magnets - equivalently, confining strings in dual lattice gauge theories - based on effective 1D Hamiltonians governing geometric fluctuations. Building on a "holographic" approach from [Phys. Rev. Lett. 129, 120601 (2022)], here reinterpreted as an exact bosonization, we uncover a rich quantum phase structure, with a variety of stiff and rough interface phases described by gapped and gapless 1D ground states, respectively, all distinguishable through the statistics of 2D wave-function snapshots. Our framework allows us to predict distinct spatiotemporal scaling laws for non-equilibrium curvature-driven interface dynamics across parameter space, which can be readily probed in existing experiments. We finally show that our approach enables the unprecedented experimental opportunity of directly measuring charge full counting statistics and symmetry-resolved properties of an encoded 1D system, as we explicitly demonstrate by numerically simulating a neutral-atom array experiment.

We construct phase transitions that proliferate condensable anyons in general 2+1d topological orders, including non-abelian ones. The central tool that provides a systematic approach to this question is the Symmetry Topological Field Theory (SymTFT). For a given topological order, we identify the relevant symmetry from the transparent lines generated by the condensable anyons, and thereby realize the topological order in terms of a 3+1d SymTFT sandwich. The proliferation phase transition is realized by coupling scalar fields to the anyons purely on the symmetry boundary of the SymTFT. We illustrate the construction for abelian theories, as well as non-abelian ones, $D(S_3)$ and $SU(2)_k$ Chern-Simons theories, and extend it to anomalous anyons.

We cast general imaging as multiparameter quantum estimation of band-limited spatial-frequency amplitudes. For separable (single-copy) measurements, we compute precision limits using semidefinite programming to evaluate the Nagaoka-Hayashi Cramér-Rao bound. We then introduce an architecture for a measurement apparatus based on diffractive optical neural networks and photon counting that saturates this bound. Extending the framework to arbitrary objects and many amplitudes, we show image reconstructions in which our architecture recovers fine features at the quantum limit, outperforming direct imaging. Together, these results open a scalable route to saturating multiparameter quantum limits in superresolution microscopy, telescopy, and remote sensing.

Quantum simulation is expected to be a main application of quantum computers with realistic utility in quantum chemistry, materials science and beyond. However, preparing excited or general eigenstates is a central challenge, particularly when the desired eigenvalue is not known in advance, or when the overlap with the initial state is insufficient. We introduce the Dominant Eigenstate Filtering via Eigenprobability Amplification and Thresholding (DEFEAT) algorithm that identifies and filters the eigenstate with the largest overlap with the supplied initial state. Our key observation is that we do not need prior knowledge of the target eigenvalue, as we construct efficient twirling superoperators that map initial states to eigenprobability density operators $ρ$, diagonal in the Hamiltonian eigenbasis and encoding its spectral weights, alongside its block-encoding implementation. Our crucial innovation is the quadratic amplification of probabilities via the factorisation $ρ=ρ_{\rm sqrt}^\daggerρ_{\rm sqrt}$, analogous to the recently introduced sum-of-squares spectral amplification (SOSSA), which we use here to amplify the separation between dominant and subdominant components. Thresholding then yields the dominant-eigenstate projector. Compared with conventional phase estimation, DEFEAT improves the dependence on the overlap with the initial state while requiring substantially fewer ancillary qubits. We prove that the query complexity of the filtering step is optimal up to logarithmic factors and establish a complementary lower bound for eigenstate preparation under purified query access to $ρ$. We validate in numerical simulations that the convergence rate of DEFEAT matches our theoretical results. Our results provide a general eigenvalue-agnostic primitive for dominant eigenstate filtering and preparation, and for estimating properties of dominant eigenstates.

A theoretical unified interferometric framework is developed for interaction-free measurement (IFM) and delayed-choice (DC) experiments. The proposed model leads to a quantum circuit based architecture in which an ancillary qubit coherently controls the interaction between a photon and a bomb, allowing the system to evolve in a superposition of interaction and non-interaction regimes. The ancillary control qubit serves as a quantum switch that continuously interpolates between IFM and DC behavior, revealing a common operational origin for both phenomena. We demonstrate that both the phenomena can be realized within this framework through controlled quantum-gate operations. The analysis shows that the framework enables a continuous transition between the particle-like and wave-like behavior in DC setup. The framework is shown to be consistent with standard quantum mechanics, preserving unitary evolution, quantum superposition and the measurement postulate.

The output state of a 2D geometrically local shallow random quantum circuit does not have long range correlations due to its lightcone structure. But this changes if one measures a subset of the qubits: long-range entanglement can be induced by the measurement process, leading to conditional correlations between distant qubits. In this paper we investigate the structure of conditional dependence in these circuits and its consequences for quantum advantage. For a tripartition $ABC$ of the qubits, we consider the ensemble of post-measurement states on $A$ that is conditioned on a specific measurement outcome on $B$ and ranges over all possible measurement outcomes on $C$. For circuit depths exceeding a constant critical value $d^*$, we conjecture that this ensemble is well approximated by a certain generalization of the Haar ensemble, called the Scrooge ensemble~[Jozsa \textit{et al.}, \href{https://doi.org/10.1103/PhysRevA.49.668}{Phys. Rev. A \textbf{49}, 668 (1994)}]; we also provide supporting numerical and analytical evidence. Our conjecture describes a precise sense in which the state retains its lightcone structure on the remaining unmeasured qubits, but also develops some globally random features arising from the measurement. A consequence is that $n$-qubit shallow random quantum circuits in two dimensions are classically efficiently simulable in the presence of a tiny depolarizing noise rate $Ω(\log(n)/n)$.

Let $\mathcal{P}_{N}$ be the $(N+1)$-dimensional Hilbert space of analytic polynomials of degree at most $N$. This is the natural environment to define $SU(2)$ (Bloch) coherent states. Let $Q_{ρ}$ be the Husimi function of a density operator $ρ$ on $% \mathcal{P}_{N}$. We prove an isospectral version of Lieb-Solovej inequality: if $ρ^{\downarrow }$ is obtained by placing the eigenvalues of $ρ$ in decreasing order along the monomial basis, then \begin{equation*} \int_{\mathbb{C}}Φ(Q_{ρ}(z))\,dm(z)\leq \int_{\mathbb{C}}Φ(Q_{ρ^{\downarrow }}(z))\,dm(z) \end{equation*}% for every convex function $Φ$ on $[0,1]$. Applying the corresponding reversed inequality to the concave function $Φ(t)=-t\log t$ gives the Wehrl entropy. In the process it is show that the output state of $ρ$ under Lieb-Solovej's channel is majorized by the output of the state $ρ^{\downarrow }$. As an application, among all measurable subsets of the sphere having a fixed area, spherical caps maximize every partial sum of the eigenvalues of Toeplitz operators with symbol $1_Ω$. Equivalently, caps maximize all Ky Fan norms, leading to the sharp inequalities, previously known for $r=1$: \begin{equation*} \sum_{j=1}^{r}λ_{j}(Ω) \leq r-\sum_{k=0}^{r-1}(r-k)\binom{N+1}{k} m(Ω)^{k}\bigl(1-m(Ω)\bigr)^{N+1-k}. \end{equation*} This implies isoperimetric inequalities for all Schatten sums of $T_Ω$, obtained without using the spherical isoperimetric inequality.

Ryu-Takayanagi established how boundary entanglement encodes bulk area. We provide the metric counterpart: boundary mutual information imposes a rigorous lower bound on bulk geodesic separation that diverges logarithmically as correlations vanish. A multiscale iteration promotes this local inequality to a global obstruction to bulk connectivity. For parallel strips in AdS$_5$/CFT$_4$, the bound necessitates a quantum resolution of the classical mutual-information transition and fixes the asymptotic growth of geodesic distance.

Efficient integration of cryptanalytic evidence with quantum verification remains a fundamental challenge in hybrid classical-quantum cryptanalysis. This work presents a capability-adaptive cryptanalytic framework that unifies linear cryptanalysis, differential cryptanalysis, and side-channel leakage analysis within a common candidate-space reduction architecture, followed by reduced-space quantum verification through amplitude amplification. A formal mathematical model is developed for candidate-space construction, adaptive filtering, verification-space reduction, and complexity characterization, supported by the oretical results establishing the relationship between candidate-space contraction and quantum verification effort. A Hamiltonian formulation is further introduced to provide a physically realizable interpretation of the reduced-space verification process. Evaluation using statistically generated cryptanalytic observations demonstrates that the proposed framework reduces an initial candidate-key hypothesis space of 4096 candidates to an effective candidate space of 13 hypotheses, corresponding to an overall reduction of approximately 99.683%. Consequently, the Grover verification requirement decreases from 50 iterations to only 2 iterations, yielding an approximately 25-fold reduction in verification effort, while reduced-space amplitude amplification achieves a target-state success probability of approximately 94.53%. These results demonstrate that adaptive cryptanalytic filtering can substantially reduce quantum verification complexity while preserving cryptanalytic admissibility, providing a practical foundation for capability-aware hybrid cryptanalysis and reduced-space quantum search.

The frustrated Ising ring is one of the simplest models exhibiting exponential closing spectral gaps, making it a paradigmatic and challenging benchmark for quantum annealing (QA). Ground-state preparation for this model has therefore been studied extensively in both continuous-time QA and digitized protocols such as the Quantum Approximate Optimization Algorithm (QAOA). Here, we use the frustrated Ising ring to investigate how the parity mapping affects the performance of both QA and QAOA. For QA, finite-size calculations show that the parity mapping increases the minimum spectral gap under the energy normalization used in this work, thereby enabling faster continuous-time ground state preparation protocols. An ideal implementation of Parity-QA, with a single global constraint, shows no evidence of exponential gap closing over the accessible system sizes, whereas a hardware-motivated decomposition into local constraints restores the exponential decrease, albeit with a smaller fitted exponent than conventional QA. For the digitized protocol, we find that the number of Parity-QAOA layers required to prepare the exact ground state remains constant over the simulated sizes, improving upon the quadratic scaling required by conventional QAOA. To investigate the role of constraints in Parity-QAOA, we further consider a modified Ising ring instance in which the constraint term is essential for preparing the target ground state. We then compare the corresponding resource requirements with those of conventional QAOA.

Reliable quantum-state engineering in periodically driven devices requires more than reproducing their excitation spectrum: the environment must resolve the transitions of the driven system. We show that two dissipative descriptions of the same parametrically coupled qubits can yield closely similar period-averaged populations yet qualitatively different asymptotic entanglement. Both retain the complete periodically driven Hamiltonian, the same microscopic bath couplings, and the same physical observables; they differ in the dynamical representation used to resolve the dissipative channels and the corresponding system operators: the static dressed basis in the partial harmonic decomposition approach (PHDA) and the Floquet basis, including all relevant drive sidebands, in Floquet-Born-Markov (FBM) theory. The population maps preserve the same resonance skeleton and remain closely similar over broad low-to-moderate drive regions, while clearer differences emerge as the modulation becomes stronger. Phase-resolved single- and two-qubit coherence observables reveal a substantially stronger redistribution of amplitudes and phases. Concurrence amplifies this hidden state-level discrepancy: Floquet-resolved dissipation selects stronger and more extended Bell-like entangled regions and a larger overlap with a fixed Bell-like reference, while PHDA generally underestimates the entanglement and its thermal persistence. A channel-resolution test verifies the secular, completely positive FBM construction throughout the relevant parameter domain. Our results establish population agreement as an insufficient benchmark for open Floquet quantum-state engineering and identify coherence-sensitive observables as the decisive validation test.

Anyon condensation that describes the transition between topological quantum field theories can be formulated in the language of tensor categories or that of operator algebras. We deploy the formalism of Doplicher-Haag-Roberts bimodules over quasi-local $\mathrm{C}^{*}$-algebras recently developed in [1] to investigate anyon condensation, which is associated with an extension of a certain operator algebra. The connection between notions in the two formulations is thereby made manifest in an intuitive, diagrammatic manner. An entropic order parameter, as the quantum information-theoretic measure characterising a condensation, is naturally defined, and we give a very simple proof of a bound on it.

Exact entanglement distillation converts a noisy bipartite state into a maximally entangled state with zero error. Under completely PPT-preserving operations, the additive min-Rains relative entropy provides a single-letter upper bound on the regularized distillation rate. An interesting problem in entanglement theory dating back to 2016 has been whether this bound is always tight. Here we resolve this question in the negative. The key is a tensor-stable rigidity absent from the min-Rains relaxation: every feasible exact-distillation effect must act as the identity on the support of the input state. We convert this constraint into a new single-letter upper bound using a generally non-Hermitian, range-supported witness. For a rank-three subspace, we show this upper bound lies strictly below the min-Rains relative entropy for every state with that support. Thus, the constraint discarded by the min-Rains relaxation remains relevant under arbitrary tensor powers. Our result rules out the min-Rains relative entropy as a closed-form formula for exact PPT distillable entanglement and reveals the subtle asymptotic structure of exact entanglement manipulation under PPT operations.

Single organic molecules are a well-established platform for high-quality single-photon generation: they can emit lifetime-limited photons with high purity and indistinguishability. However, their emission is accompanied by a pronounced red-shifted phonon sideband and higher-order vibrational peaks, which reduce the fraction of photons emitted into the desired narrowband zero-phonon line. The standard approach to suppressing this unwanted emission is to integrate the emitter into a monolithic photonic nanostructure that provides Purcell enhancement. However, incorporating organic materials using clean-room techniques has proven challenging, and has in fact so far prevented their integration into monolithic microcavities altogether. As a result, efficient, narrowband organic single-photon sources for applications in quantum information processing have remained elusive despite their considerable promise. Here, we propose three monolithic microcavity designs tailored to provide sufficient Purcell enhancement for organic quantum emitters. The Purcell effect induced by these cavities preferentially enhances emission into the 0-0 zero-phonon line, increasing spectral purity, photon extraction, and shortening the excited-state lifetime, which in turn relaxes the requirements for generating indistinguishable photons. The cavities have been optimized using Bayesian optimization and the adaptive Antoulas-Anderson (AAA) algorithm for rational approximation, which offer global optimization and the efficient reconstruction of spectra from scattering simulations, respectively. These structures are compatible with both standard clean-room processing and single-molecule preparation techniques. Therefore, they offer a clear route to realize high-quality, practically monochromatic organic single-photon light sources.

It is known that Chebyshev based polynomial approximation gives a near-optimal rate of convergence for calculating a function of a Hermitian matrix. However, previous work has not discussed the option of true minimax approximation, nor the specifics of writing a high performance implementation with a rigorous analysis of errors. This work provides such an analysis and an open-source implementation of three approximation methods in C++.

The non-equilibrium properties of open quantum systems are determined by the microscopic laws governing energy exchange with their environment. In particular, an enhancement of the performance of quantum heat engines has been predicted by speeding up the dynamics through control of the system--bath interaction. However, direct microscopic control of heat transfer between the machine and the reservoir has remained elusive so far. Here, we experimentally demonstrate such control in a quantum Otto engine realized with ultracold Cs-133 atoms coupled to an atomic reservoir of ultracold Rb-87 atoms. Heat exchange between the two is mediated by inelastic s-wave collisions whose energy-dependent scattering cross sections lead to an asymmetric equilibration dynamics in the isochoric heating and cooling strokes. By tuning the kinetic temperature of the atomic reservoir, we modify the associated microscopic scattering rates, and thereby the heat transfer law, giving control over the time allocation within the engine cycle through control over the microscopic, multi-exponential relaxation dynamics. This enables power output optimization at fixed efficiency. Our results establish microscopic control of system-reservoir interactions as a tool for manipulating heat flow at the nanoscale and engineering the finite-time performance of quantum thermal machines.

Low-entropy arrays of atomic quantum systems in optical tweezers offer unique prospects for fundamental research on few- and many-body systems as well as for extended applications in quantum technology. The significance of this approach relies on the achievable system size, its uniformity, and the rate of qubit allocation. We propel the neutral-atom quantum-technology platform by the rapid assembly of a regular two-dimensional quantum register of up to 1024 atomic qubits, enabled by a novel implementation of intensity-homogenized tweezer arrays and parallelized atom transport. Our highly efficient microoptical architecture modularizes intensity equalization and tweezer patterning in separate functional units, eliminating restrictions that arise for high-power, high-resolution, and large-scale light-field control within a single device. Arrays of precise grid structure, trap depth, and vibrational frequency with more than 3500 sites are demonstrated. Individual sites are interconnected by up to 50 parallelized transport tweezers with intensity and position control in real-time for swift qubit relocation. Multi-tweezer transport enables the operation of target patterns of up to 32 x 32 sites with sustained near-unity filling fraction. These results boost neutral-atom quantum information science above the kiloqubit level.

The $n$-qubit Pauli group is an essential ingredient to most quantum applications, from computing and error correction to benchmarking and simulation. Despite comprising merely a discrete set of operators, it exhibits many quintessential features of quantum theory, including contextuality, which has been identified as a key resource to quantum advantage in a variety of different flavours. Here, we extend this analysis, introducing the notion of a `noncontextual property' whose nonexistence proves the Kochen-Specker theorem, similarly to and generalising common arguments based on the nonexistence of valuations. We relate this notion formally to the existence of Boolean-valued frame functions, and characterise all such frame functions in the case of the $n$-qubit Pauli group. For two qubits, we show that the Pauli group admits noncontextual properties, despite admitting no valuations. We then establish this as the only nontrivial such case with $n\geq 2$, by proving that any Boolean-valued frame function on stabiliser states is constant for more than two qubits. We also perform a similar analysis for the symplectic theory underlying the $n$-qubit Pauli group, for which nonconstant Boolean-valued frame functions exist for all $n$, yet only in restricted form. By comparison, this shows that contextuality in the $n$-qubit Pauli group is not only a consequence of the projective nature of the Pauli group as a representation of its underlying symplectic vector space, but of the geometry of symplectic polar spaces itself. In geometric terms, our result determines all Cameron-Liebler sets of maximal totally isotropic flats in the binary affine-symplectic space.

The continuous-time quantum walk on an oriented circulant graph is determined by the Fourier eigenvalues of its Hermitian adjacency matrix. We classify perfect state transfer (PST) between distinct vertices in every nonempty oriented circulant graph. We show that each such graph is described by an odd primitive quadratic Dirichlet character of conductor $Δ$, a set of gcd-classes, and a choice between the two orientations of each selected class. For a graph of order $n$, we derive an explicit formula for every Fourier eigenvalue without assuming that $n/Δ$ is coprime to $Δ$. We prove that PST occurs only for $Δ\in\{3,4,8\}$ and give necessary and sufficient conditions on the connection set for each conductor. Equivalently, the square-free radicands of oriented circulant graphs with PST are exactly $1$, $2$, and $3$. More generally, when $λ_j=\sqrt{D}η_j$ with $η_j\in\mathbb{Z}$, congruences satisfied by the integers $η_j$ determine all PST pairs and times, the minimum period, and the largest vertex sets supporting multiple state transfer (MST). In this class, pretty good state transfer is equivalent to PST. We also determine the connected orders and enumerate the resulting graphs.

We develop a density-matrix theory of vortex-electron transport in accelerator lattices. In a periodic round lattice, the protected object is a Lewis-Floquet orbital angular momentum (OAM) invariant rather than the instantaneous kinetic OAM. Ideal transport has a metaplectic lift; stochastic imperfections generate a Lindblad channel. Dipole noise produces removable centroid smearing; quadrupole noise drives intrinsic $Δ\ell=\pm2$ leakage. Under explicit white-noise benchmarks, the inverse initial leakage scale is $2\times10^5$ turns for IOTA and $2\times10^6$ turns for PETRA III.

A central promise of useful quantum advantage is the ability to compute ground states of Hamiltonian systems beyond the reach of classical simulation methods. Here we demonstrate that this problem can be effectively amortized across an arbitrary and universal set of Hamiltonians by a foundation model with $\sim0.5$B variational parameters, trained with contemporary techniques from large language models and deep reinforcement learning. To do this, we formulate $\text{spin-}1/2$ quantum ground-state learning as manifold variational optimisation over centrally odd scalar functions on $\mathrm{SU}(2)^N$. This replaces explicit Hilbert-space vector amplitudes with manifold functions on which the Hamiltonian acts through Lie derivatives, evaluated by custom automatic differentiation primitives. We prove that the resulting variational principle on this manifold preserves the $\text{spin-}1/2$ sector's ground-state upper bound using the Peter-Weyl theorem, then pre-train our foundation model on a dataset of hundreds of thousands of different Hamiltonian systems, varying the connection topology, system size, interaction types and strengths, bringing together a century of many-body literature. Using a novel $\mathrm{SU}(2)$ replica-exchange Langevin sampler and sharded natural-gradient optimisation, we train our model with our own extension of the Kronecker-Factored Approximate Curvature (KFAC) optimiser on system sizes up to 64 qubits. On a held-out generalisation dataset, we fine-tune our model on system sizes of up to 1024 qubits, and evaluate on systems up to 8100 qubits.

Peaked circuits are random quantum circuits whose measurement returns one bitstring far more often than chance. They are a candidate route to verifiable quantum advantage, and the bottleneck is classical generation. Aaronson and Zhang fix a random circuit, append a trainable brickwall of half that depth, and optimize it by gradient descent to raise the probability of one chosen output string. Their method plateaus at a size-dependent ceiling, which they attribute to a barren plateau. A dichotomy remains open: either the optimizer stops short, so a better algorithm would reach higher, or no efficient method exists. We map the landscape on which the answer depends. Across 18 instances per size at n = 8-16, at fixed and converged budgets, no fixed-base exponential, the law they fit, matches the optimizer's reach: at convergence the decay steepens from 1.16 to 1.295 per qubit through n = 16 (p = 0.011 frozen and 0.025 converged, on n = 8-14 alone), leaving their n = 50 estimate unsupported; at n = 16 they report more than we reach at any budget measured. One optimizer beats ours: L-BFGS-B ends 3.9 +/- 1.6% above converged Adam at n = 16, on three instances. That margin retires our hardness conjecture under its registered rule and leaves the rate untouched: every optimizer measured loses a factor 1.3 per qubit. The barren plateau is present and cannot explain that rate: the reach sits far above the Haar floor 2^-n, and the exact second-order amplitude data are depth-independent while the reach is not. Nor do solutions cluster at that floor: they are decorrelated yet path-connected by paths 10^2-10^3 above 2^-n whose floor falls from 0.73 to 0.23 of the endpoints. Path search is one-sided, so near-optimal clustering stays open. In the deep limit we prove no poly(n)-parameter family beats poly(n) 2^-n on average. What survives: a connected landscape and a shrinking reach.

Quantum generative adversarial networks (QGANs) have attracted increasing attention for image generation using parameterized quantum circuits. Existing amplitude-based approaches face two key limitations: pixel locations are typically encoded by computational-basis indices or address qubits, causing quantum resources to grow with image resolution; meanwhile, jointly decoding many pixels from normalized quantum states introduces probability competition among pixels and limits precise pixel-wise control. To address these issues, we reformulate quantum image generation as coordinate-conditioned implicit function learning. Our method takes spatial coordinates and latent variables as inputs, uses a classical embedding network to generate input-dependent circuit parameters, and evaluates a variational quantum circuit at each coordinate. Pixel intensities are directly obtained from the expectation value of a dedicated color qubit, and a complete image is generated by querying all spatial coordinates. This design decouples image resolution from address-qubit requirements and avoids shared probability-normalization constraints across pixels. We further design a specialized variational quantum circuit to provide structural inductive bias for coordinate-conditioned generation. Simulated experiments on two benchmark datasets show that our method outperforms FRQI-based generation and PQWGAN in visual and quantitative quality while using fewer qubits, and also achieves better generation quality than the corresponding classical baseline.

Coherences between different energy levels are strongly constrained by thermodynamics. Here we ask a related question: if several coherence transfers can be optimized separately, can they also be optimized simultaneously by the same thermodynamic process? We show that this is in general a compatibility problem. Using an energy-resolved Stinespring representation of thermal operations, we express elementary coherence-transfer amplitudes as inner products of bath-weighted vectors associated with total-energy shells. Saturation of the corresponding Cauchy--Schwarz bounds requires these vectors to be collinear. Since all transfers have to arise from the same energy-preserving system--bath unitary, such saturation conditions cannot in general be imposed independently. Trace and Gibbs preservation lead to additional phase-closure conditions and to polygon inequalities that can rule out simultaneous saturation for fixed population-transfer data. We complement these analytic results with a rigorous computer-assisted semidefinite-program analysis. For the mixed-degenerate Hamiltonian $H=\operatorname{diag}(0,1,1,3)$, machine-certified primal and dual bounds show that no covariant Gibbs-preserving channel can simultaneously attain three individually optimal directional coherence transfers. Since every thermal operation is covariant and Gibbs preserving, the same triple of optimal values cannot be attained by a thermal operation. We further relate this incompatibility to range-inclusion constraints in Choi-sector Gram matrices for mixed-degenerate energy levels. Our results show that coherence transfers which are optimal when considered separately need not be compatible with one physical thermodynamic process. A full characterization of this incompatibility directly within thermal operations remains open.

Informational completeness (IC) guarantees that an inverse exists, not that it is statistically well conditioned. For minimal rank-one Weyl--Heisenberg (WH) measurements, covariance makes the nonidentity projector-Gram spectrum proportional to the fiducial's ambiguity intensities, with eigenvalues \(d|χ_φ(u)|^2\), turning stability into an explicit worst-direction design problem; write \(λ\) for its smallest nonidentity eigenvalue. Haar fiducials are IC almost surely while \(\mathbb E[λ^{-1}]=\infty\), and an explicit geometric family used to establish balanced informationally complete measurements in every dimension has a normalized spectral floor bounded above by an exponentially decaying envelope. We then construct a hierarchy of minimal measurements. A cyclic family with exactly \(d^2\) outcomes in every integer dimension has floors \(Θ(d^{-3})\) for odd \(d\) and \(Θ(d^{-5})\) for even \(d\); a finite-field family for \(q=2^m\) obeys the uniform bound \(λ\ge4/9\). Our main result treats every prime-power dimension of characteristic \(p\ge5\). A balanced one-coordinate perturbation repairs the zero ambiguity axis of a cubic Alltop state, gives an attained floor uniformly bounded below by a positive constant, and confines the entire nonidentity spectrum to \([L_q,U_q]\) with \(U_q/L_q\to1\). Its SIC-normalized minimum tends to one, and \(λ(φ_q)/Λ_q^\star\to1\) for the global finite-field WH max--min optimum \(Λ_q^\star\), without assuming SIC existence. The complete spectrum determines the exact finite-sample Hilbert--Schmidt error of canonical linear inversion at \(I/d\), while its lower edge controls local Fisher efficiency and canonical-shadow bounds.

We study the strong-coupling Birman-Schwinger analysis of the three-boson lattice Schroedinger operator at the exceptional quasimomentum K = pi. First, we provide an exact closed-form benchmark for the fiber Fredholm determinant at a distinguished flat momentum, valid for every quasimomentum K, obtained via a uniform elliptic reduction of the two-dimensional lattice integral. Second, we formulate and prove a general order-matching criterion. This criterion decides whether a leading-order Fredholm determinant asymptotic, with relative accuracy of order 1/mu, suffices to determine the constant-order additive correction in the strong-coupling energy, or if the next-order refinement is required. Applying the criterion at K = pi, we derive the complete strong-coupling ground-state asymptotics, including the coefficient of the order 1/mu term. The results are cross-validated against the exact closed-form benchmark and two independent high-precision numerical schemes. Furthermore, we determine the corresponding spectral gap and prove an exact Fredholm-determinant underestimation factor equal to 2. Additionally, we independently confirm that the previously established K = 0 constant is correctly derived and requires no analogous refinement. Finally, we compare the orders of asymptotic precision controlled across recent lattice few-body models and draw a structural parallel with the parity classification of topological band structures.

Quantum field theory allows local violations of the classical energy conditions, such as regions of negative energy density. The Ford-Roman quantum inequalities quantify how negative these regions can be and for how long. We present a derivation of these inequalities from the second law of thermodynamics, in an operational framework that couples the field to a small thermal detector. The detector acts as a physical probe of the field's energy density and, by the non-negativity of the entanglement entropy between the two systems, one can show that its heat loss is bounded from below by a state-independent quantity.

Continuous-variable (CV) quantum states are naturally characterized by their moments, defined as expectation values of products of single- or multimode ladder operators. Many CV Hamiltonians and quantum algorithms are formulated directly in terms of these moments, and therefore an efficient procedure to estimate moments with limited state measurements is necessary. In this paper, we present a protocol for shadow tomography of moment-generating functions (MGFs) of CV states based on randomized homodyne and heterodyne measurements. The resulting shadows enable an efficient and concurrent estimation of many multimode moments. Our complexity analysis shows that the number of measurements required to estimate a certain moment to a given precision grows exponentially in the order of the moments. Finally, we assess the precision of these moment estimators by applying them to two tasks: detecting entanglement in both Gaussian and non-Gaussian states via the Shchukin-Vogel protocol, and characterizing optical loss in a photonic chip. We demonstrate that both tasks can be accomplished with only a few thousand randomized measurements. The small number of required measurements, combined with efficient sample processing, makes our protocol applicable to a wide range of CV simulation tasks.

Unconventional photon blockade (UPB) provides an attractive route for generating antibunched light through quantum interference without requiring strong nonlinear coupling. In conventional Markovian systems, irreversible dissipation progressively destroys the phase coherence, even limiting the achievable single-photon purity. Here we propose a scheme for imposing non-Markovian effects on a microwave cavity where a Er$^{3+}$:Y$_2$SiO$_5$ crystal loaded into a hybrid optical-microwave system. Based on the time-convolutionless non-Markovian framework, we derive the time-dependent non-Markovian decay rate and the renormalized microwave drive in the weak-coupling regime. We show that the second-order correlation function is significantly suppressed, even to the order of $10^{-7}$, since the backflow of environmental information enhances photon blocking. In addition, this structured reservoir engineering not only provides an additional degree of freedom, but also further optimizes the blockade via optical detuning. Importantly, the delayed second-order correlation exhibits a broadened antibunching profile, thereby relaxing the timing requirements for single-photon synchronization. Our results demonstrate that environmental non-Markovianity can be transformed from a source of decoherence into a controllable quantum resource, opening new opportunities for high-purity single-photon generation.

Effective implementation of high-level quantum gates is essential for practical quantum computing. To the best of our knowledge, we present the first reported 12-CNOT decomposition of the double qubit excitation operator, improving upon state-of-the-art (SOTA) implementations with 13 CNOTs. Our new circuit has the lowest CNOT count (12), lowest CNOT depth (10), and lowest total circuit depth (16) among all the previous SOTA circuits. Further, we only added 2 extra one-qubit gates compared to the lowest one-qubit gate count (11) among the previous SOTA circuits.

We formulate a finite-proper-time construction for Euclidean scalar $λφ^4$ theory in which a retained endpoint $s_0$ is assigned to complete internal histories rather than independently to individual Schwinger segments. The theory is defined through paired open and closed spectral functions and their Fréchet/Duhamel hierarchy. Functional differentiation inserts operators along an existing proper-time history and partitions its total length, while interaction vertices sew separately complete histories. We introduce a corresponding complete-history diagrammatic calculus and derive the resulting one- and two-loop structures. We distinguish the retained endpoint from an auxiliary regulator or renormalisation-group scale and test whether its effects survive ordinary parameter matching and admissible field redefinitions. For the one-loop four-point function, fixing the renormalised mass, field normalisation, and quartic coupling leaves a finite momentum-dependent remainder. We establish a perturbative non-redundancy description of the retained endpoint against finite renormalisable-parameter redefinitions and local $S$-matrix-preserving field redefinitions at this order. The low-energy theory can be represented as an effective field theory, but its higher-derivative coefficients are not independent. This provides a concrete distinction between a retained finite proper-time scale and an arbitrary cutoff prescription.

Transversal CNOT (TCNOT) gates can accelerate fault-tolerant quantum computation (FTQC) in the surface code by reducing the number of syndrome extraction rounds required between logical operations from $O(d)$ to $O(1)$. This is particularly attractive for quantum platforms with long-range connectivity, such as neutral atoms. However, dense TCNOT schedules substantially increase the classical decoding workload. TCNOTs propagate errors across multiple surface-code patches, enlarging the spatiotemporal region that must be decoded jointly. Consequently, denser TCNOT schedules increase decoding latency and memory requirements and potentially exceed available decoder capacity. Moreover, because the detector error model (DEM) of each decoding window depends on the TCNOT schedule, exhaustively precomputing all possible window-level DEMs is infeasible, requiring just-in-time (JIT) DEM compilation. Thus, the practical benefit of TCNOT gates is limited not only by quantum hardware performance but also by classical decoding and DEM-compilation capacity. We introduce PACE, a decoder-aware scheduling framework for TCNOT-based FTQC. PACE first mitigates the decoder-side costs of aggressive TCNOT scheduling through three complementary techniques. Hybrid Window Decoding assigns different decoders for each decoding window according to its DEM structure. DEM Stitch generates schedule-specific window-level DEMs just in time by assembling reusable precompiled fragments. Sub-window Parallel Decoding decomposes large windows into smaller sub-windows with graph-coloring formulation. Building on these techniques, PACE then performs decoder-aware scheduling to maximize TCNOT concurrency within the available decoder resources. Our evaluation shows the trade-off between quantum acceleration and classical decoding cost, revealing the limitations of current decoding systems for TCNOT-based FTQC.

Telecloning -- the combination of quantum teleportation and cloning -- offers a powerful mechanism to disseminate unknown quantum states to multiple spatially separated recipients with optimal fidelity. Despite its conceptual importance for quantum networks, an experimental demonstration of symmetric qubit quantum telecloning remains elusive, particularly due to the challenges of generating multipartite entangled resource states and implementing stable multi-photon interference across distributed nodes. Here, we realize the optimal 1 to 2 symmetric quantum telecloning using a scalable silicon photonic platform. We implement a six-photon protocol using two independent, fiber-linked photonic chips: one generating a heralded input state and the other preparing a four-photon entangled resource state. By performing an interchip Bell-state measurement, we successfully distribute the input state into two optimal clones at remote nodes. We observe an interchip cloning fidelity of 78.45 $\pm$ 1.39%, exceeding the classical limit of 2/3 by 8 standard deviations. Our results demonstrate the robust generation and manipulation of complex multi-photon states between integrated chips, providing a foundational building block for large-scale multi-party quantum networks.

We show that a cyclically controlled non-coherence-generating channel supplies a two-parameter family of closed Bloch trajectories, absent in the single-parameter (temperature) cycles of the thermal Uhlmann literature, whose associated Uhlmann phase develops a genuine vortex--antivortex structure on the channel-parameter torus. A qubit prepared in a pure state, which carries no geometric phase of its own, acquires a nontrivial Uhlmann phase, obtained here in closed form, purely from a closed loop in the space of the native quantum channel parameters. The net topological charge of these defects is constrained to zero by the Poincaré--Hopf theorem. As the input-state orientation approaches its critical values, the defects merge and annihilate in pairs following a square-root coalescence law. This defect dynamics drives local geometric transitions, a mechanism that contrasts with single-parameter thermal Uhlmann transitions, where a global quantized winding jumps as a bulk invariant.

Irreversibility and time-translation symmetry are both fundamental in open quantum dynamics, and it is of great importance to study the interplay between them. In this paper, we study tabletop reversibility (TTR) for phase-covariant quantum operations and obtain sharply different conclusions for finite-dimensional and Gaussian systems. For finite-dimensional systems, we prove that any phase-covariant operation that admits a Petz recovery map can be implemented by a dilation which is both time-translational symmetric and tabletop time reversible. In contrast, for phase-covariant Gaussian operations we exhibit a concrete obstruction: any Gaussian dilation of a single-mode Gaussian amplification channel is not tabletop time reversible. As a byproduct, we find that almost every completely positive and trace preserving (CPTP) map admits a dilation that realizes TTR. These results clarify whether and how TTR can be realized under phase-covariant symmetry constraints and reveal a qualitative difference between finite-dimensional and Gaussian systems.

We study the power of quantum examples, as compared to classical examples, in the PAC learning framework. Here, we have two learning algorithms, both with access to quantum computation, but one gets quantum examples, whereas the other gets classical examples. It was previously unknown whether there were learning tasks that can be efficiently performed but not by the latter. Our primary result is to show that relative to an oracle, there are distributions that can be efficiently generated by a quantum learner with access to quantum examples, but not by a quantum learner with access to only classical examples, making progress to answering this question in the affirmative.

Quantum computation has traditionally been formulated by postulating abstract information carriers and subsequently identifying physical systems that realize them. We adopt the opposite viewpoint and ask what computational structure is supplied by a fundamental relativistic quantum system itself. Focusing on the simplest nontrivial massive spin carrier, spin-1/2, we show that its relativistic description supplies a native four-dimensional information carrier through the Dirac equation. The resulting Dirac information carrier possesses an intrinsic positive- and negative-energy decomposition that induces a physics-constrained computational structure comprising sector-preserving and sector-coupling quantum logic. Restricting the relativistic computational structure to the positive-energy sector and taking the nonrelativistic regime recovers the familiar Pauli qubit description. We distinguish mathematical unitary transformations from physically admissible gates and show how charge-conjugation structure, charge superselection, and associated reference-frame resources can constrain quantum logic beyond the sector-preserving structure. Finally, under appropriate physical assumptions, we establish the conditions under which this structure supports full single-carrier controllability. Our work establishes the Dirac information carrier as the massive spin-1/2 instance of a broader programme in which computational structures are derived from the relativistic representation carried by the underlying physical system.

Solid state quantum emitters are a leading platform for photonic quantum networking with memory nodes. However, the inhomogeneous distribution of quantum emitters, as well as several environmental factors (i.e. strain and electric fields) spread the frequency spectrum of the qubits, making them distinguishable and therefore not a reliable resource for distributed quantum entanglement. In this paper, we demonstrate a full-stack approach to integrating nearly indistinguishable tin vacancy (SnV$^-$) quantum emitters on a frequency-tunable photonic interposer that overcomes the native distribution and static variation of quantum emitters for an indistinguishable photonic quantum networking platform. We demonstrate a silicon nitride-on-insulator photonic integrated circuit (PIC) with accompanying multiphysics digital twin (MPhDT) that guides discovery of SnV$^-$ strain-tuning parameters and informs construction of a multi-channel quantum repeater node. On this node, we achieve the first simultaneous demonstration of spectral tuning of the zero phonon line (ZPL) at GHz scale; coherent electron spin control with gate times of $<80$ ns; strongly- and weakly-coupled nuclear spin detection; and commercial fiber array-coupled readout of a SnV$^-$ center. Finally, we propose and simulate improvements to the architecture that achieve 99.96% connectivity of $ N \sim 1000$ emitters spanning the inhomogeneous distribution of SnV$^-$ centers in strained diamond, where distributed quantum entanglement may be realized.

Understanding how common dielectric substrates influence the spin transport properties of graphene is essential for advancing graphene-based spintronic technologies. Here we use a comprehensive set of numerical simulations to reveal how a SiO$_2$ substrate modifies the spin texture and governs spin relaxation in graphene. Using first-principles density matrix dynamics simulations, as well as tight-binding (TB) transport simulations, we quantify the effects of electron-phonon scattering, impurity scattering, and electrostatic disorder on the spin relaxation process. We find that a 2D SiO$_2$ substrate induces a predominantly Rashba-type helical spin texture in graphene, leading to a spin lifetime anisotropy of 1/2. Meanwhile, bulk SiO$_2$ breaks in-plane symmetry in graphene, leading to anisotropic in-plane and out-of-plane components in the spin texture, which we capture with a newly-developed TB model of graphene. Transport simulations under realistic disorder conditions reveal a spin lifetime anisotropy between 0.5 and 1, similar to what is seen in measurements of graphene spin valves on a SiO$_2$ substrate. Our results reveal a more complex picture of spin relaxation at the ubiquitous graphene/SiO$_2$ interface, beyond the standard Rashba model, providing critical insight for interpreting experiments and guiding substrate engineering for graphene spintronics.

Hamiltonian simulation is a core quantum workload, underpinning variational quantum algorithms and Trotterized time evolution. Such programs are expressed as Pauli exponential sequences, exhibiting structural patterns that are highly amenable to high-level synthesis and optimization. Existing compilers, however, fail to fully unlock the optimization potential of their global algebraic structure, even when employing advanced graph- or tableau-based methods. We present Symphony, a holistic compilation approach built on the binary symplectic form (BSF) representation of Pauli strings. Unlike prior group-wise BSF simplification and path-based Pauli network synthesis, Symphony applies generalized controlled-Pauli Clifford transformations directly to a global BSF tableau, adaptively reducing active Pauli rows and emitting eligible two-qubit blocks other than single-qubit rotations in a forward Clifford frame. Following algebraic simplification, Symphony performs a causality-preserving block rescheduling heuristic that respects frame-induced dependencies while exposing extensive two-qubit block parallelism opportunities. This streamlined compilation style comprehensively exploits simultaneous simplification and commutativity opportunities, achieving efficient global optimization without relying on computationally expensive heuristics or long-horizon searches. Across the generic Hamiltonian simulation benchmarks in HamLib, Symphony achieves average reductions of 59% in two-qubit gate count and 91% in circuit depth. It strictly Pareto-dominates prior state-of-the-art compilers, requiring 1.14--1.58$\times$ fewer two-qubit gates and especially shrinking two-qubit circuit depth by a substantial factor of 1.87--5.67$\times$ on average.

Quantum-selected configuration interaction (QSCI) methods use a quantum computer to identify dominant electronic configurations in the molecular ground state, while a classical computer diagonalizes the Hamiltonian within the reduced subspace spanned by those configurations. Sample-based quantum diagonalization (SQD), a leading QSCI approach, uses iterative classical post-processing to correct noisy quantum measurement to ensure that the corresponding configurations remain physically sensible. In this work, we show that SQD performance can be strongly influenced by uncontrolled growth of the classical diagonalization subspace. When classical resources are not explicitly constrained, classical uniform random sampling can reproduce SQD benchmarks as noise increases the diversity of sampled configurations. We show any fair benchmarking protocol of SQD must explicitly control diagonalization size over unique samples. We then address the problem of efficiently discovering physically relevant, energy-lowering configurations by introducing a measurement protocol based on non-orthogonal configuration interaction (NOCI). By distributing measurements across orbital bases optimized with respect to the molecular Hamiltonian, we obtain improved sample efficiency relative to measurements performed solely in the Hartree--Fock basis. Importantly, these improvements persist even under fixed classical resource budgets, demonstrating that the resulting configurations are of higher quality rather than being more numerous. Under our proposed benchmarking procedure, we establish measurement-basis engineering as a promising route to improving quantum sampling methods for electronic structure.

Modular arithmetic is central to quantum algorithms for cryptographic problems, including Shor's algorithm and Grover-based cryptanalysis, with modular reduction contributing substantially to circuit cost. Pseudo-Mersenne moduli $q=2^n-c$ allow classical Crandall reduction to replace division with folding and constant arithmetic, providing a structural opportunity for more efficient quantum modular reduction than Barrett reduction. We translate this advantage into a reversible quantum setting by deriving explicit folding and normalization conditions for $2n$-bit inputs. To the best of our knowledge, this constitutes the first exact reversible quantum circuit formulation of Crandall reduction. Based on this formulation, we develop two variants: Crandall reduction-1 is designed to minimize execution cost through one-step normalization, whereas Crandall reduction-2 uses two-step normalization to support a wider range of $c$ with limited overhead. Logical resource estimates show that both variants require fewer qubits and lower T-count and T-depth than optimized folding Barrett reduction. At $n=10$, Crandall reduction-1 reduces both T-count and T-depth by approximately 46.9% relative to optimized folding Barrett reduction. Surface-code analysis further shows that, at $n=20$ under the Sparse Blossom decoder, the estimated runtimes of the two variants are 30.05 ms and 35.39 ms, respectively, compared with 53.77 ms for optimized folding Barrett reduction. These results demonstrate the practical value of exploiting modulus-specific arithmetic structure in fault-tolerant quantum circuit design.

We investigate the exact dynamics of first-order system--bath coherence induced by excitation exchange in bilinear bosonic models. By solving the linear Heisenberg equations, we obtain the exact evolution of system and bath operators and evaluate the first-order coherence between the system mode and the collective bath mode directly coupled to it. We analyze how this coherence depends on initial occupations, coupling strength, spectral width, and detuning, showing that its buildup and oscillatory behavior are closely related to excitation exchange and reservoir memory. We further examine controlled coherence dynamics under leakage-elimination-operator inspired modulation of the system frequency. The results show that random modulation can suppress excitation leakage and maintain finite and relatively stable coherence fluctuations at long times. These results clarify the evolution and control of first-order system--bath coherence in settings where a localized bosonic mode is coupled to a structured bosonic reservoir.

The spontaneous emission factor - often known as the \b{eta} factor - is an important quantity in the description of quantum well lasers, influencing both the threshold power as well as the general shape of the light in-light out (L-L) curve. Past work on modelling multiple quantum well (MQW) nanowire laser devices has typically assumed that the \b{eta} factor is a constant parameter that can either be estimated or fit in a post-hoc manner. However, the \b{eta} factor can be derived from the transitions between valence and conduction bands in semiconductor quantum wells, together with knowledge of the cavity modes. Here we investigate the dynamic nature of the \b{eta} factor for MQW nanowire lasers, and show how it can be computed. We also examine the dependence of the spontaneous emission rate and spontaneous emission factor \b{eta} on the charge carrier density, quantum well thickness, and composition, and discuss the impact on laser threshold and operation.

Message-passing decoders are among the most promising candidates for scalable quantum error correction, yet their behavior in the low-error-rate regime remains poorly understood under realistic circuit-level noise. In this work, we introduce a systematic framework for identifying the graph structures that govern decoder failures and for using them to predict the resulting error floor. We apply exhaustive trapping-set enumeration directly to the detector error model of a bivariate bicycle code and test all low-weight fault configurations supported on the resulting structures. This converts the analysis of extremely rare logical failures into a finite structural search, avoiding the prohibitive cost of direct Monte Carlo simulation. We evaluate the framework on three iterative decoders with substantially different architectures and decoding heuristics. Remarkably, for \texttt{RelayBP}, the resulting prediction accurately reproduces the simulated error floor; for the others, it remains within the same order of magnitude. Despite their differences, leafless elementary trapping sets capture a substantial part of the low-weight error-floor contribution for all three decoders. Moreover, each decoder admits failures caused by fault configurations well below the correction capability implied by the circuit-level distance, revealing a substantial gap between code distance and practical iterative-decoding performance. These results establish trapping-set analysis as a practical framework for predicting error floors, exposing the structural weaknesses of iterative decoders, and guiding the joint design of decoding algorithms.

Which part of a Hamiltonian spectrum is physically relevant when both the initial state and interpolation preserve several symmetries? We address this question for a compact multi-register encoding of Minimum Set Cover. The represented symmetry combines register permutations with the faithful base action of the incidence automorphism group. We distinguish its fixed, symmetry-allowed space from the generally smaller cyclic space generated by the protocol and define gaps relative to isolated bands in that space. A sector-resolved Schur-complement bound certifies cover-measurement probability whenever the sector contains feasible covers and has positive invalid-state separation; the sector kinetic floor is essential. Exact orbit quotients expose inter-sector coincidences invisible to a symmetric protocol, while a stability theorem shows that transverse dark crossings persist under small symmetry-preserving perturbations. On an even-cycle family, the original linear interpolation has an exact global multiplicity closure while the joint-fixed excitation gap remains constant. For the same family we construct a Johnson/Metropolis parent path from a Dicke state to a Gibbs-amplitude state with cover probability $1-O(n^{-5})$. A zero-range comparison and a log-concave three-box coupling give the uniform cyclic-gap certificate $Ω(n^{-13})$. Quantitative derivative bounds then yield a polynomial adiabatic runtime in the abstract Hamiltonian-access model, conditional on Dicke-state preparation and access to the parent Hamiltonian. We make no quantum-speedup claim: the result is a rigorous separation of global, symmetry-allowed, and dynamically accessible spectral structure. Changing the initial state or breaking a preserved symmetry changes that accessible spectrum.

The quantum exchange fluctuation theorem relates the probabilities of observing heat transfer along and against the temperature gradient between thermal baths at different temperatures. We investigate how this relation generalizes when the baths exhibit non-Markovian dynamics. Using a microscopic collisional model, bath memory is generated through interactions between successive bath auxiliaries before each heat-exchange collision. We derive exchange fluctuation theorems for both direct bath-bath interactions and probe-mediated heat exchange in the steady-state regime. As an illustrative example, we consider heat baths with qubit auxiliaries and show that non-Markovian memory enhances the probability of heat-transfer events against the temperature gradient, modifying the predictions made by the conventional Jarzynski-Wójcik exchange fluctuation theorem. Our results establish a microscopic connection between environmental memory and non-equilibrium heat-exchange statistics.

We study the capacity of a memory-based quantum repeater in entanglement swapping between two quantum links with either single or multiple memories, which we refer to as the end-to-end (E2E) entanglement throughput, subject to a constraint on the minimum fidelity. In order to approximate the E2E entanglement throughput, we adopt queueing models, where quantum links can have different characteristics: memory capacities, entanglement attempt rates and success probabilities, as well as classical communication latencies. We develop a model for estimating E2E entanglement fidelity, while taking into account the heterogeneous dephasing and depolarizing dynamics of quantum memories and Bell-state measurements in entanglement swapping as well as classical communication delays and noises. Finally, with the help of our models for approximating the E2E entanglement throughput and fidelity, we use the maximum waiting times of entanglements in quantum memories at the repeater as optimization variables to maximize the E2E entanglement throughput while ensuring required minimum E2E fidelity.

Multipartite entanglement admits phenomena such as the activation of genuine multipartite entanglement (GME) and the existence of inequivalent classes of entanglement, and existing bipartite entanglement measures have no unique generalization to this regime. In this work, we define the Rains, monsoon, hurricane, and squall entanglement as generalizations of the bipartite Rains relative entropy, and we establish various properties of these entanglement measures. We also prove that the Rains entanglement is monotone under selective quantum operations that completely preserve the positivity of the partial transpose. We establish single-letter upper bounds on the one-shot and asymptotic rates at which a fixed pure state can be distilled from an arbitrary state in both the standard and probabilistic approximate distillation scenarios. Among the entanglement measures we define, the tightest upper bound on the one-shot pure-state distillation rate is in terms of the Rains entanglement. However, the activation of GME (or, equivalently, the tensor instability of biseparability) makes it unclear if the one-shot bound in terms of the Rains entanglement can be extended to a single-letter asymptotic bound. Instead, we establish upper bounds on the asymptotic pure-state distillation rate in terms of the hurricane and squall entanglement. Upper bounds on the GHZ- and W-distillable entanglement follow as a consequence. Additionally, we define the multipartite max-Rains entanglement, write it as a semidefinite program, and derive a dual program for it. Finally, we analyze these measures for quantum pairwise independent networks, and we establish a conditional gradient (Frank-Wolfe) algorithm for computing the Rains entanglement.

The non-equilibrium quantum thermodynamics of many-body open systems is notoriously rich, especially in the strong-coupling regime where strong system-bath correlations develop and interactions produce non-perturbative effects. Such systems can be described by `quantum impurity models' where the system and bath are treated on an equal footing as a single composite. Paradigmatic examples are the spin-boson and Anderson impurity models, in which system degrees of freedom interact with either bosonic or fermionic gapless baths. Here we study the quantum work distribution function (WDF) of such systems following a quench. Capturing the full continuum of many-body excitations in the WDF requires a non-perturbative solution of the underlying non-equilibrium quantum impurity problem. For this purpose, we extend the time-dependent numerical renormalization group (TDNRG) approach to the calculation of the WDF, which applies directly in the thermodynamic limit, can be used for arbitrary quench amplitudes at zero or finite temperature, and provides exponentially fine low-energy resolution. Our numerically-exact solution reveals power-law threshold behavior due to the Anderson orthogonality catastrophe when the work approaches its minimum value, with universal scaling collapse of the distribution below an emergent low-energy scale induced by system-bath correlations.

We formulate Floquet Green's functions for noninteracting single-band lattice electrons driven by a reservoir-stabilized single-mode Gaussian quantum light source. The source is prescribed externally and is not updated by the many-electron polarization, while an active electronic probe still conditions the source evolution through the Peierls coupling. The two time arguments of a Green's function share one source history: the lesser and greater components are obtained by convolving a shared-history four-endpoint kernel with the continuous bath kernels before the final source trace, while the bath canonical anticommutation relation yields an equal-time covariance that seeds the retarded and advanced one-leg propagations. The Peierls coupling is treated nonperturbatively within the prescribed-source model, and classical Floquet theory is recovered in the appropriate limit. Numerical calculations on a minimal one-dimensional model show finite-coupling quantum-source corrections beyond a prescribed classical drive, together with spectral reconstruction and occupancy redistribution for squeezed vacuum and squeezed coherent sources. The squeezing parameter and phase provide additional control knobs, beyond classical amplitude modulation, for both sideband structure and occupied weight. This work provides a theoretical framework for quantum Floquet engineering of condensed matter with an externally prescribed quantum light source.

Bit commitment is impossible to achieve with unconditional security, even in quantum cryptogra- phy. We show that statistically secure bit commitment, satisfying both hiding and binding, can be constructed from hybrid locked physical unclonable functions (HLPUFs), a hardware primitive that combines classical hardware tokens and quantum communication. Our protocol uses these hardware assumptions in a novel and non-trivial way to achieve the first mistrustful two-party cryptographic protocol based on hybrid hardware modules. We prove statistical hiding and binding under natu- ral assumptions on the HLPUF and using a carefully designed challenge generation algorithm as a subroutine of our bit-commitment protocol. The construction also yields the first hardware-based coin-flipping protocol. Our results suggest a new paradigm for secure two-party cryptography in quantum networks, combining rigorous security guarantees with a concrete route toward practical implementation.

The attention mechanism forms the foundation of many modern AI models such as the Transformer. In one subclass of problems where attention is used, inputs and outputs are bound to the probability simplex so that all outputs sum to one. In this setting, softmax attention admits an exact, component-by-component quantum realization. Attention scores are Hadamard-test statistics on block-encoded projections of amplitude-encoded inputs. The exponential softmax is the interior of a cosine-squared family generated by Born-rule measurement under an exact bijection, whose boundary expresses sparse attention with exact zeros at finite parameter values. The softmax temperature is a repetition count where post-selected measurement rounds realize discretized inverse temperature exactly. Value aggregation is a deterministic column-loading channel that dilates the column-stochastic value matrix. The gated residual is the preparation angle of a single ancilla, with the additive identity at a mixing angle of π/2. Every learnable parameter is a rotation-gate angle. The composed layer is exact in the infinite-shot limit with one measure-and-reload step per attention score; a fully-coherent variant is ε-approximate via quantum singular value transformation in the infinite depth limit. The algebraic core is machine-checked in Lean 4.

Negatively charged silicon-vacancy (SiV$^-$) centers in diamond offer an attractive platform for the development of many forms of quantum technology. However, questions remain in connection to how large ensembles of SiV$^-$ centers behave in concert. Here, we develop a computational model designed to simulate recent experiments where optical multidimensional coherent spectroscopy (MDCS) was used to examine a high-concentration sample of SiV$^-$ centers in diamond, revealing significant variations in spectral signature depending on the detection scheme. Simulation results reveal that strain effects are highly random in this system, with a characteristic axial strain of $2.8 \times 10^{-4}$ and a shear strain of $3.5 \times 10^{-5}$. They suggest in addition that highly strained centers (with values exceeding $1.5 \times 10^{-5}$) may become significantly decoupled from optical emission. The results have implications for the use of SiV$^-$ centers as quantum sensors.

A technique for realizing a universal set of fault-tolerant quantum operations is the code switching method, which leverages two quantum codes with complementary sets of transversal gates. To date, the application of this technique has been largely limited to families of color codes supporting a logical $T$ gate. No analogous code switching protocols exist for many other prominent families, such as rotated surface codes, or for finer $Z$-rotation gates. In this work, we first utilize the doubling technique as a unified framework to construct a class of quantum color codes encoding a single logical qubit with an arbitrarily large minimum distance, enabling the transversal realization of arbitrary small logical $Z$-rotation gates. We investigate the structural properties of this code family, demonstrating that they improve upon the parameters of state-of-the-art triorthogonal codes, achieve lower qubit overhead compared to certain known color codes, and admit single-shot decoding of $Z$-syndromes via meta-checks. Furthermore, we show that this framework extends beyond color codes; specifically, it enables the generation of $r$-orthogonal quantum codes, $r \ge 2$, that inherit the local geometry of rotated surface codes. We then provide an overhead optimization protocol alongside several candidate codes tailored for realizing logical $Z$-rotation gates within rotated surface codes. Finally, we extend the fault-tolerant code switching protocol based on transversal CNOT gates to incorporate fault-tolerant realization of $Z$-rotation gates at any level of the Clifford hierarchy for geometries compatible with rotated surface codes. We present the first demonstration of fault-tolerant magic state preparation by means of code switching within a distance-three rotated surface code using a total footprint of only 45 physical qubits, and evaluate its performance through a simulation.

We study the sample complexity of estimating the von Neumann entropy of an unknown $d$-dimensional quantum state. All previously known estimators require $Ω(d^2)$ samples, and plug-in estimators are known to face a quadratic barrier. We give the first subquadratic-sample estimator: for additive error $\varepsilon$, our estimator uses \[ O\!\left(\frac{d^2 \log^2(\log(d)) \log(1/\varepsilon)}{\varepsilon^2 \log^2(d)} + \frac{\log^2(d/\varepsilon)}{\varepsilon^2}\right) \] samples. In particular, for constant $\varepsilon$, the complexity is $O_\varepsilon(d^2\log^2(\log(d))/\log^2(d))=o(d^2)$. Our analysis introduces a new pinching inequality that bounds the entropy loss under a space direct-sum decomposition, together with a bias-corrected estimator for large eigenvalues and a new bounded-coefficient polynomial estimator for small eigenvalues.

We determine the smallest number of active questions per player at which a four-player binary exclusive-or (XOR) game of commuting-operator value one need not admit a Greenberger--Horne--Zeilinger (GHZ) equatorial realization. Such a realization uses the four-qubit GHZ state and equatorial qubit observables, reducing perfect play to additive phase equations. We prove that every four-player XOR game with commuting-operator value one and at most three active questions per player has a perfect GHZ-equatorial strategy. Conversely, we construct a uniform eight-clause game with four active questions per player whose commuting-operator value is one but whose phase equations are inconsistent. Thus four is the sharp local-question threshold. The positive result follows by lifting every integral incidence obstruction to an ordered noncommutative refutation, using primitive circuits, forest matchings, and ternary Hamming geometry. For the separating game, a Klein four-group incidence relation obstructs the phase system, while an even-subgroup normal form and degree-one and degree-two Magnus coefficients exclude refutations of arbitrary length.

We present a full-oscillator analysis of a finite-energy GKP CHSH test whose observed score yields robust Bell-pair self-testing. Periodically binned position and momentum give the Pauli settings, while a fixed binary coarse-graining of photon number modulo four and its displaced conjugate realize the tilted settings. For a number-filtered GKP source, we retain the finite codeword overlap, define the measurements on all photon-number sectors, and compute the physical correlations without logical post-corrections. With the canonical ideal-logical displacement \(d=\sqrtπ\), the CHSH value exceeds the local bound above \(4.56\) dB of per-peak squeezing, and Kaniewski's extractability bound becomes nontrivial above \(5.02\) dB. Calibrating only \(d\) using an independently characterized finite-energy parameter lowers these model thresholds to \(4.21\) dB and \(4.58\) dB, respectively; at \(12\) dB, it raises the score from \(2.69486\) to \(2.78858\) and the corresponding target-state overlap bound from \(0.90758\) to \(0.97243\). This calibration is fixed before Bell-test data are collected. The displacement activates the odd modulo-four sectors, so their fixed a priori assignments are a genuine finite-energy component. The large gain is specific to the deterministic phase-bit coarse-graining; independently calibrating the one-bit POVM with randomized odd-sector outcomes gives only a much smaller improvement. These are honest-model predictions, not loss, detection-efficiency, or finite-sample thresholds. In an experiment, a device-independent guarantee for an extracted Bell pair follows by inserting a confidence lower bound on the observed CHSH score into the self-testing theorem.

Quantum sensors promise measurement sensitivities that can scale at the Heisenberg limit, but in practice their performance is often degraded by noise, finite sampling, and implementation imperfections. In this work we present a general framework for improving parameter estimation in such settings by exploiting intrinsic structural constraints of time-domain correlation functions. Our approach builds on the observation of Kemper et al. [PRL 132, 160403 (2024)] that two-time correlation functions of Hermitian observables generate Gram matrices that are positive semidefinite, a property that can be violated in experimentally acquired data. We formulate signal reconstruction as a convex optimization problem that enforces positive semidefiniteness, Toeplitz structure, and low-rank priors motivated by the underlying dynamics. We show analytically that, under suitable conditions, the ground-truth signal can be uniquely identified in the noiseless case and recovered stably in the presence of noise. We further demonstrate numerically, in a GHZ-based magnetometry protocol, that enforcing these physical constraints can significantly improve frequency estimation from sparse and noisy data. In particular, we observe a clear advantage in the data-starved regime, where only a small number of time samples are available and standard spectral estimation methods, including matrix pencil techniques, provide limited or unstable improvement over direct fitting. While the reconstructed signals do not in general reach the shot-noise-limited performance, the proposed approach consistently reduces estimation error and recovers much of the underlying structure of the signal. These results indicate that incorporating universal physical constraints into data analysis can enhance the practical performance of quantum sensing protocols without requiring additional hardware resources or calibration.

In semiconductor single-spin qubits, high-fidelity quantum gates have been demonstrated; however, achieving consistent performance remains challenging due to variations in driven qubit coherence, which is less explored than free-evolution coherence such as $T_2^*$. Here, we report single-qubit gate fidelities above 99.999%, achieved by dramatically extending the driven-spin coherence time and suppressing off-resonant driving effects that are detrimental to accurate fidelity benchmarking. We demonstrate that removing proximal reservoirs significantly enhances the spin-locking coherence time ($T_{1ρ}$), a critical metric for qubits under microwave driving. Furthermore, we reveal that in typical spin qubit setups using parity readout and rectangular pulses, off-resonant excitation of neighboring qubits causes substantial benchmarking artifacts. By optimizing device conditions to mitigate microwave-induced degradation and implementing spectrally tailored pulse shaping, we achieve a $π/2$ gate fidelity of 99.99920(2)%, with remaining errors primarily limited by incoherent noise. These results showcase the mechanisms that bound fidelity benchmarking in state-of-the-art silicon spin qubits and provide practical guidelines for achieving and verifying high fidelities in these systems.

We prove inference-time quantum coordination advantages for specified AI state-tracking tasks. A solver compresses semantic history into a future-accessible boundary state and later answers a query. We count communication $B$, persistent instance-dependent memory $M$, and local work $D$; classical recurrence, caches, tools, and recomputation are allowed and charged. The central result is a boundary-preserving semantic-compilation theorem. It maps a finite one-way, streaming, or adaptive causal task into a semantic AI interface while preserving event order and access to past input. Classical boundary-state lower bounds and quantum-memory upper bounds transfer up to explicit compiler overhead, independently of the finite-precision recurrent architecture. Two applications have classical semantics. Matched-entity synopsis QA inherits the hidden-matching separation between $O(\log N)$ qubits and $Ω(\sqrt{N})$ classical boundary bits. Continual requirements auditing inherits a Max-$k$SAT streaming separation: a recurrent solver uses $O(\log^5 n\log(1/δ))$ qubits and polylogarithmic classical workspace to obtain a $0.7172$-approximation, whereas every classical one-pass finite-information solver attaining that ratio requires $Ω(\sqrt{n})$ coordination width. As a quantum-native compiler test, a stabilizer latent-state dialogue uses $n$ qubits, while every exact finite-state classical causal online realization satisfies $B+M \ge \frac{1}{2}n^2+(\frac{3}{2}-\log_2 3)n+O(1)$. The source protocols, streaming algorithms, and stabilizer witness are imported; the new result is their architecture-independent semantic transfer. These are memory and coordination separations, not runtime or empirical advantages for present-day language models. The stabilizer result assumes exact simulation and ideal noiseless quantum memory.

We study the role of ancillary entanglement in quantum channel parameter estimation and investigate the minimal ancilla dimension required to achieve the maximum Fisher information. We introduce the $k$-ancilla Fisher information, which quantifies the optimal estimation precision achievable with input states of rank at most $k$, and derive a variational characterization in terms of a rank-constrained optimization problem. This formulation leads to a simple characterization of the minimum ancilla dimension $k^*$ required for optimal estimation, given by the minimum rank among the maximizers of the associated variational problem. We further identify sufficient conditions under which ancillary entanglement provides no advantage, including channel families admitting a fixed measure-and-prepare representation and channels satisfying a natural horizontality condition. In addition, we derive a bound on the incremental gain in Fisher information obtained by increasing the ancilla dimension under suitable structural assumptions on the optimal input states. The general results are illustrated through explicit examples, including unitary channels, qubit depolarizing and amplitude damping channels. These results provide a systematic framework for understanding and quantifying the entanglement resources required for optimal quantum channel estimation.

Protected zero modes are a hallmark of topological phases of matter and are exponentially localized at sharp interfaces between distinct gapped phases. We investigate how this picture changes for smooth interfaces in a broad class of inhomogeneous Su-Schrieffer-Heeger (SSH) models. Combining an exact lattice solution with an inhomogeneous Dirac description, we show that the associated Jackiw-Rebbi zero mode becomes spatially extended. For arbitrary smooth hopping profiles, its lattice extension universally scales as the square root of the system size, independently of the microscopic details of the interface. This emergent length defines a mesoscopic critical region separating two gapped phases, within which correlations decay algebraically before crossing over to exponential decay. In addition, the entanglement entropy scales as the logarithm of the emergent length near the interface, confirming the interpretation of a mesoscopic critical region. Our results establish a universal critical length governing the low-energy physics of smooth topological interfaces.

Classical identification via a noisy channel is a communication task in which the receiver is not required to reconstruct the full transmitted message, but only to decide whether it coincides with a message of interest. This relaxation allows the number of identifiable messages to grow doubly exponentially with the blocklength. For quantum channels, the resulting (doubly exponential) identification capacity $C_{\mathrm{ID}}$ can strictly exceed the ordinary (exponential) transmission capacity $C$. In this paper, we prove that the entanglement-assisted transmission capacity $C_E$ is a strong converse bound for this task: $C_{\mathrm{ID}}\leq C_E$. For sufficiently low-noise channels, this bound can also be achieved via the Hayden-Winter (quantum) identification + fingerprinting codes. This yields an exact characterization $C_{\mathrm{ID}}=C_E$ of identification capacity for such channels. However, for general channels, we prove that this upper bound can be strict. We exhibit an explicit family of transpose-depolarizing channels for which $C_{\mathrm{ID}}<C_E$. As a consequence, we also obtain the first example of strict superadditivity of the identification capacity $C_{\mathrm{ID}}$.

Full quantum network nonlocality (FQNN) describes a scenario where all sources in a network are nonlocal. Existing criteria of FQNN can only be verified in star networks by violating a single Bell-like inequality. Here we propose a method that certifies FQNN in general quantum networks using only a single Bell-like inequality. We show that the topological obstacle to one-shot detection can be overcome by expanding the original network with a carefully chosen number of auxiliary local sources and parties. The correlations of the enlarged network are then tested with a single inequality; a violation implies that all original sources must be nonlocal. Our approach provides an efficient, experimentally friendly way to verify FQNN in any network topology.

We investigate the steady-state phase transition in a one-dimensional hybrid contact process. We implement the single-site and cluster mean-field approximations based on the effective fields and present all the possible steady states of the system. We show the existence of the stable absorbing and active phases, and the bistable region in the long-time limit. The saddle-node bifurcation is observed at the boundary between the absorbing phase and the bistable region, suggesting a discontinuous phase transition. While the absorbing to active phase transition is continuous. To characterize the nonclassical scaling behavior of the continuous phase transition, we extract the true critical points and exponents by means of the coherent anomaly method.

Two-photon blockade (TPB) besides the conventional one-photon blockade can control the photon at the level of individual quanta in the input-output measurements of light-matter coupling systems. Apart from conventional TPB (C-TPB) with opened cascade decay channel, unconventional TPB (U-TPB) with closed cascade decay channel may open novel avenues for manipulation of TPB. However, currently found U-TPB in linear coupling is limited in a narrow coupling window and the blockade strength is weak, which would hinder its applications. In the present work we propose to enhance the U-TPB by the Stark nonlinear coupling. Indeed, the introduction of the Stark nonlinear coupling to the linear coupling enables tuning of both cascade energy level and the anharmonicity which play key roles in the formation of TPBs. By investigating photon correlation functions and extracting phase diagrams in dissipation, we demonstrate that our scheme not only dramatically broadens the window of U-TPB to cover the entire strong-coupling regime but also deepens the blockading degree of the U-TPB by two orders. The cascade decay rates, state populations and the anharmonicity, are examined to identify and track the U-TPB and C-TPB. In the overview of phase diagrams we also reveal a broad U-TPB in ultrastrong couplings, with a crossover to the C-TPB. Since the Stark nonlinear coupling is realizable and tailorable, our proposal may pave a practical way for manipulation of the TPB.

We study pure disjoint $(r,δ)$-quantum locally recoverable codes (qLRCs) without assuming a stabilizer structure. We formulate local Knill--Laflamme conditions for recovery from up to $δ-1$ erasures within a recovery block, and introduce blockwise Shor--Laflamme and unitary weight enumerators that capture how error weight is distributed across recovery sets. We establish several properties of these enumerators and use them to derive a Singleton-like bound that strengthens the known bound for disjoint $(r,δ)$-qLRCs under a purity assumption, as well as a linear-programming upper bound on the code dimension. These results provide a non-stabilizer, weight-enumerator-based approach to the study of pure disjoint $(r,δ)$-qLRCs.

Understanding how fermionic exchange and Coulomb repulsion jointly shape two-electron correlations is essential for identifying genuine quantum signatures in multi-electron interference experiments. To address this interplay, we investigate Hanbury Brown and Twiss interference of two electrons generated by two independent needle-tip emitters within a full quantum-mechanical framework. In the absence of Coulomb interaction, the approach reproduces the results previously obtained within a quantum path formalism. For Coulomb-interacting electrons, we predict characteristic features absent in a semiclassical description: a pronounced Coulomb-dominated suppression region as well as Coulomb-induced phase offsets and fringe shifts. At the same time, outside of the Coulomb-dominated region, the spatial oscillation frequency is essentially governed by fermionic exchange symmetry. Our results establish quantitative parameter regimes for disentangling Coulomb interaction from fermionic exchange symmetry in such experiments.

Dynamical decoupling protocols provide a versatile toolbox for robust control of quantum systems, suppressing noise that would otherwise limit their performance. This tutorial aims to provide an intuitive interpretation of these protocols. Written from an experimentalist's perspective, we use the Bloch sphere picture to visualise quantum dynamics for a range of sequences. Here each dynamical decoupling operation can be viewed as an "effective field vector", whilst the phase and population of the two-level system is encoded into a "Bloch vector". The two-level dynamics are calculated by the cross product between these two vectors, such that the quantum state represented by the Bloch vector rotates around the effective field vector. Several prominent control schemes are simulated using this picture, starting with a Rabi oscillation, followed by the Ramsey sequence and a selection of pulsed and continuous dynamical decoupling techniques. These sequences are engineered to preserve control of the quantum system for as long as possible, with their efficacy often quantified by a coherence time. We clarify the definition of the longitudinal $T_1$, transverse $T_2$ and inhomogeneous $T_2^*$ coherence times, which are used across the literature. Each simulation has an accompanying animation to illustrate the protocol's two-level dynamics on the Bloch sphere. The custom simulation and Bloch sphere plotting scripts are also provided in an open access repository to allow the reader to reproduce, modify, and explore these results. Dynamical decoupling sequences have established themselves as an invaluable tool across the entire quantum technologies remit; by providing an open framework alongside this tutorial, we aim to make these protocols more accessible to new researchers discovering this thriving field.

In this work, we study $(r,t,x)$ quantum locally recoverable codes (qLRCs) with locality $r$, $t$ recovery sets per qudit, and intersection parameter $x$. We first show that, assuming the underlying classical codes have dual minimum distance at least two, a CSS code is an $(r,t,x)$-qLRC if and only if the underlying classical codes are $(r,t,x)$ classical LRCs (cLRCs) with common recovery sets. We then use subset-inclusion matrices to construct families of binary dual-containing $(r,t,x)$-cLRCs, which yield binary $(r,t,x)$-qLRCs via the CSS construction. For CSS $(r,t,x)$-qLRCs, we derive upper bounds on the dimension and rate, minimum-distance bounds in the pure case, and a Singleton-like dimension bound in the exact case. Finally, we show that these families attain high rates and nontrivial minimum distances.

The formation of Fabry Perot and guided wave self hybridized exciton polaritons in two dimensional materials results in long range exciton energy transfer and strong exciton exciton interactions. Here, we demonstrate that the coupling strength between photonic modes and excitons is significantly boosted by embedding the active excitonic layer in a metal clad WS2 waveguide. The photonic modes in this waveguide exhibit modified dispersion properties for both Fabry Perot type and guided wave exciton polaritons compared to pure WS2 flakes, and show an increased couplingr strength. Our results provide a robust approach for controlling exciton photon interactions and their coupling strength in hybrid heterostructures.

Optomechanical systems offer a promising platform for observing dynamical signatures of quantum gravity through precision measurements of quantum harmonic oscillator dynamics. However, most existing analyses consider only the linear radiation-pressure interaction while neglecting higher-order optomechanical couplings and laser phase noise. These neglected contributions can be comparable in magnitude to the predicted quantum-gravity corrections and may therefore introduce spurious signals or mask the genuine physical effect. Here we reanalyze two experimentally realized platforms, a Fabry-Perot optomechanical system and a membrane-in-the-middle optomechanical system, by incorporating the complete nonlinear dynamics and realistic laser phase noise. Using measured device parameters, we derive revised protocols for generalized uncertainty principle tests and establish practical sensitivity bounds. Our results demonstrate that previous idealized estimates significantly overestimate the achievable resolution, underscoring the necessity of including higher-order interactions and implementing effective laser phase noise suppression in realistic assessments of optomechanical quantum gravity tests.

Quantum software patterns provide high-level abstractions for building quantum programs, but there is still little empirical evidence on how they are adopted in practice. In prior work, we extended an existing quantum-pattern atlas into a 61-pattern catalog, created a knowledge base that links framework components to those patterns, and built a tool that mines pattern implementations from open-source code. We applied this tool on 80 projects and find that all 23 patterns occur in practice. In this work, we extend the tool with two additional matching channels and a vocabulary expansion step, and execute a quantitative evaluation of its accuracy on Qrisp, a framework not present in the knowledge base, reaching a micro-F1 of 0.712 against 0.449 without the expansion step. We then construct composition graphs that record calls among the high-level framework components associated with patterns and store them in a graph database. We use these graphs to examine how pattern implementations are assembled inside each framework, why patterns co-occur, and how much of a pattern's detection count comes from components called directly by developers rather than introduced through internal framework calls. We release qpa, an open-source mining pipeline, together with the knowledge base, which maps 286 framework components across five sources to the pattern catalog, maintained with the support of an LLM ensemble that classifies newly extracted components, and the resulting pattern usage dataset, to support reproducible studies on the adoption and evolution of quantum patterns.

We develop an analytical theory of anomalous transport in a noninteracting Anderson model with heavy-tailed hopping amplitudes. The broad distribution of hopping amplitudes gives rise to an extended intermediate-time regime with a subdiffusive effective exponent, despite the absence of interactions or genuine many-body effects. By solving the transport equations analytically, we derive the time dependence of the mean-square displacement and identify a continuous crossover from an intermediate anomalous regime to asymptotically diffusive transport. As the localization transition is approached, the spatial extent of the subdiffusive window diverges parametrically, while the crossover to conventional diffusion remains finite in units of $Γ_0^{-1}$. This produces an increasingly broad anomalous transport regime in space that can closely resemble Griffiths-type transport observed near the many-body localization transition. Our results demonstrate that rare hopping processes alone provide a microscopic single-particle mechanism for robust transport anomalies, establishing an analytical benchmark for distinguishing interaction-induced effects from disorder-driven dynamics.

Although considered a niche technique, muon spectroscopy provides a unique and complementary insight into a range of different materials from hard condensed matter to biological samples and everything in between. In matter, the muon has a mass of $\frac{1}{9}~m_p$ or $207~m_e$, and is a local probe of quantum states that can provide a focus on the bulk properties of materials. While often interpreted in a classical framework, the muon is itself a quantum particle and it is increasingly common for researchers to take account of this when thinking about muon spectroscopy experiments. In this perspective, we focus on the power of using this quantum treatment of muon spectroscopy, which is a key future direction for the technique.

Free electrons, driven by rapid advances in photon-induced near-field electron microscopy, have emerged as a promising platform for quantum information processing, including quantum computing and quantum sensing. However, conventional measurements that rely on the electron energy loss spectrum (EELS) are inherently destructive to electron qubits, thereby constraining their applicability. In this Letter, we propose a scheme that performs projection measurement on the electron comb basis, where high measurement precision can be achieved with bright squeezed vacuum states and strong PINEM couplings. Notably, this approach is not only nondestructive to electron qubits but also maximally incompatible with energy measurements, enabling alternative quantum information applications, such as quantum error mitigation and Einstein-Podolsky-Rosen steering detection. Our findings open an avenue towards a systematic understanding of quantum free electrons and towards the development of nondestructive free electron quantum information tasks.

For the often encountered problem of the Poisson equation, this work presents a quantum algorithm solving it based on the quantum Fourier transform (QFT) for periodic boundary conditions as well as free field conditions, where the latter is realized via the Hockney method. Besides the QFT and an initialization procedure for amplitude encoding, the algorithm just uses a procedure for multiplying the state vector by a diagonal matrix w.r.t. amplitude encoding. For the latter, two alternative implementations are considered here. The first variant is a version of the LCU method and the second is a sequence of multi-controlled rotation gates that represents a factoring of the multiplied values into absolute values and complex phase factors. The functionality of the algorithm is verified via comparing the results obtained from state vector simulations for one- and two-dimensional test examples with their analytical solutions. For the considered test examples, it is found that the success probability for obtaining the desired ancilla qubit subspace in the LCU version is a factor of around two higher than that for the sequence of multi-controlled rotation gates. However, the LCU version requires a number of ancilla qubits up to the number of qubits that is set to store the discretized source term of the Poisson equation in amplitude encoding, whereas the sequence of multi-controlled rotation gates demands only one ancilla qubit. Computations of the success probabilities for both variants furthermore indicate that the success probability converges for a specific problem with increasing resolution. Concerning the required computational resources for the quantum algorithm, the conclusion is drawn that while the QFT is a more efficient procedure than its classical counterpart, the current implementations of the other necessary steps in the algorithm diminish the efficiency w.r.t. the runtime.

Crystal anisotropy provides a powerful route for realizing direction-dependent transport in solid-state systems. While its influence on electronic transport is well established, the role of anisotropy in magnon spin transport in van der Waals magnets is largely unexplored. Here, in a nonlocal geometry, utilizing the monoclinic van der Waals antiferromagnet CrPS$_4$, we observe pronounced anisotropy in both electrically and in thermally excited magnon spin transport. Electrically generated magnons exhibit a magnon spin conductivity at least 2.2 times larger and a spin diffusion length at least 2.7 times longer for transport along the crystallographic-b axis compared to the crystallographic-a axis, where $λ_m^{a} \sim$ 211 nm and $λ_m^{b} \geq$ 575 nm. In comparison, at 8T, we find the nonlocal second-harmonic resistance associated with thermally excited magnons to be $\sim$7 times larger along the crystallographic-b axis at 25K. We further show that a magnon spin diffusion length cannot be reliably extracted from the nonlocal second-harmonic resistance, owing to the extended temperature profile within CrPS$_4$. Likewise, we show that the anisotropy in the spin Seebeck coefficients cannot be reliably estimated from the thermally excited magnon spin transport alone, as it is intertwined with the anisotropic heat conductivity of CrPS$_4$. Utilizing the electrically generated magnon spin transport, we demonstrate that intrinsic crystalline anisotropy serves as an effective control parameter for tuning magnon spin transport, opening new avenues for magnonic device engineering.

This paper develops a resource-bounded framework for evaluating practical controllability in open quantum systems using a trained graybox response model. Rather than treating controllability as a binary property of an idealised Hamiltonian model, the proposed approach evaluates the best-achievable process fidelity over a finite, hardware-realisable pulse family under explicit control constraints. The graybox model retains the known coherent dynamics while learning control-dependent open-system distortions from pulse-response data. The resulting surrogate predictions are used to reconstruct the implemented processes and compare them with Haar-random target gates. Practical controllability is then characterised through the distribution of best-achievable infidelities and an area-based summary metric. The framework is demonstrated for a driven qubit under closed-system, classical-noise, and combined quantum-plus-classical-noise dynamics, with pulse amplitude and inverse Gaussian width used as the control-resource coordinates. The results show how finite control resources and open-system noise jointly constrain the gate performance attainable by the chosen pulse family.

In systems with infinitely many degrees of freedom, fundamental results from quantum information theory can fail. An important example is the uniqueness of purifications: Even when two subsystems, described by commuting von Neumann algebras $A$ and $B$, are tomographically complete, purifications of a state on $A$ need not be related by unitaries in $B$. It was recently shown that this occurs precisely when Haag duality fails, i.e., when the commutant $B'$ is strictly larger than $A$. This raises the question of which fundamental entanglement properties survive in such a setting. We show that, for a pure global state, the ability to steer any ensemble decomposition of the marginal state on $A$ by measurements on $B$ is equivalent to the existence of a state-preserving conditional expectation from $B'$ onto $A$. This establishes a direct connection between quantum steering and subfactor theory. The key observation is that steering is equivalent to the existence of extensions of ensemble decompositions from $A$ to $B'$. Working with general Jordan algebras, we prove that unital positive maps have state-preserving left inverses if and only if ensemble decompositions can be lifted. For the inclusion $A\hookrightarrow B'$, a left inverse is precisely a conditional expectation, yielding the characterization above.

Two alternative approaches for studying Helium-like atomic ions in non-relativistic quantum mechanics are proposed: (I) a numerical approach, based on the Lagrange-mesh method which can easily reach up to 14-15 significant digits in the energy spectrum for any nuclear charge $Z$ with modest CPU time in single processor mode and (II) a highly-accurate, few-parametric interpolation formula for the energies {\it vs.} $Z$. The interpolation formula of general nature is proposed, it can be applied to the energies of any excited state of the helium-like sequence. It is based on matching the $1/Z$-expansion at large $Z$ and the Puiseux expansion with integer and half-integer powers around the so-called second critical charge $Z_B$, introduced by F and D Stillinger (1969, 1974), confirmed by the present authors in 2019 for the ground state $1^1 S$, then revisited here, and extended to the excited states in the present work. For example for the first two spin-singlet $1^1 S$, $2^1 S$ and the first two spin-triplet $2^3 S$, $3^3 S$ states this interpolation formula with nine free parameters can reach an accuracy of 10-14 significant digits (s.d.) in the energies for any physically-relevant nuclear charge $Z$, giving absolute accuracy at large $Z$. Many results are obtained for the first time.

The Uhlmann fidelity ${\rm F}(ρ_0,ρ_1) = {\rm tr}|\sqrt{ρ_0}\sqrt{ρ_1}|$ is one of the most fundamental quantities in quantum information theory for quantifying the closeness between two quantum states. Estimating the Uhlmann fidelity to within additive error $\varepsilon$ requires a number of copies of the states, or queries to their state-preparation circuits, that depends at least linearly on the smaller of the ranks of $ρ_0$ and $ρ_1$. Consequently, this rank dependence disappears when either state is pure, in which case the query and sample complexities depend only polynomially on $1/\varepsilon$. However, the known optimal estimator for ${\rm F}(ρ,|ψ\rangle\!\langleψ|)$ due to Fang and Wang (ESA 2025) requires prior knowledge of which state is pure. In this work, we remove this mathematically unnecessary prior-knowledge requirement and establish an optimal estimator for ${\rm F}(ρ, |ψ\rangle\!\langleψ|)$ under the sole promise that one of the two states is pure, without knowing which one. Our estimator is obtained by specializing the refined algorithmic Uhlmann transform of Utsumi, Nakata, Wang, and Takagi (2025) to the case where one state is pure. In this setting, the Uhlmann fidelity can be recovered as follows: apply a unitary dilation of ${\rm tr}_{\sf A}(|ψ_0\rangle\!\langleψ_1|)$ (or its inverse) to the reference register $\sf R$ of the purification $|ψ_1\rangle$ (or $|ψ_0\rangle$) on the registers $\sf A$ and $\sf R$, estimate the corresponding square-root amplitude in each case, and take the maximum of the resulting two estimates.

Computational electromagnetics plays a central role in many industrial applications but often requires substantial computational resources, particularly when fine spatial discretizations are needed. While classical approaches remain the standard, quantum computing offers the potential to accelerate large-scale simulations by encoding them with a limited number of qubits. Here, we investigate the performance and resource scaling of the Harrow-Hassidim-Lloyd (HHL) and Quantum Singular Value Transformation (QSVT) algorithms for solving linear systems generated by the finite-difference time-domain (FDTD) method, a widely adopted numerical scheme for discretizing Maxwell's equations. We benchmark their performance across representative industrial use cases, including radar propagation, lens simulations, and beamforming processes. Our results demonstrate the validity of the approaches, achieving state infidelities smaller than $2\cdot 10^{-3}$ with success probabilities greater than $10^{-3}$, compatible with practical quantum state sampling. Overall, we observe that the QSVT method consistently delivers higher accuracy. We further observe that the condition number of the linear matrix, a key factor governing the performance of quantum solvers, saturates as the number of spatial lattice points increases. This implies that the spatial grid can be scaled to realistic industrial dimensions without increasing the HHL or QSVT circuit depth due to ill-conditioned matrices.

Understanding how complex connectivity emerges in networks is a fundamental challenge in classical and quantum science. In classical random networks, complex subgraphs typically require relatively high connection probabilities, whereas quantum random network theory predicts that such structures can arise at a single, lower threshold through entanglement and local operations. Here, using an integrated silicon photonic chip, we experimentally realize a quantum subgraph predicted by quantum random network theory in a four-node quantum random network. Our integrated platform exploits probabilistic photon-pair sources and coherent control of path modes to prepare a structured quantum subgraph through local transformations and postselection, operating in a threshold regime that differs from classical random networks. We verify that the subgraph state exhibits genuine high-dimensional multipartite entanglement across the nodes, providing experimental evidence that quantum entanglement enables connectivity structures beyond classical accessibility.

In this paper, we investigate zero transfer on mixed graphs. Zero transfer is a quantum walk phenomenon in which the transition amplitude between two vertices is identically zero for all times, so that no quantum state transfer occurs between them. Using the Hermitian adjacency matrix, we derive necessary and sufficient conditions for zero transfer in mixed graphs. We then specialize these criteria to oriented circulant graphs, obtaining nonexistence results for prime order, structural restrictions for even order, and exhaustive computational classifications for small orders.

Group-IV color centers, such as the silicon-vacancy (SiV) defect, are highly promising for solid-state quantum technologies. However, nanodiamonds typically exhibit significant lattice strain and structural disorder, which degrade their optical properties and hinder the resolution of the fine spectral structure at cryogenic temperatures. High-pressure high-temperature (HPHT) annealing offers a potential route to relax internal strain, although the phase stability of diamond at the nanoscale under such conditions remains poorly constrained. Here, we investigate the structural evolution of nanodiamonds during HPHT annealing using a Paris-Edinburgh press coupled with in situ synchrotron X-ray diffraction at SOLEIL. A dedicated sample assembly combining nanodiamonds - NaCl - Pt enabled accurate pressure-temperature calibration and real-time monitoring of phase transformations. The diffraction data reveal that the onset of diamond-to-graphite transition occurs at approximately 1800 K at 2 GPa and 2120 K at 4 GPa under the applied HPHT heating protocol. These experimentally determined graphitization onsets define a practical pressure-temperature processing window for HPHT annealing of nanodiamonds while avoiding detectable graphitization and provide a calibrated framework for reliable off-beam annealing treatments that avoid graphitization. Photoluminescence measurements on samples annealed below the graphitization threshold show improved optical response, with partial resolution of the SiV fine structure at 12 K. These optical measurements suggest a relationship between nanoscale phase stability and the optical response of individual SiV-containing nanodiamonds following HPHT annealing. The experimentally established HPHT processing window provides a practical framework for the controlled processing of quantum nanodiamonds while avoiding graphitization.

GKP states enable fault-tolerant CV quantum computation, but their generation remains experimentally challenging due to their highly non-Gaussian and infinite-energy ideal structure. In this work, we present a realistic and scalable protocol for generating finite-energy resource states, specifically the qunaught state, using Schrodinger cat states generated in a strongly coupled quantum dot-cavity system. Our scheme combines deterministic squeezed cat-state generation, cat-breeding protocols, and homodyne measurements. Using numerical simulations, we analyze the role of various parameters of the quantum dot-cavity system in the generation of practical qunaught states. Furthermore, we quantify the trade-off between the fidelity and generation probability of these states and exploit the fact that accepting a structured set of homodyne outcomes can significantly enhance the overall success rate. The proposed approach is compatible with integrated photonics and telecom wavelengths, offering a promising route toward scalable CV quantum information processing.

In fault-tolerant quantum computing, fast and accurate decoding is crucial. Snowflake is a decoder for the surface code that runs in a streaming fashion. In this paper, we implement Snowflake on commercial FPGAs and validate them at room and cryogenic temperatures. Our results demonstrate high decoding throughput for small code distances that, when extrapolated, remains within acceptable limits for larger distances. Further, we incorporate the calculation of certain decoder confidence scores with negligible overhead both in terms of latency and physical resource utilisation. We note that implementing a large-scale system would require either a large FPGA beyond today's technology or clusters of FPGAs connected via a high-speed bus. Thus, we discuss an alternative architecture that exploits the locality of Snowflake by processing 2D slices of the 3D decoding window and offloading segments of the 3D structure to a high-speed memory.

Exact cylindrical solutions of the free Dirac equation provide natural single-particle modes for a broad class of axially symmetric relativistic fermion systems, including electron vortices, twisted-particle scattering, rotating matter, and cylindrical field quantization, but are commonly formulated in different internal bases. We derive the general regular positive-energy cylindrical solution at fixed energy, transverse and longitudinal momenta, and total angular momentum, and show how the commonly used spin-polarized, separation, helicity, and transverse-helicity modes are embedded in the resulting two-dimensional solution space. A conserved transverse operator resolves the residual doublet into two symmetry-defined branches. Their parameter-dependent eigenspaces admit a gauge-invariant quantum-geometric characterization, with opposite Berry curvatures, a common quantum metric, and saturation of the two-level metric--curvature relation. We further derive symmetry constraints on branch conversion and the corresponding reduced two-state dynamics. The resulting framework connects mode classification, symmetry resolution, quantum geometry, and dynamics across distinct cylindrical Dirac settings.

A nonzero commutator proves that two orderings differ as operators, but it does not ensure that a physical state can reveal the difference. We ask when non-Abelian ordering information becomes dynamically invisible. For Hermitian operators $B$ and $C$, we compare the evolutions generated by the opposite-order products $M=(B+iC)(B-iC)$ and $\widetilde M=(B-iC)(B+iC)$, and define their operational visibility from the minimum overlap of the output states over a normalized time window. This visibility bounds the difference produced by the two orderings in every observable on the chosen state. An exact one-qubit solution shows that the same fixed pair can be perfectly invisible in one state and visible in another. We then keep the ordered generators fixed and vary only the many-body ground state across a quantum phase transition. The same ordering difference is nearly invisible in one regime and clearly visible in the other. Moreover, states with identical leading quadratic decay can develop sharply different finite-time visibility because their first distinction appears at higher order. The effect persists across distinct operator pairs and coefficient perturbations. Thus dynamical Abelianization is a property of the state-dependent process, i.e., non-Abelian ordering information can become operationally inaccessible even though the underlying operators remain non-commuting.

Quantum metrology achieves Heisenberg-limited precision in single-parameter estimation, but its multiparameter extension is fundamentally constrained by both parameter-encoding and measurement incompatibility. Noncommuting signal generators may cause incompatible parameter-encoding, preventing the quantum Fisher information matrix from simultaneously achieving the Heisenberg scale for all parameters. Due to incompatible optimal measurements, the classical Fisher information matrix represents the practical attainable precision. Here, we introduce a multiparameter metrology framework based on indefinite evolution (IE), in which different control operations and signal reversal are placed in a coherent superposition. For a single-qubit probe with mutually orthogonal signal generators, IE enables compatible parameter encoding and optimal measurement without the signal reversal. For parallel generators, where only signal reversal realized by its generator is available, IE can achieve the same performance. We further extend this mechanism to noisy, many-body, and high-dimensional probes, and establish general conditions for achieving the simultaneous Heisenberg-limit. In contrast, definite evolution cannot achieve the same performance under compatible optimal measurements, even when signal reversal is available. Our results identify IE as an operational resource for overcoming multiparameter incompatibility and open a route toward attainable Heisenberg-limited sensing in interferometric platforms.

Universal approximation in reservoir computing is typically associated with a class of reservoirs. We show that universality can be associated with a single reservoir, considering a minimal setup of a single atom in front of a mirror. In its linear-transducer limit, our reservoir is a universal approximator of fading-memory maps under an operating class of checkable conditions, with a rate constant measured at the operating point. A given reservoir can reach arbitrary accuracy by changing measurement settings. The proof gives an explicit recipe: for a target accuracy, it specifies the required physical resources and resonator modes. Enlarging the number of accessible modes increases the matchable kernel span without reducing capability. Beyond the linear limit, the atom's saturation replaces high-order polynomial readouts, and the device operates on real-world tasks alongside classical baselines. Our results highlight an example of universality with a minimal quantum setup.

We show that private correlations in a bipartite quantum state constitute a metrological resource for distributed sensing assisted by a possibly noisy channel from one party to the other. We begin with an example with distillable secret key but poor locally accessible sensing performance and show that an assisting channel substantially improves its performance. We then prove a general theorem showing that positive private information in the encoding basis certifies a quantitative lower bound on the locally accessible sensing capability after assistance. We further show that classical correlations alone provide no analogous guarantee, whereas, in the absence of the assisting subsystem, the privacy-based guarantee reduces to an entanglement-based one. Finally, in a channel formulation, we show that a channel with positive private information allows nonzero locally accessible sensitivity when paired with a suitable assisting channel.

We study local marginals in one-dimensional translation-invariant quantum systems that may hide finite-period structure. Given an $n$-site reduced density matrix, we ask whether it can be obtained by repeating a finite $p$-site block state along the chain and averaging over the $p$ lattice translations. This defines a symmetrized block-product periodic marginal problem, which provides a route both to diagnosing hidden periodic order from local data and to upper bounding ground-state energy densities of infinite translation-invariant local Hamiltonians. We develop two complementary methods. The first is a semidefinite-programming relaxation based on block permutation symmetry and positive partial transpose constraints, which outer-approximates the convex hull of such marginals and yields certified infeasibility tests. The second is a symmetrized matrix product state ansatz, which constructs explicit block-product periodic states and gives variational upper bounds. We benchmark the framework on the Majumdar-Ghosh model, transverse-field Ising, XX, XXZ, and contextuality-related spin models. The results show that the method captures the expected finite-period structure in exactly solvable cases and gives systematically improving variational energies as the period and bond dimension increase. We also formulate a periodic-NPA relaxation for translation-invariant contextuality witnesses and recover the known quantum limits in the tested examples.

The redistribution of the wave feature, particle feature, and mixedness is investigated for two-qubit isotropic states in Schwarzschild spacetime under Hawking radiation and environmental decoherence. It is shown that Hawking radiation changes their relative weights among different horizon regions rather than simply suppressing them. The analysis is further extended to phase damping, phase flip, and bit flip channels. Phase damping monotonically suppresses the wave feature and enhances mixedness, phase flip produces a symmetric death-and-revival behavior of the wave feature, and bit flip mainly reshapes the particle feature and mixedness through diagonal population redistribution. However, although Hawking radiation and channel noise affect the distribution of wave feature, particle feature, and mixedness in the subsystems, the triality relation among them still holds and remains unaffected by thermal and environmental noises.

We introduce a programmable Heisenberg-limited bosonic quantum sensor based on a nonlinear quantum energy pump, implemented with a Kerr-nonlinear resonator coupled to multiple high-Q microwave terminal resonators. For parameter estimation encoded in an arbitrary number-conserving Hamiltonian acting on the terminal modes, we analytically construct optimal sensing protocols that attain the maximal quantum Fisher information, including initial-state loading, probe preparation, and readout. For diagonal multiparameter signals, we further show that the full phase-sensing quantum Fisher information matrix can be obtained from correlations of locally measured physical terminal works, providing a signal-free calibration of the metrological resource. We numerically demonstrate the construction and its robustness using realistic circuit-QED parameters while including experimentally relevant imperfections.

Multiparameter estimation remains a fundamental challenge in quantum estimation theory because the optimal measurements associated with different parameters are generally incompatible. In this work, we develop a Bayesian framework for the simultaneous estimation of multiple parameters. Our approach builds on Personick's method, in which the estimation problem is reduced to a set of Lyapunov equations whose solutions define optimal observables for the individual parameters. Since these observables generally do not commute, we construct a convex combination of the solutions, parameterized by a set of variational parameters. The spectral decomposition of the resulting operator defines a parametrized projection-valued measure. The resulting projective measurement determines the likelihood function, from which the minimum mean-square error estimators and the corresponding Bayesian mean-square errors are obtained, following standard Bayesian procedures, as functions of the variational parameters. To determine their optimal values, we formulate a minimax optimization problem based on the normalized Bayesian mean-square errors, introducing a min-max normalization procedure that enables a meaningful comparison of estimation errors associated with different parameters. This optimization yields a variationally optimized projective measurement for simultaneous Bayesian estimation. Two qubit examples, involving phase estimation and the estimation of parameters defining convex combinations of unitary operations, demonstrate the construction of optimized projective measurements and the corresponding minimum mean-square error estimators within the proposed framework for finite data sets.

We study incomplete sets of orthogonal stabiliser states that cannot be extended by a further stabiliser state orthogonal to all of its members. Such sets are the stabiliser analogue of unextendible product bases (UPBs), and we thus call them unextendible stabiliser bases (USBs). Leveraging the symplectic geometry underlying the $n$-qudit Pauli group in prime local dimension, we explicitly construct USBs for systems of four qubits and three qudits of odd prime local dimension. Moreover, we show that these are the respective minimal qubit, respectively qudit numbers for which such bases exist, and that USBs exist for all $n\geq4$ qubit and for all $n\geq3$ odd-prime-dimensional qudit systems. Finally, we compare the resource-theoretic aspects of USBs with those of UPBs. We establish that, analogous to the case of UPBs, the orthogonal complement of every unextendible stabiliser set is a stabiliser-free subspace, and its normalised projector is necessarily magic; moreover, it is bound magic in odd prime dimension, yet need not be for qubits. We also show that USB unextendibility alone imposes no uniform quantitative obstruction to discrimination by stabiliser operations.

Quantum coherence underlies collective quantum phenomena and emerging quantum technologies. Quantum gas microscopes have transformed quantum simulation by providing projective snapshots of many-body states with single-atom resolution, but spatially resolved measurements of off-diagonal correlations have remained elusive. Here, using the Talbot effect, we introduce a quantum coherence microscope that maps off-diagonal correlations onto site-resolved density signals with near-single-site resolution. We use this technique to locally probe the superfluid-Mott transition in a layer of a three-dimensional optical lattice and to measure coherence beyond nearest neighbors in an engineered potential landscape. By mapping off-diagonal correlations onto density signals through controlled Talbot evolution, this work opens new possibilities for accessing observables beyond the density basis through tailored matter-wave evolution and recapture.

The boundary quantity that captures the growth of black-hole interiors quantified by holographic complexity remains unknown beyond 2d dilaton gravity. We provide a critical analysis of a partition-function construction of Krylov spread complexity for thermofield-double states that provides a dimension-independent boundary reconstruction from semiclassical holographic partition functions, while developing the present dynamical and bulk construction for the BTZ saddle. In the double-scaled Sachdev-Ye-Kitaev model, where exact and semiclassical results can be compared, we show that the classical limit is reliable only when taken after the complexity has been reconstructed; taking this limit at the level of individual Lanczos coefficients discards essential information. Applying the construction to a large-central-charge two-dimensional conformal field theory above the Hawking-Page temperature dual to a Bañados-Teitelboim-Zanelli black hole, we find an intermediate departure from early-time quadratic growth followed by behavior compatible with a return toward asymptotically quadratic growth, rather than the linear late-time behavior of the volume and the standard finite-functional complexity = anything class. We then match this boundary behavior to a generalized complexity = anything bulk object built from an infinite series of extrinsic-curvature invariants. The construction provides a systematic route from black-hole thermodynamics to Krylov dynamics and can naturally be extended to higher-dimensional holographic black holes.

Two-dimensional translation-invariant topological CSS codes on qubits are known to be locally equivalent, after coarse-graining, to stacks of toric codes. However, existing constructions generally break more translation symmetry than is required to remove anyon-permuting translations, leaving open whether any further obstruction exists. We prove that no such obstruction occurs: after passing to the maximal anyon-preserving superlattice, every such code admits a local unitary decoupling into toric codes and product states. We further provide an efficient algorithm for explicitly constructing the decoupling map, together with bounds on the required supercell size and operator spreading. The decoupling requires no additional ancillas in generic cases and extends to finite systems with suitable boundary conditions.

Koszul-complex stabilizer models unify the toric-code hierarchy and bivariate-bicycle codes in one homological framework. To study translation-symmetry-enriched topological (SET) phases in these models and, more generally, in translation-invariant Calderbank-Shor-Steane (CSS) codes with stabilizer maps $(\varphi_X,\varphi_Z)$, we introduce the associated topological superselection profile $\mathscr S_σ:=τ_{\geq1}\mathbf R\!\operatorname{Hom}_R(\overline{\operatorname{coker}\varphi_σ},R),\ σ=X,Z$. Its cohomology layers $E_σ^\ell:=H^\ell(\mathscr S_σ)\cong_R\operatorname{Ext}_R^\ell(\overline{\operatorname{coker}\varphi_σ},R)$ encode sectors, fusion, and translation action. When finite, the $\ell=1,2,\ldots$ layers describe pointlike, looplike, and higher-dimensional excitations; $\mathscr S_σ$ retains inter-layer gluing. For regular Koszul models, we compute $E_σ^\ell$ explicitly, find $\mathscr S_σ$ single-layer, and obtain finite-size $Z$-logicals from $\operatorname{Tor}$. Single-layer means that at most one positive-degree layer $E_σ^\ell$ is nonzero. Our matrix-level Schanuel-lemma method proves rigidity: under a finite-resolution hypothesis, the nonzero layer and degree uniquely determine a topological CSS code's translation SET order at the stable translation-invariant Clifford level. For prime qudits the hypothesis is automatic, and a finite layer's translation kernel gives the exact minimal coarse graining to a toric-code stack. We realize admissible single-layer data. Beyond this regime, split and nonsplit extensions of 3D qubit toric codes yield eight models sharing all identical $E_σ^\ell$ layers with trivial translation action but having distinct size-dependent ground-state degeneracies, hence distinct translation SET phases. Thus inter-layer gluing carries SET data invisible to individual layers.

Learning algorithms for structured quantum unitaries and Hamiltonians have primarily considered classes of processes that are local or sparse in the Pauli basis. We turn our attention to learning $n$-qubit quantum unitaries $U$ and Hamiltonians $H$, given query access to $U$ or the unitary evolution of $H$, that may be dense in the Pauli basis but still admit concise Clifford decompositions. Specifically, we consider unitaries (or Hamiltonians) of the form $U = \sum_i α_i C_i$ over Cliffords $C_i$ with bounded Clifford extent $\sum_i |α_i|$. To extract this Clifford structure, we introduce an agnostic tomography protocol for Clifford unitaries that given query access to an unknown unitary $U$ with optimal Clifford fidelity $\textsf{opt}$, outputs a Clifford unitary witnessing fidelity $\geq \textsf{opt} - \varepsilon$ for some error $\varepsilon > 0$, in time $\textsf{poly}(n,(1/\varepsilon)^{\log(1/\varepsilon)})$. We then apply this protocol to obtain tomography protocols for unitaries and Hamiltonians that have bounded Clifford extent. This extends learnability of Hamiltonians from those with sparse Pauli decompositions to those that are dense (i.e., has sparsity $Ω(2^n)$) in the Pauli basis but are Clifford structured.

Silicon T centers are promising spin-photon interfaces in solid-state platforms for telecom-compatible, scalable quantum information technologies. A major challenge for T centers in nanophotonics is spectral diffusion, where fluctuations in the local electric-field environment from surface and bulk charge states broaden the optical transition and reduce photon indistinguishability. Strategies that directly suppress spectral diffusion are therefore critical for improving T-center-based quantum photonic devices. Here, we use atomic-layer-deposited Al2O3 to passivate the silicon surface and demonstrate a systematic narrowing of T center optical linewidths. Across our measurements, Al2O3 passivation reduces the T center emission linewidth by up to 57%. Complementary above-bandgap illumination and spectral hole burning measurements show that the remaining linewidth contains a significant spectral-diffusion component caused by adjacent charge traps, while placing an upper bound of approximately 75 MHz on the homogeneous linewidth. This work provides a CMOS-compatible path toward generating indistinguishable photons from silicon T centers for scalable quantum photonic applications.

Nonlinear stochastic differential equations (SDEs) underlie molecular modeling and drug discovery, quantitative finance, stochastic learning, and uncertainty quantification. Their expectations, event probabilities, and time correlations are therefore natural targets for quantum computation, but nonlinear drift and averaging over noise realizations obstruct a direct quantum representation. We develop an exact \emph{Kolmogorov--Lindblad mapping} (KLM) at the level of the probability law, encoded natively as a trace-one quantum density operator. For each Brownian realization, the pathwise density admits a half-density whose evolution is a stochastic Schrödinger equation. Averaging the associated pure states yields a Lindblad equation for $Γ(t)$ whose diagonal kernel is exactly the Fokker--Planck density, $p(t,x)=Γ(t;x,x)$, with classical diffusion represented by decoherence through Hermitian jump operators. Statistical observables become quantum expectations without the unknown time-dependent normalization introduced by direct amplitude encoding of the density, and classical two-time correlations admit an exact quantum regression formula. A structure-preserving Galerkin projection retains the Lindblad form at finite dimension, placing classical SDEs and open quantum dynamics on the same quantum-native computational footing. Numerical experiments for double-well Langevin dynamics and noisy Lorenz--63 exhibit rapid convergence of statistical observables. KLM thus provides a mathematically controlled path from general nonlinear stochastic dynamics to quantum channels, while isolating function approximation and coherent operator access as the remaining determinants of algorithmic efficiency.

In this work, we define entanglement-assisted quantum locally recoverable codes with availability, in which any set of up to $δ-1$ erased qudits can be recovered from any one of $t$ local recovery sets, each of size at most $r+δ-1$, with the recovery sets intersecting exactly in the erased coordinates, where $r$ is a (small) positive integer. We show that shared entanglement permits $t>1$, meaning that multiple local recovery sets can be available for the same set of up to $δ-1$ erasures. We establish a Singleton-like bound for this family of codes and present random constructions based on classical linear codes with Vandermonde parity-check matrices. We also provide explicit constructions of entanglement-assisted quantum locally recoverable codes with availability from several classical code families and their folded versions, including Tamo-Barg codes, fiber-product codes, and algebraic-geometry codes such as one-point Hermitian and Suzuki codes.

The description of open quantum system dynamics beyond the perturbative treatment (usually associated with Markovian master equations) is a computationally challenging task due to the unfavorable exponential scaling of memory kernels. Developed over recent decades in the context of quantum information and condensed matter, tensor networks provide both a new formalism and a toolbox for overcoming previous computational bottlenecks. This framework enables the formulation of non-perturbative, numerically exact methods for describing the dynamics of open quantum systems to controllable numerical accuracy. In this review, we present these methods and discuss their commonalities and differences to paint a comprehensive view of the field.

A quantum state is called absolutely separable (resp. absolutely positive partial transpose (APPT)) if it remains separable (resp. positive partial transpose (PPT)) under any global unitary transformation. It is known that the set of all absolutely separable states is a subset of the set of all APPT states. Moreover, these two sets are identical for qubit-qudit systems. In this note, we give an upper bound for the purity of APPT bipartite states (and therefore for the purity of absolutely separable bipartite states). For qubit-qudit systems, this upper bound becomes the maximum purity of APPT (and absolutely separable) states.

We revisit the notion of ``quantum information flow'' introduced in Bob Coecke's early work and seek to give it an explicit string-diagrammatic formalization. Given a semantics preserving string-diagram rewriting sequence, we first distinguish apparent through-paths, which depend on the current graphical presentation, from genuine through paths, which can be compatibly inherited through successive rewrites to a terminal decoupled bare wire factor. We then formally define a ``Coecke flow line'' in terms of this compatible inheritance relation. In particular, we use the ZX calculus, i.e., the ZX string diagram rewriting system, to illustrate the resulting formalism. In the physical setting of quantum protocols, a Coecke flow can be interpreted as a constrained, quasi-local, line-like presentation of a target bare wire morphism factor within the protocol string diagram.

The barren plateau (BP) phenomenon poses a fundamental challenge to the trainability of variational quantum eigensolvers (VQEs) by causing exponentially vanishing gradients as the system size increases. While extensive studies have investigated the geometric origins of BP, its impact on the optimization dynamics and complexity of practical algorithms under finite-shot measurements remains poorly understood. In this paper, we develop a theoretical framework that characterizes how the BP affects the optimization dynamics of the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm and quantifies the resulting iteration complexity and measurement budget. We derive non-asymptotic bias and variance characterizations of the SPSA gradient estimator, introduce a signal-to-noise ratio analysis to quantify gradient reliability, and establish convergence guarantees for SPSA under finite-shot measurements. Our results show that the exponentially decaying gradient energy associated with BP leads to an exponential increase in the number of iterations required to achieve a fixed relative optimization accuracy, which in turn results in an exponential increase in the total measurement budget.

Carleman lifting converts nonlinear polynomial dynamics into finite linear systems, but the resulting truncations are generally nonunitary and need not correspond to physical quantum evolution. We prove that a finite linear endpoint admits an autonomous Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) realization on vacuum coherences if and only if it is invertible and power bounded. The construction is explicit and realizes the nonunitary map directly as open-system dynamics, with no endpoint postselection and with one encoding and one decoding over repeated timesteps. We apply the result to the complete D2Q9 multiple-relaxation-time lattice Boltzmann (LB) timestep by compiling collision and periodic streaming into a single Carleman endpoint. The resulting GKSL evolution reproduces the classical Carleman trajectory over multiple timesteps, while the remaining discrepancy from nonlinear LB dynamics is the expected Carleman truncation error. The result establishes a general criterion for autonomous open-quantum realization of finite nonunitary dynamics, with Carleman--LB dynamics as a concrete example.

Detection-efficiency mismatch is a common problem in realistic quantum key distribution (QKD) systems. The existing security proofs for the case of the passive basis choice provide a nonzero secret key rate only for a small detection-efficiency mismatch. Unfortunately, in realistic setups, the detection-efficiency mismatch can be significant. Here we present a more precise estimation of the secret key rate for the BB84 protocol with the passive basis choice, which accounts for the detection-efficiency mismatch between four threshold detectors as well as an adaptation of the decoy-state method. The suggested approach is used to estimate the secret key rate in a QKD experiment between the Micius satellite and the Zvenigorod ground station.

Open boundaries host symmetry-protected Majorana modes, yet their imprint on the stabilizer Rényi entropy is obscured by a nonuniversal volume law. At Rényi index $α=1/2$, we isolate a bulk-subtracted boundary response in free-fermion BDI chains using exact finite-open-chain relations, large-$L$ Pfaffian evaluations, and direct positive-weight checks. Across a mass inversion, this response approaches $|Δω|\ln 2$, where $Δω$ is the change in winding number. The response survives primitive bulk deformations, the tested local boundary perturbations, and broken bulk duality. Thus, for the families studied here, the boundary response counts the Majorana channels that change the fermionic SPT index.

Quantum computing is a promising way to study problems that are difficult for classical methods, but current quantum hardware still faces limits in scale, noise, and fidelity. Running quantum algorithms on physical machines can also be costly. Quantum circuit simulators therefore remain important because they let researchers design and test algorithms on classical computers before using quantum hardware. Most high-performance simulators provide GPU backends, while few offer native support for NPUs. This gap limits the computing platforms available for quantum-algorithm research. We developed Aicir to provide a full-stack quantum circuit simulator with a native Huawei Ascend NPU backend. Aicir connects circuit construction, several state representations, measurement, differentiation, variational algorithms, quantum machine learning, and quantum architecture search through one programming model. It also supports noise simulation, tensor-network and matrix-product-state engines, and distributed state simulation. On the NPU, paired real tensors, fixed-rank gate views, and hardware-specific formulas keep the tested simulation paths on the device. The same representation lets Aicir partition a state across $2^{p}$ NPUs while retaining reverse-mode differentiation. We validated native execution with CPU fallback disabled and checked distributed communication and gradients on 2, 4, and 8 NPUs. For the tested fused layered circuits, Aicir's CPU runtime is within $0.97$--$1.28\times$ that of Qiskit Aer and $0.76$--$1.10\times$ that of Cirq. These results place its CPU execution in the same range as established simulators for this workload, while the NPU tests establish correct native execution rather than CPU-to-NPU speedup.

Fault-tolerant quantum computation architectures are frequently bottlenecked by the overhead of producing high-fidelity magic states. In this work, we use algebraic geometric techniques to construct codes over binary extension fields $\mathbb{F}_{2^s}$, thus discovering new protocols for the distillation of qubit magic states, where our focus is on the regime of practical qubit-based quantum computing architectures. To do this, we show that multi-qubit gates of interest such as $\text{CS}$, $\text{CCZ}$, and $\text{TOF}\# = \text{CCZ}_{123}\text{CCZ}_{345}$, can be packaged into simple gates over the larger fields, and we derive simple algebraic conditions in the extension fields allowing the distillation of these gates. Because they are derived from Galois qudits, the corresponding qubits codes naturally handle the correlated errors present on such multi-qubit states. Moreover, the protocols we discover are extremely compact; for example, we show that 4 $\text{CS}$ states can be distilled to 1 $\text{CS}$ state at distance 2, using only 4 logical qubits. For a case study, we consider the distillation of $\text{CS}$ and $\text{CCZ}$ states from injected $\text{T}$ and $\text{CS}$ states. When optimized for magic state production per unit time, or logical spacetime volume, we find that our protocols outperform the state-of-the-art in almost every situation, both at input error rates $10^{-3}$ (direct injection), and $10^{-6}$ (allowing some cultivation pre-injection).

We study the emergence of complexity in finite-size quantum systems as their dynamics transition from closed and coherent evolution to interacting and effectively open behavior. Using a state-based geometric framework, we represent mixed quantum states as probability measures on complex projective Hilbert space. This representation allows us to track how interactions reshape the underlying pure-state geometry. We introduce two complementary diagnostics: a distinguishability measure, based on the Wasserstein distance between probability-measure representations of mixed states, that quantifies sensitivity to initial states, and a state-space coverage index that measures long-time exploration of the subsystem state space. These diagnostics provide a geometric perspective on the emergence and evolution of quantum dynamical complexity. When applied to the quantum kicked top, both diagnostics generally increase with interaction strength. Their dependence on environment size is structured by parity symmetry, with integer-spin systems often exhibiting greater sensitivity and state-space coverage than half-integer-spin systems. These results highlight finite-size quantum effects and provide a geometric approach to quantifying dynamical complexity deep in the quantum regime

We investigate the dynamics of entanglement in a generalized version of the kicked Ising chain, extending the model from the standard qubit case (local dimension $q=2$) to higher local dimensions ($q > 2$). We identify the existence of ''dual-unitary'' points where the model's space-time duality allows for exact analytical solutions. Our analysis reveals that while a few unique dual-unitary points exist analytically for systems with local dimensions $q=3$ and $q=4$, such points do not exist for $q \ge 5$ due to the lack of a unique kicking strength that satisfies the required matrix element conditions. Utilizing the transfer matrix method and a replica trick specifically adapted for higher dimensions, we derive exact expressions for the growth of entanglement entropy in the $q=3$ (kicked Potts-type) model starting from a class of solvable initial states. Our results demonstrate that at the dual-unitary point, both Rényi and von Neumann entanglement entropies grow linearly with time until reaching a maximum value determined by the subsystem size.

We investigate the role of symmetry-protected dark states and metastable-like frozen states in the autonomous charging dynamics of open quantum batteries described by a transverse-field Ising model. By comparing local and collective dissipation over a range of system sizes, temperatures, and magnetic phases, we demonstrate that collective dissipation generates symmetry-protected dark states together with a much larger set of frozen (metastable) states, forming an extended protected Hilbert space. We derive the multiplicity of the collective dark sector analytically, showing that it follows the Catalan sequence for even system sizes, while such states are absent for odd sizes. Our results show that collective dissipation can enhance ergotropy and charging power, with its advantage depending on temperature, magnetic phase, and system size. While the number of dark and frozen states is identical in the ferromagnetic and antiferromagnetic phases, the achievable ergotropy differs substantially because of the different spectral locations of these protected states. In particular, the antiferromagnetic configuration exhibits considerably larger extractable work owing to the favorable positioning of the protected subspaces within the many-body energy spectrum. Finally, we analyze the active Hilbert-space fraction and show that metastable protection provides an effective mechanism for suppressing dissipative losses while preserving efficient charging pathways. These results establish the dark-state and frozen-state sectors as key resources for optimizing the performance of open quantum batteries through engineered dissipation.

Quantum algorithms for nonlinear partial differential equations remain challenging because nonlinear dynamics are not directly amenable to unitary quantum simulation. Building on the level-set formulation, we construct a quantum algorithm and provide an explicit gate-level implementation for solving scalar conservation laws. The nonlinear equation is first lifted to a linear Liouville equation, discretized by finite differences, and then embedded into a unitary evolution through Schrödingerisation. We further develop quantum procedures for estimating relevant observables from the evolved state. Error bounds and gate-complexity estimates are established for the complete algorithm. The resulting complexity comparison demonstrates a quantum advantage for observable estimation in sufficiently high spatial dimensions, under standard assumptions on state preparation and oracle access. Finally, numerical experiments validate the accuracy, multidimensional applicability, and predicted scaling of the proposed method.

Practical quantum key distribution (QKD) receivers may leak information about their measurement outcomes and settings to the channel (e.g., through detector backflashes or back-reflected Trojan-horse light) that could compromise the protocol's security. Here we present a simple finite-key security proof based on phase-error estimation for prepare-and-measure QKD in the presence of either a priori information leakage about the basis choices and/or a posteriori information leakage about the measurement outcomes. The proof requires only a bound on the distinguishability of the side-channel states. Furthermore, the analysis is modular and compatible with existing security proofs that address detector and source imperfections, making it applicable to a wide range of practical QKD implementations.

We study effective spin interactions arising from quantum electrodynamics (QED) scattering between localized fermionic spins. By integrating out photon and mediator fields, the dynamics reduce to an effective spin Hamiltonian. For two qubits in the nonrelativistic regime, the resulting interaction takes a tensor dipolar form with an asymptotic decay proportional to \(R^{-3}\). We obtain analytical expressions for the entanglement negativity, highlighting its dependence on coupling strength and spatial configuration. We then examine a setup in which two bath spins interact via a sequential exchange with an intermediate fermionic mediator. At the perturbative order considered, the mediator remains unentangled and induces an effective bath--bath interaction with stronger spatial suppression than in the photon-mediated case. Extending the construction to an \(N\)-spin setting yields an effective interaction network mediated by virtual exchange processes, which can support the generation of multipartite entanglement across the system.

Correlations that do not admit a deterministic explanation are a central feature of quantum theory and a key resource for quantum information processing. Identifying and certifying such correlations, however, remains a fundamental challenge. In this work, we advance on this problem by considering deterministic correlations in the prepare-and-measure scenario consistent with a wide range of communication restrictions. To certify correlations incompatible with such deterministic models, we ask whether they admit a scenario in which measurement outcomes can be perfectly predicted by an adversary equipped with classical side-information. We show the usefulness of this approach and propose semidefinite programming relaxations tailored to three representative communication restrictions: fixed ensemble, bounded overlaps and restricted observables.

Fluid dynamics workloads are dominated by repeated solves of large, structured linear systems, motivating the search for quantum acceleration. The Variational Quantum Linear Solver (VQLS) is a leading near-term candidate, but practical deployment on hybrid quantum--high--performance computing (HPC) systems faces three persistent challenges: (i) the linear-combination-of-unitaries (LCU) encoding of the system matrix explodes in memory and runtime as the problem size grows, (ii) ansatz selection is largely empirical, with no clear link between standard circuit metrics and solver convergence, and (iii) end-to-end VQLS pipelines have rarely been exercised on production HPC hardware at non-trivial qubit counts. This work addresses these challenges through three contributions. First, we benchmark four matrix-encoding strategies---naive LCU, PennyLane-integrated, Fast Walsh--Hadamard Transform (FWHT)-based parallel Pauli decomposition, and an singular value decomposition (SVD)-based two-term LCU---and show that the FWHT approach reduces peak memory by up to $1298\times$ on an $11\times 11$ Hele--Shaw grid, while the SVD-based coherent VQLS delivers over $10{,}000\times$ per-iteration speedup over standard Pauli-based VQLS at 8 qubits. Second, we evaluate 11 ansatz families with gradient-free and gradient-based optimizers on canonical Hele--Shaw flow, and find that expressibility and entanglement metrics correlate only weakly with VQLS convergence, motivating problem-aware ansatz design. Third, we deploy the full workflow on the OLCF Frontier supercomputer and successfully simulate a 15-qubit tridiagonal Toeplitz system on a single node. Together, these results establish a practical baseline for VQLS in hybrid quantum--HPC computation fluid dynamic (CFD) workflows and identify the remaining bottlenecks for larger problems.

A key challenge when designing hybrid quantum-classical workflows is the identification of quantum candidates, that is, determining for which specific problems quantum advantages could potentially be achieved. When choosing between several candidates, it is crucial to consider the characteristics specific to the problem, as these can fundamentally determine how successful quantum or classical approaches will be. This implies that specialized expertise is needed to use hybrid quantum-classical workflows successfully. To address this challenge, we propose a domain-specific language (DSL) to express best-practices in solution strategies using a universal representation that is easy to use and share. This DSL provides a flexible approach to design hybrid quantum-classical workflows and to automate decisions for a wide range of problems, supporting decisions down to problem-specific details while remaining technically independent. Furthermore, we propose a framework that is built around our DSL that enables the execution of defined workflows using the ProvideQ toolbox as an orchestration layer. All contributions from this publication are open source.

In the Noisy Intermediate-Scale Quantum (NISQ) era, limited qubit availability and hardware noise constrain the practical deployment of quantum machine learning (QML). Existing quantum neural network (QNN) and quantum convolutional neural network (QCNN) architectures often require increasing quantum resources as the input dimension grows, limiting scalability on near-term devices. We propose QSVM-RQNN, a low-qubit framework integrating centroid-based Quantum Support Vector Machine (QSVM) similarity learning with Recurrent Quantum Neural Networks (RQNNs) for fault classification. The framework reduces the feature space using principal component analysis (PCA), partitions the reduced representation into sequential timesteps, and processes them using a compact three-qubit recurrent quantum architecture with shared parameters. Two complementary variants are developed: QSVM-RQNN-V1 performs class-conditioned joint quantum encoding of input and centroid segments, whereas QSVM-RQNN-V2 performs recurrent learning over timestep-wise quantum similarity representations. Experimental evaluation on multiple fault diagnosis datasets shows competitive and, in several cases, state-of-the-art performance compared with QSVM, QNN, QCNN, QSVM-QNN, QSVM-QCNN, and RQNN models. The proposed architectures provide favorable performance-efficiency trade-offs, improved recall, and enhanced fault detection on highly imbalanced datasets. These results demonstrate that integrating centroid-based quantum similarity learning with low-qubit recurrent representation learning provides an effective and scalable approach to condition monitoring and fault classification on resource-constrained NISQ devices.

Projective measurements are foundational for quantum physics in general and quantum information tasks in particular. However, their direct implementation is often not warranted. Here, we investigate under what conditions continuous monitoring that manifests in quantum jump trajectories realises projective measurements over time. Considering finite-dimensional quantum systems and single, diagonalisable jump operators, we show if and how the detected quantum jump statistics force, and allow inferring, the convergence of individual quantum trajectories towards eigenstates of an observable in the long-time limit. We identify a necessary non-degeneracy condition that is related to the presence of a strong symmetry with non-degenerate symmetry sectors. We derive analytical expressions for the rate of convergence and the time-error relationship in finite-time measurements. Our results provide a transparent framework for understanding the emergence of projective measurements from continuous monitoring, with direct implications for the optimisation of quantum measurement protocols in experiments.

Diffusion-based quantum state tomography (QST) has shown promising results, but all existing methods implicitly adopt a single parameterization---typically Cholesky---without systematic evaluation. We present a design space study of density matrix parameterizations for diffusion QST, introducing a geometric framework based on the Jacobian Gram matrix $\mathbf{J}^\top\mathbf{J}$ that quantifies two competing criteria: isometric conditioning and physical constraint satisfaction. Our calibration of seven parameterizations at 2- and 3-qubit scales reveals three key findings. First, isometry and constraints are orthogonal criteria---no single parameterization optimizes both. Second, theoretical elegance does not predict geometric quality: the exponential map exhibits a spectral range of $149\times$ at 2 qubits and $75\,658\times$ at 3 qubits, while simpler parameterizations remain well-conditioned. Third, geometric conditioning alone does not fully predict end-to-end performance: without classifier-free guidance (CFG), Hermitian direct outperforms Bloch despite worse local isometry; under CFG, the ranking reverses due to amplified boundary effects. End-to-end training confirms that better-conditioned parameterizations converge faster and achieve higher fidelity in the absence of CFG. We provide actionable selection guidelines to guide future QST method design.

In this work, we study the emergence of relativistic effects in a composite quantum clock within the Page-Wootters relational formulation of quantum mechanics. We consider a system with internal and center-of-mass degrees of freedom and analyze the conditioned evolution of the center-of-mass relative to the internal system treated as an internal clock. We show that the internal sector exhibits an effective time dilation. Retaining the full mass-energy structure of the composite particle, a back-reaction of the internal energy on the center-of-mass sector appears through an operator-valued normalization factor. As a direct consequence of the back-reaction, the conditioned center-of-mass dynamics is governed by a Schroodinger equation that is non-local in the clock time, with an effective temporal non-locality of the order of the Compton time of the composite system. Applying the formalism to a center-of-mass momentum superposition, we find that the interferometric visibility acquires a correction that is quadratic in the internal energy, and therefore depends on the absolute distribution of clock energies rather than only on the energy gaps that control the standard time-dilation dephasing. Although this correction is parametrically small, it is a generic feature of relativistic composite clocks and can, in principle, be isolated through a differential visibility measurement comparing clocks with equal transition frequency but different mean internal energies.

A well-balanced decoder has been central to the development of modern fault-tolerant quantum computing. However, the inherent topologies of quantum error correcting codes can limit the performance of many well-studied decoding algorithms. In this work, we introduce Noise Assisted Ensemble Decoding (NAED), a highly accurate decoding framework with a significant advantage in real-time speed. NAED constructs an ensemble of Tanner forests, obtained as acyclic subgraphs of the original Tanner graph, and performs exact inference on each Tanner forest using a lightweight dynamic programming algorithm. The forest construction is guided by synthetic soft information derived jointly from the measured syndrome and channel statistics, with controlled noise perturbations generating diverse yet informative decoding matrix column orderings for the Tanner forest construction across the ensemble. Our benchmark results show that the proposed synthetic soft information-driven construction and inference on the Tanner forests can achieve improved or comparable decoding performances to the state-of-the-art decoding solutions, such as BP+OSD$0$, while also providing orders-of-magnitude improvements in per-round decoding speed under circuit-level noise.

Automatic uncomputation aims to provide programming-language-level support to facilitate the correct and safe use of ancilla qubits in quantum computing, but efforts have only been made for clean ancillas, leaving dirty ancillas unexplored. We present a unified formalization of the uncomputation of both clean and dirty ancillas. For the first time, we prove that checking the existence of uncomputation is coNP-hard. We introduce two complementary synthesis-oriented existence-checking methods: a rewrite-based normalization algorithm (RwUn) and a template-based reasoning system (TpUn) that guarantees uncomputation through structured Store-Use patterns. We implement prototypes of both methods in Qiskit and Python. Compared to the state-of-the-art Reqomp~\cite{reqomp}, RwUn achieves 100% coverage on practical complex-dependency benchmarks, twice the coverage on random classical circuits, and about 50% coverage on random quantum circuits beyond the scope of existing methods, demonstrating broader applicability.

Continuous monitoring can convert a dissipative channel into a resource for accelerating otherwise slow multiphoton transitions. We consider a three-level atom in a $Λ$ configuration and condition the evolution on the absence of photon emission through an auxiliary monitored decay channel. The resulting no-jump dynamics is governed by a non-Hermitian Rabi-type Hamiltonian. Using Floquet theory and Brillouin--Wigner projection-operator perturbation method, we derive effective two-state descriptions of odd-multiphoton resonances in the semiclassical and quantum Rabi models. The effective population-transfer rate, defined as the inverse of the time required for the first complete transfer between the atomic states, is maximized at an exceptional point, where its enhancement factor approaches $π/2$, corresponding to an approximately $57\%$ increase over the Hermitian value. Numerical results for three- and five-photon resonances closely reproduce the analytical transition times and yield non-negligible postselection probabilities. By contrast, the complete unconditioned dissipative evolution does not exhibit the same population-transfer enhancement. These results demonstrate a speed--success trade-off for measurement-conditioned multiphoton state transfer.

Coordination is a fundamental primitive in communication and information theory, in which distributed systems must collectively generate correlated behavior rather than merely exchange messages. In quantum networks, the nature of entanglement, quantum measurements, and nonclassical correlations introduces coordination possibilities unavailable classically. This article reviews recent advances in coordination over classical and quantum communication networks, focusing on empirical and strong coordination in multi-user settings. We consider the implications of coordination for nonlocal games, showing how it provides a natural framework for understanding the correlations that enable spatially separated players to improve their probability of winning. We present a unified framework for coordination using classical or quantum communication and pre-shared correlation resources. The review covers simulation of both entanglement and separable correlations across a variety of network architectures, including two-node, cascade, broadcast, and multiple-access networks. We study the operational differences between empirical and strong coordination, and the tradeoffs between communication and correlation resources, such as pre-shared randomness and entanglement. Coordination plays a major role in device-independent quantum key distribution (DI-QKD) schemes, in which parties can generate a secret key even if the devices used in the process have been prepared by an adversary. Furthermore, we examine the role of coordination in quantum repeaters, where distributed entanglement serves as a resource for long-distance quantum communication. The review highlights connections between coordination theory and applications such as distributed quantum systems, quantum internet architectures, and future communication networks.

Compound beams composed of simple experimental blocks (detected in simultaneous detection windows) that form specific quantum-correlated structures are suggested for simulating the properties of different quantum operations used for creating highly nonclassical and entangled multi-mode states needed in quantum communication, metrology, and information protocols. Qualitative and quantitative comparison of multi-photon addition and subtraction in compound multi-mode thermal as well as sub-Poissonian beams and multi-mode twin beams with their intensities extending over two orders in magnitude is provided. Adding and subtracting up to twenty photocounts, optimal conditions for the generation of experimental nonclassical states are identified. In general, photon addition is identified as advantageous over photon subtraction for the multi-mode thermal and sub-Poissonian beams: It induces (enhances) the nonclassicality in the former (latter) state. Contrary to this, photon subtraction outperforms photon addition in the multi-mode twin beams. Moreover, exploiting temporal photon-pair correlations in compound twin beams when post-selecting, nearly ideal experimental photon(s) addition is demonstrated.

We study algorithms for approximating the multimarginal optimal transport (MOT) distance, a generalization of the classic optimal transport distance, between $m$ discrete probability distributions each supported on at most $n$ points. We give a classical algorithm that computes a coupling between these marginals whose expected transportation cost is within an additive $\varepsilon > 0$ of the MOT distance in time $O(m^2 n^m \varepsilon^{-1}\mathrm{polylog}(m,n,\varepsilon^{-1}))$. This is, to our knowledge, the first bound for general MOT problems with simultaneous linear dependence on the dimension $n^m$ and on the accuracy parameter $\varepsilon^{-1}$, improving the prior state of the art. On the quantum side, we give two algorithms that achieve speedups in dimension, though with worse accuracy dependence than classical approaches. First, we construct a quantum projected subgradient method for estimating the MOT distance within an additive $\varepsilon >0$ with runtime $O( m^3 n^{\frac{m}{2}+1} \varepsilon^{-2} \mathrm{polylog}(m,n,\varepsilon^{-1}))$. This algorithm works with the linear programming dual of the MOT problem, and does not return a coupling. We also give a quantum multimarginal Sinkhorn algorithm for entropy-regularized MOT. This algorithm returns an implicit description of an approximately optimal coupling with runtime $O(m^8n^{\frac{m+1}{2}} \varepsilon^{-5} \mathrm{polylog}(m,n,\varepsilon^{-1})))$ after the usual reduction from entropic MOT to unregularized MOT. We also record query lower bounds: for any precision $\varepsilon<1/2$, randomized classical algorithms require $Ω(n^m/(1+\varepsilon n))$ queries and quantum algorithms require $Ω(\sqrt{n^m/(1+\varepsilon n)})$ queries.

Boson sampling arising from multiphoton interference in linear-optical networks is a prominent non-universal model for quantum computation. Here, by encoding the multi-qubit state to bosonic Fock state, we present a scalable quantum-circuit framework for simulating boson sampling on a universal quantum computing platform. Beginning with balanced beam-splitter transformations on the single- and two-photon sectors, we derive equivalent quantum-circuit implementations and unify them within a common Hilbert-space representation using an ancilla-assisted encoding. This construction is then generalized to arbitrary interferometers by replacing each optical beam splitter with a repeating quantum-circuit unit that selectively acts only within the relevant local interference subspace, requiring $N+1$ qubits for a two-photon $N$-mode interferometer and a linear-overhead subspace-identification procedure. Using this framework, gate-based quantum circuit for a four-mode boson-sampling circuit is developed and experimentally implemented on a four-qubit gate-based photonic qubit system. The qubit framework for emulating boson sampling of $n-$photons in $m-$mode will be useful to solve a broad class of sampling complexity problem on a gate-based quantum computers.

The existence of genuinely unextendible product bases (GUPBs), incomplete orthogonal sets of fully product states whose orthogonal complements contain no product vector across any bipartition, has remained an open problem. Here we construct GUPBs for any number $N\geq3$ of parties using classical maximum distance separable (MDS) codes. The MDS property imposes a rigidity on the induced product tiling across every bipartition; combined with Fourier mode deletion and a stopper state, this rigidity enforces genuine unextendibility. Consequently, the orthogonal complement of each GUPB is a genuinely entangled subspace whose normalized projector is invariant under partial transposition across every bipartition, yielding an explicit family of multipartite bound entangled states. We further construct GME witnesses that detect these states even though no fully decomposable witness can do so. Moreover, the resulting indistinguishability persists under arbitrary finite tensor powers and measurements separable across any bipartition. These results establish a direct connection between error-correcting codes and multipartite entanglement and provide an algebraic route to certifying genuinely multipartite bound entanglement.

Accurately determining the ground-state properties of quantum many-body systems remains a central challenge. In this work, we introduce an autoregressive projective quantum Monte Carlo (PQMC) framework that leverages recurrent neural networks (RNNs) to guide the stochastic dynamics. By incorporating autoregressive sampling into PQMC, we demonstrate substantial improvements in accuracy compared to standard unguided PQMC, while retaining polynomial computational cost. We benchmark our approach against conventional variational RNN ansätze and find that the autoregressive PQMC consistently achieves lower energies and higher fidelity, regardless of system size or whether the Hamiltonian is Hermitian or non-Hermitian. Our results highlight the versatility and power of neural-guided PQMC methods, paving the way for promising scalable simulations of low-energy states in complex quantum many-body systems.

Ordered magnets harbor intrinsically squeezed ground states and magnonic excitations characterized by entanglement between spins and nonclassical magnon number composition. A pathway to detecting the superpositions of noneigenmode magnon number states underlying these nonclassical magnetic ground states has recently been demonstrated by utilizing a qubit coupled to the magnon mode via a direct dispersive interaction. Here, we theoretically develop this qubit spectroscopy further delineating the capabilities and limitations of this qubit spectroscopy for sensing the quantum superpositions that underlie the excited states. We demonstrate that the spectroscopy lends itself naturally to unraveling the superpositions that underlie the various quantized squeezed-magnon number states. However, excited states comprising superpositions of multiple squeezed Fock states become increasingly hard due to the large number of possible transitions, and resulting peaks, in the qubit spectroscopy thereby requiring qubits with narrower linewidths. Along the same lines, we theoretically demonstrate the qubit spectroscopy of a low amplitude coherent squeezed-magnon state analyzing the tradeoff between frequency crowding due to multiple transitions and peak linewidths. Our work lays the groundwork and design equations for deploying high-quality qubits towards sensing the composite nature of spin excitations in magnetic systems.

Quantum heat transport for non-equilibrium steady state (NESS) exhibits a characteristic turnover effect, where the heat current reaches a maximum and subsequently declines as system-bath coupling increases. Although numerically exact methods can simulate this non-monotonic behavior, they offer limited information on the thermal state of the heat baths. Here, we introduce a frequency-selective thermometric protocol to probe the baths sustaining an NESS. By extracting a frequency-resolved effective temperature spectrum using a tunable two-level probe, we demonstrate that spectral dispersion serves as a direct witness for the non-equilibrium state of the heat baths. To demonstrate the protocol, we applied the hierarchical equations of motion to spin-boson and two-qubit models, though any exact method can be used. For both models, the turnover effect can be explained by how the thermal state of the heat baths evolves as the system-bath coupling strength increases.