Quantum Physics Paper Analysis

Photonic quantum sensing often uses low-rank entangled probes such as Greenberger-Horne-Zeilinger (GHZ), Bell, and NOON states. Although these probes are ideally rank-1, practical quantum state tomography (QST) can produce density-matrix estimates with many small finite-shot and noise-induced eigenmodes. This eigenvalue contamination can increase the estimated entropy of the reconstruction and reduce the quantum Fisher information (QFI) available for downstream sensing, while fixed rank-1 purification can discard valid signal modes when real probes acquire additional signal modes. We introduce Spectral Subspace Purification for Quantum State Tomography (SSP-QST), a rank-adaptive post-processing layer for least-squares quantum state tomography (LS-QST). SSP-QST eigendecomposes the least-squares estimate, computes a Weyl-motivated noise floor from the measured spectrum and shot count, removes eigenmodes below this floor, and renormalises the retained subspace. It requires no rank prior, no iterative optimisation, and only one eigendecomposition. In Qiskit Aer simulations, SSP-QST achieves the highest fidelity among the tested non-iterative baselines across the evaluated probe ranks, with a maximum fidelity gain of $+0.584$. It also improves shot efficiency by at least $8\times$ within the tested range. These results show that SSP-QST can make photonic QST more reliable under finite-shot noise while providing a lightweight reconstruction primitive for feedback-oriented quantum sensing pipelines.

We give, to our knowledge, the first plain-model, one-time information-theoretically secure, efficient unclonable encryption scheme for one classical bit. Previous work by Bhattacharyya and Culf (Nature Physics, 2026) and Bhattacharyya, Broadbent, and Culf either only showed $1/\mathsf{poly}(λ)$ security loss or required inefficient encryption/decryption operations. We avoid both of these caveats; in doing so, we obtain (to our knowledge) the first plain-model construction of many-time secure $1 \to 2$ unclonable encryption for arbitrary polynomial-length messages, assuming the existence of pseudorandom function-like states (Bartusek and Goldin). The key is a uniformly random non-identity phase-free Pauli on $n$ qubits, and bit $a$ is encrypted as a random $(-1)^a$ eigenstate of that Pauli. The scheme is exponentially secure; we prove that the probability that both receivers recover the bit is at most $\frac{1}{2}+\frac{1}{2}\sqrt{{2^n}/({4^n-1})} = \frac{1}{2} + O\left(2^{-n/2}\right).$ By a lower bound due to Broadbent, Culf, and Rochette, this is the best probability bound achievable with $n$-qubit ciphertexts (up to the constant hidden in the $O(\cdot)$). The main conceptual idea is to leverage, in a precise spectral sense, the balanced commutation-anticommutation structure of the Pauli group. The proof is intricate but completely elementary and makes use of standard spectral bound techniques. The main technical workhorse is a standalone linear-algebraic lemma that informally relates the positivity of two different operators, each capturing the intuition that if the two receivers can individually decrypt unusually often then they must also disagree often. GPT-5.6 Sol Ultra found this proof in an extended conversation with the author and drafted a preliminary version of this paper. The author is fully accountable for the correctness of this paper.

Nonreciprocal control of thermoelectric responses offers a promising strategy for next-generation thermal-management and energy-conversion. While nonlinear electrical transport has recently emerged as an intrinsic property of low-symmetry quantum materials, their thermoelectric counterparts have not been demonstrated. Here, exploiting harmonic detection with gradient-reversal techniques, we report intrinsic nonlinear thermoelectric responses up to room temperature in the low-symmetry type-II Weyl semimetals $T_\mathrm{d}$-WTe$_2$ and TaIrTe$_4$ in the absence of magnetic fields or magnetic materials. We resolve all symmetry-allowed components of the second-order thermoelectric tensor, including the nonlinear Seebeck, nonlinear Nernst, and nonlinear mixed-directional thermoelectric effects and demonstrate that both Berry-curvature-related and scattering-induced contributions govern the different nonlinear thermoelectric responses. Our results show that nonlinear thermoelectricity arises intrinsically from reduced crystal symmetry and that engineering effects related to scattering in these materials provides a versatile platform for exploring higher-order heat-to-charge current conversion beyond the linear response.

The mean-field Heisenberg ferromagnet is a quantum spin model on the complete graph with isotropic spin-1/2 interactions. This non-commuting Hamiltonian is permutation and $\mathsf{SU}(2)$ invariant, and its Gibbs states undergo an $\mathsf{SU}(2)$ symmetry breaking phase transition at inverse temperature $β=2$. We consider the associated Davies generator, a canonical model of open-system thermalization, and prove tight asymptotic estimates for its spectral gap at all noncritical temperatures. For fixed $β<2$, the gap as a function of number of qubits $n$ is $Θ(1)$, while for fixed $β>2$ the gap is $Θ(n^{-1})$. The matching upper bound of the spectral gap is witnessed by the total magnetization order parameter, suggesting that the low-temperature ($β>2$) slowdown is associated with broken continuous symmetry. Two key ingredients in our approach are a comparison argument, which introduces auxiliary generators to bound dissipation on nontrivial representations of the symmetry groups $\mathsf{SU}(2)$ and $\mathsf{S}_n$, and a decomposition of the space of observables into spherical tensor operators to reveal a form of monotonicity.

Nonlinearity at the scale of zero-point motion opens new possibilities for the control and readout of nanomechanical systems, but achieving this remains a formidable challenge. Here we demonstrate that ultrastrong coupling (USC) between a nanotube mechanical oscillator and a double-quantum-dot electronic two-level system enables a mechanical Kerr (Duffing) nonlinearity at the zero-point motion scale. In the dispersive regime, this large coupling yields a mechanical anharmonicity of $α= 1.4\%$ - three orders of magnitude larger than in previous work - while preserving the predominantly mechanical nature of the lowest energy states. We further demonstrate a purely quadratic cavity-based continuous readout of the mechanical motion. This continuous nonlinear optomechanical readout is enforced by a double-quantum dot symmetry, which can be broken by gate tuning to introduce a large linear transduction. These results establish a tunable USC platform that enables strong mechanical anharmonicity and nonlinear continuous readout at the zero-point motion scale.

In quantum systems, the contact with the environment is detrimental to the purity of the state, thus limiting the practical use of entangled sources in quantum information applications. This loss of purity is observed in the form of additional noise in the tomography of the state. We investigate this noise dependence in $Si_3N_4$ micro-cavities, previously used for quantum state generation, and demonstrate that the dependence of this noise on the temperature is compatible with a coupling of the photonic chips to a thermal reservoir. The control of this noise source is a necessary condition for the efficient implementation of these devices as sources of entangled states in quantum networks.

Recent results demonstrate that there exists a sharp, Page-like transition for the complexity of subsystems of Haar-random states as their fractional subsystem size surpasses one half. They further demonstrate that this transition also occurs for the holographic complexity of boundary subregions of eternal AdS black holes, assuming the Complexity$=$Volume (CV) proposal for subregions. We interpret this transition as a crossover from spectrum-dominated to basis-dominated subsystem complexity, reflecting the breakdown of approximate thermality beyond half-system size. We then apply this reasoning to an evaporating AdS black hole coupled to a bath, modeled by a quantum circuit undergoing random evolution on an interior subsystem of diminishing size. Using the basis-spectrum decomposition of subsystem complexity, we argue for a similar Page-like transition in the radiation complexity. We then show, using CV for subregions, that the same transition appears in the holographic complexity of the radiation subsystem through the emergence of an island, whose volume gives the dominant contribution. We argue that the island volume contribution resolves an apparent complexity paradox analogous to the information paradox.

Recent work has constructed higher-dimensional analogs of non-invertible symmetries similar to 1+1d Kramers-Wannier duality. Although their continuum descriptions often treat purely gravitational topological terms as inessential counterterms, these terms can have an essential lattice manifestation: they distinguish states prepared by finite-depth quantum circuits (FDQCs) from those entangled by nontrivial quantum cellular automata (QCAs). Motivated by this mismatch, we show that QCAs associated with gravitational topological responses arise in several related settings: (1) lattice realizations of projective $\mathrm{SL}(2,\mathbb{Z}_N)$ relations generated by topological operations on symmetries; (2) squares of dualities that generalize the relation between fermionization and Kramers-Wannier duality; (3) lattice implementations of QCAs through higher-form gauging; and (4) invertible phases protected by generalized time-reversal symmetries. We derive new projective $\mathrm{SL}(2,\mathbb{Z}_N)$ relations whose projective phases are gravitational topological responses constructed from Stiefel-Whitney classes. We furthermore give a general protocol for preparing the associated QCA-entangled states using finite-depth unitary circuits, measurements, and error correction. These results unify the study of gravitational topological responses in field theories, higher dimensional dualities, and quantum cellular automata.

Lorentz transformations in time and two space dimensions consist of boosts and rotations, and combinations thereof. In general, the combination of two boosts is not another boost: It is a boost followed by a rotation. The rotation angle is called the Wigner angle. Although it is straightforward to determine the energy and direction of the combined boost, it is difficult to determine the Wigner angle. In this article, the vector, matrix and spinor derivations of formulas for the Wigner angle are reviewed, and the underlying mathematics and physics are discussed briefly. Although the derivations are different, the results they produce are equivalent, as they should be. Like many physics problems, if one looks at the problem in the right way, it is not difficult to solve.

Silicon spin qubits are a leading platform for scalable quantum computing, but their performance is limited by charge noise, widely attributed to two-level fluctuators (TLFs). The location of individual TLFs is generally unknown, and existing methods to localise them does not scale favourably with device size. Here, we show that electron shuttling turns a single mobile spin into a scanning probe of individual defects. We show that by shuttling a spin over a range of distances and tracking its coherence loss, one can localise defects along the channel and constrain their switching rate and fluctuation amplitude. Because one shuttled electron sweeps an extended region, the approach scales more favourably than previous methods. Our protocol requires no additional hardware and provides a practical route to mapping the charge-defect landscape of large silicon devices, enabling defect-aware calibration and avoidance in shuttling-based architectures.

Continuous-variable quantum state tomography is limited by the cost of resolving non-Gaussian structure in high-dimensional phase space. We introduce QST-Flow, a quantum state tomography framework via flow-based generative modeling that represents experimentally accessible phase-space quasiprobability distributions with normalized, samplable neural densities rather than a truncated density matrix. The framework has two variants: QST-QFlow models the positive Husimi-$Q$ function with a single normalizing flow, while QST-WFlow models sign-changing Wigner functions as a trainable difference of two normalized flows. This construction preserves quasiprobability normalization and enables exact density evaluation, direct sampling, and importance-sampled learning from finite phase-space measurements without a fixed grid. Benchmarks on non-Gaussian cat, binomial, Gottesman-Kitaev-Preskill, number, and Fock states show accurate single-mode reconstructions, extension to multimode states, robustness on noisy Wigner data, and improved reconstruction error compared with prior machine-learning tomography methods. QST-Flow opens a promising route toward scalable, measurement-efficient phase-space tomography of nonclassical bosonic systems.

Tuning the coupling strength $g$ of an interacting quantum system may drive a sudden change in its ground-state or thermal properties. To identify and grasp non-analytical, or even discontinuous, transitions in far-from-equilibrium dynamics proves more challenging. Recently Krylov complexity $C_K$ has offered fresh insights about operator growth, thermalization, and chaos in quantum dynamics. Yet it remains unclear if, and how, changing $g$ can trigger a sharp transition in the complexity measures. Here we present evidence for such a transition by mapping out the complexity phase diagram of the paradigmatic Dicke model describing two-level atoms coupled to a cavity photon mode. Two qualitatively different regimes of dynamics are identified and characterized. At the transition, the slope of $C_K$ changes suddenly to coincide with a jump in the Krylov entropy. We elucidate the nature of the regime change from the wave packet dynamics in Krylov space, where a particle is confined by a roughly linear potential but hops as if it lives in a Rindler reference frame. The competition between confinement, which leads to bouncing, and deconfinement by Rindler hopping, which leads to the destruction of wave packet analogous to gravitational spaghettification, is sensitive to the disorder in Lanczos coefficients. The framework outlined here can be applied to other quantum many-body systems.

Spin relaxation is conventionally described by two independent phenomenological rates - longitudinal ($R_1$) and transverse ($R_2$) - whose separation obscures a deeper structural unity. Here we develop a geometric framework in which dissipation is represented by a single covariant relaxation tensor acting in Liouville space, from which $R_1$ and $R_2$ emerge as complementary projections. This tensor structure is not merely formal but is experimentally accessible through pulse sequences that probe noncommuting directions in spin space. Using hyperpolarized $^{13}C$ spins in diamond with nitrogen-vacancy centers, we show that commuting pulse trains yield effective relaxation matrices that are approximately diagonal, while noncommuting sequences produce off-diagonal components that vary with transmitter frequency offset and pulse ordering, providing evidence that relaxation is a directional process governed by a tensor rather than a pair of scalar rates. Complementary measurements of geometric phase demonstrate that noncommuting dynamics introduce ordering-dependent effects that are separable from dissipation, consistent with the interpretation of relaxation as geometric transport on the state manifold. This framework unifies Bloch, Redfield, and Lindblad descriptions within a coordinate-independent formulation and provides a natural language for relaxation in driven, anisotropic, and non-equilibrium spin systems.

To maximize the value of fault-tolerant quantum computers, it is essential to develop concrete applications beyond well-established domains such as chemistry and condensed-matter physics. Here we construct and compile quantum algorithms to simulate the structure of atomic nuclei -- a topic that has received relatively little attention from the quantum computing community despite its similarities to the electronic structure problem in chemistry -- via effective shell-model Hamiltonians and no-core-shell-model Hamiltonians with three-body interactions derived from chiral effective field theory. Furthermore, we provide quantum resource estimates, in terms of Toffoli gate and qubit counts, for these algorithms, which, to our knowledge, are the first such estimates for fault-tolerant quantum simulation of atomic nuclei. Notably, the estimates for $^{32}$Mg and $^{219}$At shell-model Hamiltonians are comparable to recent estimates of Femoco simulations, a standard benchmark in chemistry. For no-core-shell-model Hamiltonians suitable for light nuclei (up to $^{40}$Ca or so), we find that resource requirements are significantly higher, suggesting that more bespoke strategies are required to make such simulations practicable. Throughout this work, we draw upon the similarities between nuclear and electronic structure problems, while also highlighting challenges that are specific to the former. We hope this work will spur long-term collaborations between the nuclear and quantum computing community with the ultimate goal of realizing useful nuclear simulations on quantum computers.

Entanglement purification protocols (EPPs) are essential for improving entanglement fidelity to support fault-tolerant distributed quantum information processing. Practical entanglement sources are often heterogeneous and source labels may be unavailable at the EPP layer. We show that classical shared randomness, together with buffer memories, can enhance entanglement purification when source labels are unavailable, without state characterization or EPP circuit optimization. The strategy is to accumulate multiple entanglement distribution rounds and then use shared randomness to shuffle all the stored entangled states before packaging them as inputs to the EPP. For any $n$ Werner sources and any fixed $n$-to-1 bilocal Clifford EPP, we prove that accumulating and shuffling improves the expected success probability and the success-weighted output Bell fidelity over the baseline without accumulating and shuffling, for every $n$, for every finite number of accumulation rounds and in the asymptotic limit, and the improvement increases monotonically with the number of accumulation rounds.

We present a strategic plan for neutral atom quantum computation, bringing together hardware development and theory advancements to achieve the goal of practical quantum advantage. The concept of practical quantum advantage is defined, along with how to verify claims of advantage, and approaches to designing quantum algorithms that deliver practical advantage. Future directions for neutral atom quantum processor hardware are described: scaling-up system size, Qubit encodings and atomic platforms, going further below threshold with neutral-atom logical-qubit performance, continuous reloading of qubits, and fast readout. We also explore opportunities for scalable integrated photonic control technologies. Alongside hardware advancements, new developments in quantum error correction and compilation of quantum circuits are proposed. Finally, we examine the opportunity of networking multiple neutral atom quantum processors together to perform distributed quantum computing and overcome possible limitations of a single system.

We give an unconditional construction of information-theoretically secure one-time private-key unclonable encryption scheme for one-bit messages, with efficient encryption and decryption and exponentially small unclonable-indistinguishability advantage.

Variational quantum algorithms are a leading approach to near-term quantum computing, but their scalability can be limited by barren plateaus and the sampling cost of resolving small changes in the loss landscape. Here, we study the trainability of passive linear-optical quantum circuits and introduce a framework based on the ratio of sample variance to circuit variance. This ratio determines the number of circuit samples required to resolve local loss differences and gradients to proportional accuracy. We apply this framework to photon-number observables and identify both trainable and non-trainable regimes. Supported by analytic results and a numerically observed polynomial decay of the circuit variance, we find that fixed-order photon-number polynomials require only polynomially many samples as the system size grows, whereas high-order polynomials and observables based on output probabilities generally require exponentially many samples. Within the trainable regime, we further identify classes of observables in which quantum estimation achieves a polynomial speed-up over multiple classical methods. Within this family, neural network observables provide one practical construction that allow measurement outcomes to be efficiently processed into the desired polynomial. These results establish photonic variational quantum computing as a promising platform for near-term applications.

Entanglement entropy at one-dimensional criticality typically follows the Calabrese-Cardy scaling. In non-Hermitian critical chains near exceptional points, however, we show that the biorthogonal entropy of a finite system retains an additional sensitivity to a small energy gap \(Δ\) even when \(Δ< 1/L\). On top of the usual Calabrese-Cardy term, we find an interval-independent contribution \(S_{\rm res}=\log(ΔL)\), visible as a vertical offset and detectable even for a one-site subsystem. This behavior has no Hermitian analogue: a sub-finite-size gap is effectively invisible to entanglement in unitary critical chains, whereas here the entropy continues to resolve such a gap through its dependence on \(ΔL\). We interpret the result within the de Sitter geometry generated by non-unitary continuous multiscale entanglement renormalization: because the dS extremal surface reaches the IR endpoint, entanglement necessarily retains the endpoint contribution. On a finite ring, a regular circuit cannot terminate at a one-site product state and instead leaves an entangled two-site IR state. Computing the entanglement of the IR state recovers the same \(\log(ΔL)\) term, identifying this additional long-range entanglement as the residual entropy left after finite-depth disentangling.

Formal verification is becoming increasingly practical for quantum computing, yet the ability of AI agents to construct machine-checkable proofs in this domain remains unmeasured. We introduce Lean-QuantumAlg-Bench and Lean-QIT-Bench, two Lean 4 benchmarks containing 36 and 40 theorem-completion tasks for quantum algorithms and quantum information theory, respectively. Every task compiles in a fixed environment and is evaluated by deterministic proof checking and targeted semantic review, with difficulty weights assigned before model execution. We evaluate four models-GPT-5.5, Kimi K3, DeepSeek V4-Pro, and MiniMax M3-within a common theorem-proving framework under two settings: a task-only baseline and library-augmented deduction (LAD), which additionally provides access to a verified domain library. The highest difficulty-weighted scores are 60.4 out of 100 on the quantum-algorithm benchmark and 59.6 out of 100 on the quantum-information benchmark. LAD improves both score and completion rate in all eight model-benchmark comparisons, with gains of up to 15.9 points, providing evidence that verified libraries can strengthen domain-specific proof agents. The results reveal recurring weaknesses of agentic proving in areas such as quantum simulation, quantum learning, quantum information measures, and entanglement theory. Monetary and wall-clock costs per score point also vary substantially across models, highlighting important capability-efficiency trade-offs. We expect these benchmarks to establish a reproducible baseline for developing more capable and reliable proof agents, and to pave the way toward self-evolving AI scientists for advancing quantum information science.

In a two-dimensional electron gas, a strong perpendicular magnetic field confines electrons to quantized cyclotron orbits, giving rise to Landau levels with discrete orbit radii. Even the smallest Landau orbit, set by the magnetic length, spans tens of nanometers for fields of a few Tesla, imposing an intrinsic nonlocal response to electromagnetic excitations. From a microscopic theory of the nonlocal susceptibility, we derive the Green's function, the central quantity governing all electromagnetic interactions, and evaluate Purcell factors, Lamb shifts, and emission spectra from a proximal dipole emitter beyond the Markov and rotating-wave approximations. Significant nonlocal effects resulting from spatial dispersion of the Landau level response modify the response for experimentally relevant situations up to distances of hundreds of nanometers and, in particular, brighten locally dipole-forbidden transitions due to near-field gradients at multiples of the cyclotron frequency. The relevant length scales are typical of state-of-the-art nanostructured terahertz architectures, and some of our nonlocal features are consistent with recent experiments using Landau level polaritons.

In classical and quantum statistics, high-dimensional unknown parameters are abundant and it is often prudent to make minimal assumptions about them using so-called semiparametric models. To attack a wide range of semiparametric problems in one broad stroke, we present a unified treatment of statistical efficiency for classical and quantum semiparametric models, generalizing the Cramér-Rao and Helstrom bounds beyond finite-dimensional parameters. We introduce the fundamental concepts in abstract and geometric terms before applying them to many examples, covering general classical and quantum models as well as the paradigmatic special cases of Gaussian and Poisson fields. We give an in-depth treatment of channels in the semiparametric efficiency theory and advocate the use of the singular value decomposition to elucidate the statistical effects of channels. To demonstrate the utility of the formalism, we apply it to coherent and incoherent optical imaging problems, assuming an arbitrary field or intensity on the object plane without parametric assumptions. Our formalism enables us to compute classical and quantum limits to coherent and incoherent imaging resolution in statistical terms. For subdiffraction incoherent imaging, we demonstrate that spatial-mode demultiplexing can be far superior to direct imaging in estimating generalized Fourier coefficients and come closer to the quantum limits. We envision our theory becoming an essential tool for both classical and quantum statistics with useful applications to sensing and imaging, whenever minimal assumptions about a high-dimensional parameter should be made.

A central challenge for cavity-QED-based quantum technologies is to make high-cooperativity optical interfaces compatible with site-resolved arrays of single atoms. Here, we demonstrate optical tweezer arrays of individual $^{87}$Rb atoms inside a fiber Fabry-Perot microcavity with single-atom cooperativity $\mathcal{C} \sim 90$. We combine background-free site-resolved fluorescence imaging of extended arrays with collective coupling to a common cavity mode for arrays with a mean atom number up to $\bar{N} \simeq 36$. These results establish a high-cooperativity platform for many-body cavity-QED with site-resolved detection and control.

We study how local sensitivity to an encoded parameter, captured by the quantum Fisher information, flows between a spin chain, a coupled bosonic bath, and their quantum correlations, where we treat the bath as a full many-body quantum system beyond the Lindbladian approximation. We analyze how the coupling symmetry determines the destination of the departed sensitivity directly at the level of the Hamiltonian. We consider an excitation-exchanging Jaynes--Cummings coupling, which preserves the total number of excitations, and a spin-excitation-conserving Holstein coupling. We find that the Holstein coupling leaves the bath with no first-order information about the phase and stores the lost sensitivity entirely in spin--bath correlations, whereas the Jaynes--Cummings coupling passes this sensitivity to the bath, in full for a single excitation. The bath spectrum then governs whether the sensitivity ever returns to the spins. It revives fully and periodically when the coupled-system frequencies share a common period, but when those frequencies disperse the departed share dephases across the bath modes and never returns. We note that a transported metrological register loses more sensitivity than its arrival fidelity implies.

Solid-state spin defects encode local perturbations as measurable shifts in spin-transition frequencies, but mechanical actuation and quantum readout remain physically separated, resulting in a discrete measurement setup. Integrating these functions requires an on-site mechano-quantum interface that programs the lattice state of a defect host and quantitatively maps it onto the spin Hamiltonian. Here we first report an on-chip programmable mechano-quantum transducer (OCPMQT) that integrates voltage-defined micromechanical actuation with in situ spin-frequency readout in a two-dimensional van der Waals quantum-defect host. Mechanically programmed lattice states are encoded as shifts in the axial zero-field splitting parameter and resolved by optically detected magnetic resonance (ODMR) spectroscopy. Within a chip volume of 2.05*10^-2 cm^3, the transducer accesses ODMR-inferred strains as low as 0.0080% and delivers a volumetric force density of approximately 2.6*104 N/m^-3. A micromechanical-to-spin-Hamiltonian framework links on-chip electromechanics, interfacial strain transfer, and strain-spin coupling, enabling the electrical control micromechanical input to be measured directly as spin-frequency response.

Product testing, i.e., deciding whether a pure multipartite quantum state is fully unentangled across a specified tensor decomposition, serves as a bridge between quantum property testing, unentangled quantum proof systems, and tensor optimization. Despite being a fundamental property testing task and having many applications, the product test's exact (worst-case) acceptance probability curve has yet to be fully determined. In this work, we determine this curve exactly. Let $ω$ be the maximum squared overlap of the input with a product state, and let $\mathrm{PT}_n(ω)$ be the largest possible acceptance probability of the product test over all $n$-partite pure states with product overlap $ω$, allowing arbitrary finite local dimensions. We prove that, for every $n\ge 2 $ and every $ω\in(0,1] $, $$ \mathrm{PT}_n(ω)=\frac12\left(1+mω^2+(1-mω)^2\right), $$ where $m=\lfloor1/ω\rfloor $. The formula recovers the previously known tight section of the curve for $ω\ge 1/2 $, resolves all low-overlap regimes $ω<1/2 $, and implies $\mathrm{PT}_n(ω)\to 1/2 $ as $ω\to 0$ answering an open problem in [Soleimanifar and Wright, SODA 2022]. As a complexity-theoretic application, our results improve the one-shot soundness parameter in the Harrow-Montanaro reduction from $\mathsf{QMA}(k)$ to $\mathsf{QMA}(2)$. Our techniques, built upon those of Soleimanifar and Wright, allow us to resolve these open questions while remaining surprisingly elementary.

We propose a relational bundle-geometric formulation of the gravitational path integral by invoking the new tool of quantum reference frames (QRFs), which in gravity are gauge-covariant coordinate systems constructed from the available field content. Formulated in terms of relational (frame-dressed) observables, this yields a manifestly gauge-invariant path integral without ghosts and anomalies, and in which observables and their correlators are local to a frame. While eliminating the need for gauge fixing, it is equivalent to Faddeev-Popov versions in which the QRF is gauge-fixed, recovering certain previous proposals. A key feature is its covariance under QRF changes: it is a perspective-neutral path integral which encodes all internal QRF perspectives and the transformations between them. This leads to several qualitative predictions: local correlators and time evolution of relational observables in one QRF perspective become fuzzy in another, and a new spectrum of relational vacua arises. Comprised of frame-dependent no-boundary and asymptotic ground states, a vacuum from one perspective appears generally excited in another. Finally, we construct gauge-invariant, yet frame-dependent effective actions by coupling sources exclusively to relational observables, setting the stage for a relational definition of renormalization.

For quantum light sources in everyday telecommunication networks, quantum science needs to be fully transformed into quantum technology. The first necessary step to move outside a well-controlled lab environment requires the use of quantum light sources operating in the technologically relevant telecom O- and C-band. This can be provided using epitaxial quantum dots as deterministic sources of quantum light. Particularly intriguing is that emitters operating at telecom wavelengths are rapidly catching up with their short wavelength counterparts in terms of performances. Here, we make a decisive step forward in the development of quantum communication networks: a state-of-the-art source of quantum light, a semiconductor quantum dot (QD), with record coincidence rate for entangled photon emission in the telecom C-band, is operated inside an optimized rack-based setup. This setup includes a tunable pulsed laser for the QD excitation (from quasi- to fully resonant excitation), all optics for the excitation filtering, and QD signal coupling into single-mode fibers. Overall, the setup allows for above $50\%$ transmission for both exciton and biexciton photons. These results show that quantum dots-based telecom light sources can now be transported and integrated into existing fiber infrastructures, an important step to demonstrate the feasibility of the upcoming quantum internet.

Chiral quantum light-matter interfaces, where the internal spin state of a quantum emitter determines the direction in which it emits, are essential building blocks of non-reciprocal quantum devices, deterministic quantum logical gates and entanglement generation protocols. Yet, a chiral quantum interface that operates at telecom wavelengths, and is compatible with telecommunication infrastructure and silicon photonics, does not yet exist. Here, we report on an integrated chiral quantum interface in the original telecom band (1260-1360 nm), created by interfacing InAs quantum dots with a waveguide-coupled InP microdisk. We tune the quantum dot transitions through the photonic cavity using a strong magnetic field, observing a peak cavity enhancement of 3.3 and an emission directionality of 0.985, demonstrating the near-ideal chiral quantum coupling required for quantum information processing on integrated photonic devices.

Financial fraud detection is challenged by decentralized data, severe class imbalance, and privacy constraints. This paper presents QuantumChain, a secure Quantum Federated Learning (QFL) framework that combines hybrid quantum-classical neural networks, encrypted federated aggregation, blockchain-based auditability, and quantum-secure communication. Each client trains a local hybrid model in which a variational quantum circuit is embedded between classical neural layers, while model updates are protected through homomorphic encryption, threshold secret sharing, and QKD-based keying. A permissioned blockchain records aggregation events and supports reputation-weighted trust among participants. We evaluate QuantumChain on financial transaction data using a compact, size-matched classical baseline to isolate the effect of the quantum layer. Results show that the HQNN achieves comparable accuracy while improving fraud-class recall in most settings, reaching 94.6% recall compared with 93.2% for the classical model. The Deep QLayer improves performance in full-data settings, suggesting that added circuit depth helps recover representational capacity when the shallow circuit becomes limited. Mixed-state simulations further show that the recall trend persists under non-ideal quantum evolution. In federated deployment with 10 heterogeneous clients, global accuracy increases from 97.7% to 98.8% over five rounds before stabilizing. These results show that QuantumChain can integrate depth-aware hybrid quantum models into a secure federated fraud-detection pipeline while maintaining stable global convergence.

The entanglement of quantum systems is commonly restricted by their coupling Hamiltonian and initial state properties. Here, we prove by exact analysis of tunnel-coupled bosonic field modes, that factorized multi-boson two-mode states can become fully entangled via stroboscopic sign flips of the two-mode coupling. Their entanglement can exponentially grow with the number of flips. With the exception of specific prohibitive states that are invariant under such sign-flip control, this effect universally applies to two-mode state preparation. Remarkably, this linear control may provide entanglement resources for diverse quantum technological applications by readily available means.

Quantum transfer learning (QTL) is often evaluated by replacing a classical classifier with a fixed variational quantum head, but this hides a key question: when is the quantum branch actually useful? We propose QSTAR: Quantum Selective Transfer with Adaptive Routing, a selective QTL framework that keeps high-confidence classical predictions and routes only low-confidence samples to a fallback branch. Using a frozen ResNet18 backbone on Fashion-MNIST, we compare manually designed QTL heads, KetGPT-designed quantum heads, and parameter-matched classical baselines under a common data split and optimization schedule. Standard QTL heads reach at most 57.0% accuracy, while the strongest KetGPT head in the main filtered sweep reaches 78.5% accuracy and 0.785 F1-score. Although the strongest fixed classical head remains higher at 81.6%, selective routing gives the quantum branch a clearer role. On low-confidence samples, KetGPT #180 improves accuracy over a parameter-matched MLP fallback by 6.82, 4.31, and 3.03 percentage points at thresholds of 0.70, 0.80, and 0.90. At the full-system level, Adaptive KetGPT-QTL reaches 80.9% accuracy and 0.807 F1-score, outperforming the adaptive classical baseline. A separate compact-circuit ablation identifies KetGPT #160 as a stronger fixed-head candidate, reaching 81.9% accuracy with only 10 quantum parameters and 9 gates. These results suggest that architecture-searched quantum heads are most useful as targeted fallback branches for uncertain inputs rather than uniform replacements for classical classifiers.

A central challenge in quantum machine learning is understanding the scaling behavior of parameterized quantum circuits (PQCs). In particular, it remains unclear how their performance on unseen data changes as the number of trainable parameters increases. Prior works have derived formal generalization guarantees for quantum models, but it is well-known that many such results do not fully characterize generalization behavior in practice. In this work, we show that gradient-based PQCs can exhibit improved performance on unseen data as model size increases, displaying the phenomenon of double descent. This contrasts with the traditional view that larger models lead to degraded generalization. We provide analytical results rigorously underpinning this behavior by leveraging add-one-in perturbation techniques and spectral properties of random matrices. We support these results with numerical experiments on re-uploading PQCs across several data sets and training set sizes, consistently observing the predicted double descent behavior. While other obstacles on the path toward practical quantum machine learning remain, our finding that deeper parameterized quantum circuits do not necessarily exhibit degraded performance provides reasons for cautious optimism.

Accurate modeling of bond breaking remains a central challenge for reduced density matrix functional theory (RDMFT). Although some modern functionals can yield reasonably accurate dissociation energies, they often fail to reproduce key properties of the dissociated fragments, such as a vanishing fragment population covariance (also known as the delocalization index) and the correct total spin angular momentum of each fragment (local spin). In this work, we revisit the construction of natural orbital functionals by correcting the cumulant contribution produced by the PNOF5 functional. Our method enforces known contributions of the cumulant to local spin fragments and the delocalization index at the dissociation limit. We obtain the closest cumulant consistent with these physically motivated constraints and subsequently purify the corresponding one- and two-electron reduced density matrices by imposing the standard $P, Q, \text{and } G$ $N$-representability conditions. The resulting functional yields improved behavior in strongly correlated regimes. Benchmarking on the dissociation of the singlet states of \ce{N2}, \ce{NO+}, \ce{O2}, \ce{S2}, and \ce{CO} shows that in the dissociation regime the energies computed from the updated cumulant exactly reproduce the complete active space self-consistent field (CASSCF) energies. We further analyze the limitations of the approach and identify scenarios in which the current approach performs poorly. This work provides a pathway for systematically improving natural orbital functionals to achieve reliable bond-breaking calculations within RDMFT.

Entanglement distillation is a fundamental task in quantum information theory. In this work, we prove that Werner states in arbitrary dimension are 2-copy distillable if and only if they are 1-copy distillable. This answers the longstanding open question of the 2-copy distillability of Werner states. This is an important step on determining whether every non-positive partial transpose (NPT) state is distillable, which remains one of the central open problems in the field of entanglement distillation.

Implementing controlled dissipative dynamics is a powerful approach for state preparation in a variety of contexts, including the preparation of remote entangled states. Here, we show that by going beyond the standard setting of time-independent dissipative dynamics, one can realize even more powerful non-unitary protocols. We introduce dissipative Floquet protocols for stabilizing remote entanglement of logical qubits, where continuously-running dissipation is interleaved with a periodic sequence of unitary gates. These protocols harness existing experimental capabilities, and overcome time-entanglement limits that constrain standard approaches. They also implement an autonomous form of entanglement distillation. We show how these protocols give enhanced protection against waveguide loss, and as an example, analyze a specific implementation using cat-qubits and transmons in a superconducting circuit.

Recent experiments on quantum computers have challenged the limits of classical computation in chemistry, simulating ground states of strongly correlated molecules. Many of these experiments have utilized the unitary cluster Jastrow ansatz, a quantum circuit inspired by the unitary coupled cluster ansatz that can be tailored to current quantum hardware. Notably, the largest experiment in Sci. Adv. 11, 25 (2025) executed a quantum circuit with 77 qubits and 10,570 gates on an IBM quantum computer and performed classical post-processing with up to 6400 nodes on Fugaku to compute ground state energies better than Hartree-Fock. In this work, we present a polynomial time classical algorithm to compute the energy of any single-layer unitary cluster Jastrow circuit, independent of locality constraints for quantum hardware. Our algorithm can reproduce the largest experiment from Sci. Adv. 11, 25 (2025) in less than a minute on a laptop, and through circuit optimization enabled by fast simulation we achieve a lower ground state energy than the experiment.

Quasiparticles are a prominent decoherence source in superconducting qubits, but their effects are notoriously difficult to isolate in fluxonium. Unlike a transmon, fluxonium is insensitive to offset charge, precluding charge-parity detection of quasiparticle tunneling. We address this challenge by measuring the excitation and de-excitation rates in a fluxonium qubit under controlled on-chip quasiparticle injection. We show that to accurately model the external magnetic flux dependence of the quasiparticle-induced transition rates, it is necessary to account for the superconducting gap asymmetry across the Josephson junctions. A comparison between theory and experiment constrains the relative quasiparticle contributions of the junction array and the small junction and helps explain previously reported discrepancies between the bounds on the quasiparticle densities inferred for these two circuit elements.

Repeated-interaction machines distinguish heat-like from work-like resources through the steady states they generate, but whether topology can control this distinction remains unknown. Here we reveal the role of topology in the process by showing that topological edge states can act as pure-thermalization fuels. For an open Su-Schrieffer-Heeger chain used as the fuel source of a micromaser, edge eigenstates suppress both displacement and squeezing and drive the cavity to a Gibbs state, whereas bulk eigenstates activate coherent channels and yield thermo-mechanical operation. This edge-bulk thermodynamic dichotomy remains robust under realistic decoherence, cavity loss, bond disorder, and moderate onsite disorder. We further design a superconducting implementation in which a sixteen-site SSH eigenstate is deterministically compressed into a four-qubit fuel register. The resulting cavity response provides a transport-free classifier of topology and identifies a topology-thermodynamics link that extends beyond cavity-QED to repeated-interaction settings more generally.

We demonstrate that fluctuation-induced bistability is a robust and generic phenomenon in strongly interacting many-body systems with strong light-matter coupling. We identify a common microscopic mechanism based on resonances between photonic transitions and many-body energy scales, unifying the emergence of fluctuation-induced bistability across a broad class of models, including interacting spins, fermions, and bosons coupled to cavity modes. We develop complementary methods to study both the steady-state properties of fluctuation-induced bistability and its dynamical formation at finite times. In particular, we introduce the dressed-state rate equation approach, which reveals rich metastable dynamics and enables the investigation of its system-size dependence. By comparing its predictions with numerically-exact tensor-network simulations, we identify signatures of fluctuation-induced bistability already in small systems on finite timescales. Our results establish fluctuation-induced bistability as a universal feature of dissipative cavity-coupled many-body systems and provide a general framework for the investigation of its non-equilibrium dynamics across a wide range of hybrid quantum platforms.

The three-qubit CCZ state is the smallest rank-three hypergraph state and an elementary entangled magic resource. Its cubic phase is governed by generalized stabilizers that are not Pauli strings, so standard graph-state self-testing arguments do not apply directly. We show that twenty correlators, all obtainable from five of the eight global input triples in the tripartite two-input, two-output scenario, determine this state and the action of the Pauli $X/Z$ measurements up to local isometries. The proof fixes eight equally weighted computational branches and propagates conditional $X$-flip relations across the branch cube, recovering the minus sign of the $111$ amplitude. These five-context correlations are nonlocal, but the canonical Pauli measurements cannot attain the largest quantum value of any Bell inequality that they violate: whenever they maximize a Bell expression, its local bound has the same value. Introducing an independent third measurement makes self-testing from maximal Bell violation possible. We construct an explicit Bell inequality whose maximal quantum violation self-tests the CCZ state and all three local measurements. An exact sum-of-squares decomposition proves the quantum bound, and its equality conditions yield an analytic SWAP extraction. Together, these results give two explicit device-independent self-tests of the CCZ state and demonstrate that determining a state and its measurements from several correlator equalities is distinct from identifying them through the maximal violation of a single Bell inequality.

Quantum annealing and related combinatorial optimization methods typically accept quadratic unconstrained binary optimization (QUBO) problems as input, whereas many practical models include constraints and continuous variables. Standard QUBO conversions discretize continuous variables, increasing the binary dimension and often making feasible low-energy states harder to sample. We develop a finite-temperature formulation for a separable class of mixed-binary quadratic programs (MBQPs) that avoids this discretization. At fixed Lagrange multipliers, the continuous sector is integrated out analytically and enters only the multiplier update, leaving a QUBO over the original binary variables. We evaluate the method on the continuous relaxation of the quadratic $p$-median problem. Compared with a penalty-based QUBO formulation, it generates feasible solutions more reliably. At an appropriate inverse temperature, its conditional relative error is comparable to that of local search for small instances and often lower for the larger tested instances. In the time-to-target experiment, it also reaches the target faster than a commercial mixed-integer optimization solver toward the upper end of the tested range.

We construct a covariant representation of the causal logic for the Dirac system and the electron, based on the conserved Dirac probability current and a general current-to-localization procedure for achronal regions. A polynomial decay estimate, derived by a non-stationary phase argument, verifies the conditions required to define covariant achronal localization for the full Dirac system. Extending this localization to complete spacetime regions yields the corresponding causal-logic representation; restriction to the positive-energy invariant subspace gives the analogous construction for the electron. We establish several structural properties. On Euclidean space, Dirac localization agrees with canonical projection-valued localization, while its position operator differs from the Newton--Wigner operator by an explicitly determined bounded self-adjoint correction. Full Dirac achronal localization is projection valued and represents achronal separateness by orthogonality, thus satisfying microscopic causality. After compression to the electron subspace, it becomes positive-operator valued while preserving causality. We further extend known results from spatial to general achronal regions, prove separation and norm-one criteria, and analyze the high-boost limit, obtaining Lorentz contraction in a precise probabilistic sense. Finally, we discuss the electron--positron decomposition and the state transformation induced by position measurements, showing that measurement-induced positron production is universal and independent of the specific measuring device.

As quantum key distribution (QKD) progresses from laboratory demonstrations toward practical deployment, quantum communi- cation networks increasingly require higher key rates and the ability to distribute independent secret keys among multiple users and network nodes. In this paper we present a promsing approach with multi-plane light conversion (MPLC) for demultiplexing entangled photons, transmitted through a few-mode fiber (FMF). We experimentally demonstrated a spatially multiplexed BBM92 QKD scheme. The modes are selectively excited through separate single-mode-fibers and subsequently separated by MPLC into distinct output ports. Unlike high-dimensional QKD based on coherent modal superpositions, our approach exploits distinguishable guided modes as parallel channels while preserving the entanglement required for QKD. For the multiplexed links, we obtain quantum bit error rates of $1.9 \pm 0.4\%$ for the channel 1 and $6.8 \pm 0.8\%$ for the channel 2. These results are relevant for scalable quantum-secured networks, space-division-multiplexed QKD systems, multi-user entanglement distribution, and future quantum internet architectures, where parallel quantum channels must be implemented without compromising the quantum correlations required for security.

We theoretically demonstrate that the molecular orientation angle $θ$ provides a structurally intrinsic, continuously tunable control parameter for engineering optical Schrödinger cat states via high-harmonic generation (HHG) in H$_2^+$. Coupling time-dependent Schrödinger equation simulations to the fully quantized HHG framework, we evaluate the Wigner functions of the post-selected harmonic-mode states under two complementary conditioning strategies. Conditioning on resonance-enhanced low-order harmonics exploits the complementary dipole selection rules of the $1σ_g\to1σ_u$ and $1σ_g\to1π_u$ transitions, driving a kitten-cat crossover whose direction is opposite in the two channels as $θ$ is varied. Conditioning on plateau harmonics instead exploits two-center destructive interference, producing a reentrant cat$\to$kitten$\to$cat transition controlled by the order-dependent interference angle $θ^*(q)$. In both cases the crossover is decoupled from the laser intensity, focal geometry, and molecular density, offering a degree of control with no counterpart in atomic targets.

The recovery of quantum information after subsystem loss is a central challenge in quantum information processing. However, some states remain beyond the reach of any recovery strategies. Here we identify the algebraic origin of irrecoverability, the ghost information---correlations encoded in the global state that leave no trace on any accessible subsystem. We introduce a scalar measure quantifying its magnitude and prove a universal error floor below which no virtual recovery map can operate, irrespective of resource investment. We further uncover a spectral phase transition in the sampling cost: bounded when the underlying linear map exhibits a spectrum gap, and divergent with a universal exponent in the gapless regime. Together with the universal error floor, this dichotomy organizes all multipartite quantum states into four classes. Moreover, it is revealed that conditional mutual information---the standard entropic diagnostic---is fundamentally irrelevant to virtual recoverability. As an implication, we show that the error floor imposes a detection threshold for loss-tolerant quantum metrology.

The Kramers-Wannier duality is the prototypical example of a non-invertible symmetry, yet little is known about its fate away from criticality and out of equilibrium. We introduce the Kramers-Wannier entanglement asymmetry, a quantum-information measure that quantifies the breaking of this non-invertible symmetry in the transverse-field Ising chain. We first investigate its equilibrium properties, showing that it exhibits a striking crossover between the ordered and disordered phases together with a pronounced dip at the critical point that becomes increasingly sharp with subsystem size. We then study quantum quenches from both gapped phases to criticality and show that the Kramers-Wannier entanglement asymmetry decays to zero, signaling the dynamical restoration of the non-invertible symmetry. Remarkably, we uncover the emergence of a quantum Mpemba effect: under suitable conditions, states initially farther from equilibrium restore the Kramers-Wannier symmetry faster than states prepared closer to it. We provide both analytical and numerical evidence for this phenomenon and identify the mechanism responsible for its occurrence. Our work establishes entanglement asymmetry as a powerful probe of non-invertible symmetries beyond equilibrium and opens new perspectives on the dynamics of dualities in quantum many-body systems.

Neutral atom quantum systems offer a promising pathway to large-scale quantum computing due to high qubit uniformity and flexible connectivity. To exploit this architecture, compilers must coordinate dynamic atom transport alongside highly parallel entangling gates. As circuits scale, the interplay between these operations becomes a system bottleneck, introducing denser logical interactions and longer temporal dependencies. Compilers must simultaneously satisfy rigid spatial constraints and complex movement schedules. Existing joint spatiotemporal compilation methods face an exponentially expanding search space, incurring substantial overheads or compromising fidelity as circuit size grows. In this work, we propose ARGON, a scalable compilation framework that introduces a spatiotemporal decoupling paradigm for neutral atom processors. Our key novelty is offloading static geometric conflict resolution to an offline phase, precomputing a library of hardware-certified, high-parallelism spatial layouts. To guide temporal routing, we deploy a Graph Neural Network (GNN) predictor to evaluate candidate layouts against deep temporal horizons, proactively evading downstream kinematic bottlenecks. Finally, a heuristic router translates the selected sequence into collision-free physical transport. Evaluations show ARGON completes compilation in under 10 seconds, delivering up to a >10^4x and 600x average speedup over state-of-the-art baselines. ARGON also minimizes routing decoherence and reduces Rydberg stages, improving execution fidelity by up to 10^2x on dense circuits.

Quantum circuits are often drawn as complete processes, with fixed inputs and outputs. In many quantum-information tasks, however, the natural object is only a fragment of such a circuit: an unknown source of non-Markovian noise to be probed, a subroutine to be inserted into a larger algorithm, or an agent implementing an adaptive strategy. In finite dimensions, the link product provides a systematic means to analyze how such circuit fragments interact and compose. Here, we develop the corresponding framework for continuous-variable systems. We introduce continuous-variable circuit fragments and associated link products that stitch such fragments together into larger processes. We show that the formalism simplifies substantially in the Gaussian regime, where link products can be evaluated efficiently using covariance-matrix representations. We use the formalism to construct non-Markovian processes and adaptive agent-environment interactions from modular components. This extends the quantum-comb toolkit to continuous variables, providing systematic methods for adaptive sensing, non-Markovian noise mitigation, and higher-order quantum circuit design.

Numerous studies have analyzed the use of hybrid quantum-classical convolutional neural networks as a promising alternative to classical deep learning. However, network components on quantum hardware impose fundamental limitations, while the scalability of quantum circuits leads to trainability issues. In this work, we investigate whether small, classically-emulated quantum circuit components can play a meaningful role within complex models, offering an alternative to purely classical convolutional architectures. To this end, we present a systematic study of the effectiveness of a Hybrid Quantum-inspired Convolutional Neural Network (HQiCNN) compared with a parameter-matched classical Convolutional Neural Network (CNN) that differs only in an intermediate dense neural layer. Both models are evaluated on two real-world medical datasets while systematically varying the different hyperparameters, ensuring a fair model comparison that is both dataset and hyperparameter independent. The results show that no architecture consistently dominates the other: the HQiCNN achieves its largest gains in intermediate-data regimes, whereas the CNN reaches the highest accuracies for the largest training sets in both datasets. Furthermore, removing entanglement produces comparable performance while enabling substantially better scalability of quantum simulations, and richer observable sets become beneficial only when sufficient training data are available. Finally, we propose two SHAP-based explainability tools for comparing the predictions between both models, $|SHAP|$IoU and $EMD_{pos}$ metric, to demonstrate that both architectures consistently attend to anatomically plausible regions. Thus, we provide a comprehensive benchmark showing that, under certain conditions, hybrid quantum-inspired models are an alternative that can offer benefits in practical tasks such as medical image classification.

This work examines the thermal dynamics of basis-independent quantum coherence and correlation-based quantum resources for two dipole-dipole-coupled electrons confined in spatially separated quantum-dot (QD) molecules. Single-dot quantum superpositions and inter-subsystem coherence are characterized by using localized and collective coherence. Quantum correlations between the two double quantum dots are quantified by employing Bures distance entanglement, Local quantum uncertainty (LQU), and local quantum Fisher Information (LQFI). The findings show that dipole-dipole coupling $K$ is the most effective protective parameter, extending the entanglement sudden death temperature, diminishing the local quantum superpositions and enhancing the collective coherence. The dipole-dipole interaction has also a crucial impact on protecting LQU and LQFI beyond the entanglement sudden death temperature. Coulomb repulsion $J$ reinforces this protection through an independent channel, projecting the thermal state onto the entangled $\{|0_A 1_B\rangle,|1_A 0_B\rangle\}$ subspace; their combined action is required to approach the entanglement maximum, and it enhances collective coherence and extends the temperature range over which LQU and LQFI remain appreciable. Energy detuning $\varepsilon$ can enhance localized coherence but paradoxically accelerates the entanglement sudden death and quenches LQU and LQFI by weakening two-body correlations. Inter-dot tunneling $Γ$ enhances local superpositions at low temperature, but it reduces collective coherence, lowers the entanglement sudden death temperature, and disrupts other nonclassical correlations.

Decoherence, when viewed in the Heisenberg picture, can turn incompatible measurements into jointly measurable ones. This provides an observable-level description of emergent classicality in terms of the incompatibility destroyed by a noise channel. The corresponding loss of incompatibility can be captured by the channel's \emph{compatibility region}---the observables in a probe class that become jointly measurable with every noisy observable. The geometry and volume of this region provide a refined operational way to compare noise channels. We apply this framework to decoherence channels, each of which acts by Schur multiplication with extreme points of the convex set of unit-diagonal positive semidefinite matrices. Restricting to extremals eliminates convex mixing and reveals subtle phase-dependent decoherence effects thar are not captured by damping rates or conventional coherence quantifiers. Such channels have a rigid dilation structure described by a rank-one operator frame, which reduces joint measurability to a positivity test, making the compatibility region analytically tractable, and its volume computable from the frame's Gram matrix. If the frame can be normalised to a minimal informationally complete (MIC) POVM, the compatibility region acquires a geometric interpretation in the associated probability representation of the quantum state space, familiar with Qbism. Among maximal-rank extremals, those associated with symmetric informationally complete (SIC) POVMs maximise the compatibility volume and hence destroy the greatest amount of incompatibility, providing an operational characterisation of the special role of SICs in terms of joint measurability. This leads to a new formulation of the well-known SIC existence problem as a joint measurability question for noisy mutually unbiased bases.

Error correction thresholds are often treated as the primary figure of merit for comparing quantum error-correcting code families. We show that the optimal error correction threshold for many commonly considered codes is constrained to a single universal value at leading order in a replica limit. Through a statistical mechanical mapping, we demonstrate that duality constrains all zero-rate em-symmetric CSS codes to have the same optimal code capacity threshold. Here, em symmetry means that the X- and Z-type parity-check matrices are equivalent up to row and column permutations. Under this statistical mechanical mapping, em-symmetric CSS codes are self-dual under a generalized Kramers-Wannier duality up to a mixing of logical sectors. For zero-rate code families, this mixing contributes only subextensive corrections, so the thermodynamic bulk free energy is self-dual in the trivial logical sector. This self-duality fixes the clean critical point and constrains the disordered phase boundary. We also show that self-duality is preserved under code concatenation, and that optimal decoding of concatenated codes can be reformulated as a renormalization group flow on a hierarchical lattice. Our results provide a common framework for analyzing topological, concatenated, and more general quantum low-density parity-check code families, including both their optimal code capacity thresholds and their sub-threshold logical error suppression.

In this article, we demonstrate that weak topology can be formulated geometrically in terms of exceptional singularities of an analytically continued Bloch Hamiltonian. A general plaquette chiral model in two dimensions serves as a minimal realization of dual weak topology, possessing two independent families of weak topological invariants, one for each spatial direction. The weak-topological edge states correspond to exceptional points in complex momentum space, while corner zero modes emerge from exceptional curves obtained by complexifying both momenta. Compact localized states arise when the exceptional roots collapse to the origin. This framework provides a unified complex-momentum description of edge, corner, and compact localization.

In this work, a quantum architecture search framework for approximate quantum state preparation (QSP) is proposed. QSP is a challenging task, since the search space grows exponentially with the number of qubits, making the identification of the optimal circuit non-trivial. To address this problem, deep reinforcement learning is employed through an agent based on proximal policy optimization. The objective of the agent is to identify the best possible approximation of the target state while simultaneously minimizing the number of gates used. At each step, the agent appends a new gate to the circuit and recomputes the fidelity between the approximated state and the target states. Various experiments have been performed from 2 to 5 qubits. Both predefined states, such as Bell, GHZ, W, and Dicke states, and completely random states are considered. The proposed framework is able to achieve approximation errors of $10^{-14}$.

We examine how Eisert--Wilkens--Lewenstein (EWL) quantization affects evolutionary stability in a symmetric $2\times2$ game whose interior mixed Nash equilibrium is not evolutionarily stable. In the restricted two-parameter EWL strategy space, the quantum equilibrium $s^*=(π/2,π/4)$ becomes a strict symmetric Nash equilibrium, and hence an evolutionarily stable strategy, for every $γ>0$. Extending the admissible pure strategies to the full three-parameter $SU(2)$ family preserves the Nash equilibrium but introduces a continuum of payoff-neutral mutants, causing strictness and the second ESS condition to fail. Thus, entanglement stabilizes the equilibrium only within the restricted EWL strategy space; the effect does not survive enlargement to full $SU(2)$.

We examine conditional probabilities derived from the joint noisy measurement of two complementary observables. We show that conditioning on one variable can lead to reduction of uncertainty in the other one, even completely eliminating uncertainty. We show that the conditional distribution cannot, in general, be represented in Born form using the marginal positive operator valued measure and any physical system state, nor can it be derived from typical rules of state reduction. We examine these issues in two basic quantum-optical schemes. These are double homodyne detection and a qubit measurement.

Time-evolving entangled states describe quantum particles whose correlations evolve in time according to a well-defined dynamics. Such states can be generated in a variety of physical systems and are promising resources for several quantum technologies, ranging from quantum clock synchronization to quantum communication. However, their full potential is currently limited by the fact that the entanglement dynamics often occur on timescales comparable to the achievable synchronization precision, especially in experiments aimed at distributing entanglement through noisy urban channels. In this context, accurate timing is not merely a technical detail, but a fundamental requirement for faithfully observing and exploiting the underlying quantum correlations. Here, we demonstrate the faithful distribution of a fast-evolving entangled state over a 270 m free-space channel connecting two buildings in the center of Rome. The developed system incorporates a synchronization device capable of achieving sub-50 ps timing accuracy between the two ends of the link while simultaneously supporting channel stabilization. Our results demonstrate that time-evolving entanglement can be reliably transmitted through a noisy urban free-space channel, representing an important benchmark toward long-distance free-space quantum communication and the future implementation of time-correlated entangled states in demanding scenarios such as satellite-based quantum networks.

We investigate cooperative light scattering by an ordered chain of multilevel atoms, which possess two quasi-resonant transitions with parallel dipole moments. Interference between dipole transitions induced by coupling with the vacuum gives rise to so called cross-damping and cross-shifts, that modify the incoherent and coherent dynamics and can be manifest in the spectroscopic properties of the emitted light. We determine the excitation spectrum when the atomic chain is driven by an external laser in the limit in which the dipolar transitions can be described by harmonic oscillators and the scattering is coherent. We show that the interplay of multilevel interference and superradiance can give rise to measurable effects in chains of alkali-metal atoms.

We expand the Einstein-Hilbert action to cubic order about the Schwarzschild horizon, in the even Regge-Wheeler gauge of the Gaddam-Groenenboom-'t~Hooft (GGV) near-horizon framework, and derive the cubic graviton self-interaction. Our central result is a `vanishing theorem': at leading soft order the self-coupling of the purely traceless longitudinal polarizations is identically zero, because with the trace/transverse-scalar sector switched off the fluctuation reduces to a two-dimensional block whose $\sqrt{-g}\,R$ is a total (Euler) derivative at every order in $κ$. We prove this by an explicit closed-form reduction and exhibit the cancellation term by term. It is a `framework-specific' statement, even RW gauge, GGV sector, leading soft order, not a gauge-invariant theorem of general relativity. The theorem is exact, but the quantized vertex inherits a $\sim\!20\%$ soft/scheme systematic at the only simulable multiplet ($\ell=2$), which we state explicitly. We then simulate the real-time dynamics of the resulting Hamiltonian on IBM Qiskit/Aer with exact cross-checks. Two structural facts, a conserved charge that only the cubic vertex violates, opening $φφ\to hh\to4φ$, and a provably resonance-free boost spectrum (gap $\to1/2$), already predict that the longitudinal channel is perturbatively rigid; the simulation confirms this quantitatively and measures the residual dressing ($d_{\rm eff}=1.06$; multiplicity far from thermal, Poisson, and Haar references) rather than discovering it. A symmetry-exact total-occupation truncation yields the first sector-resolved level statistics, indicative of intermediate behaviour on Hilbert spaces too small to be decisive. All circuit results agree with exact diagonalization, every headline number carries a stated systematic, and hardware execution is deferred behind a quantified noise budget.

Fermion pairing underlies collective quantum phenomena across widely different forms of matter. In extended systems such as ultracold Fermi gases, pairing is commonly understood through the BCS--BEC crossover, where the pair size evolves from large, overlapping Cooper pairs to tightly bound dimers. In finite systems such as atomic nuclei, superconducting grains and quantum dots, however, the same pairing tendency competes with confinement, shell filling and spatial inhomogeneity, making the microscopic structure of pairs much harder to access. Here, we image pair correlations in a finite, tunable system of few fermionic atoms with single-particle resolution and full counting statistics. We observe that confinement and shell structure re-organize pairing in real space: In the weakly interacting, confinement-dominated regime, closed-shell configurations suppress correlations in the high-density trap center. Pairing is mainly observed toward the low-density surface. Open-shell systems, however, support substantially stronger central pairing. Already for surprisingly small systems, increasing either interaction strength or particle number restores a locally bulk-like Cooper-pair profile in the trap center, whereas the edge retains dimer-like correlations. By resolving where pairs form and how their character changes from localized dimers to overlapping Cooper pairs, our measurements provide a microscopic view of pairing in finite fermionic matter and connect the physics of mesoscopic cold atoms to pairing phenomena in nuclei and superconducting nanostructures.

Pauli Correlation Encoding (PCE) is a heuristic framework for binary optimisation that encodes classical variables into many-body Pauli observables. While PCE requires fewer qubits than other approaches, it relies on estimating a large number of Pauli expectation values whose signs determine the variables' values, which can incur substantial measurement overhead. Here, we introduce efficiently simulable PCE, a class of dequantised PCE realisations where all expectation values needed can be computed efficiently classically. We instantiate this idea using free-fermionic evolutions, realised by matchgate circuits, and Instantaneous Quantum Polynomial (IQP) circuits. On MaxCut, Maximum Independent Set, Multi-Dimensional Knapsack, and Max3SAT benchmarks, these methods produce high-quality solutions across problem sizes ranging from tens to thousands of variables. Our results show that PCE is naturally understood as a correlation-based optimisation framework with both quantum and classically simulable realisations. This yields a dequantised baseline for evaluating future quantum PCE implementations.

Programming distributed quantum systems requires multiple actors to coordinate precise sequences of quantum operations, classical communication, and entanglement generation. Writing such protocols directly as distributed processes is tedious and error-prone, and subtle mismatches can cause deadlock or silently incorrect quantum states. We present Qoreo, a choreographic programming language for quantum distributed systems in which an entire protocol is expressed as single, global program (a choreography) rather than as a collection of independent actor processes. Qoreo includes a local quantum language with linear types that enforce the no-cloning principle; a choreographic language that combines local quantum computation with inter-actor classical and quantum communication; and a process language for individual network nodes. We prove type safety for choreographies, guaranteeing that well-typed programs implement well-defined quantum operations, and we define endpoint projection~(EPP), which automatically derives a network of independent processes from any choreography. We prove EPP sound and complete with respect to the choreographic semantics; as a corollary, every well-typed choreography projects to a deadlock-free process network. The metatheory of Qoreo is fully mechanized in Rocq, and we provide an extraction pipeline to NetQASM for simulation and deployment on quantum network hardware.

We deform the Carlen--Maas--Wirth framework for noncommutative dynamical optimal transport by an Arnold--Nielsen type complexity operator. A positive state-independent operator $G$ compatible with the Hilbert bimodule structure of a noncommutative differential calculus $\partial\colon\M\to\Hcal$ can be absorbed into the calculus itself, \[ \partial_G:=G^{1/2}\partial. \] The corresponding complexity-weighted transport problem is exactly the unweighted transport problem generated by $\partial_G$, whenever the deformed quadratic form remains Dirichlet. In finite dimensions we prove existence of minimizers for density-dependent Petz-class metrics and for fixed physical complexity weights, the latter without commutation between $G$ and the state-dependent mobility. On unitary orbits we identify the induced distance with a quotient metric coming from a right-invariant complexity geometry. This yields an exact Bell-state preparation result via Clairaut's relation and an exactly computed restricted-path upper bound for GHZ preparation; the Lindblad detailed-balance case is included only as entropy-gradient-flow background.

Quantum-kernel methods encode a dataset's geometry in a Gram matrix, so learning claims on hardware kernels assume the intended geometry survives execution. We measure that survival for one frozen four-qubit ZZ feature-map kernel on $N=24$ real indoor air-quality windows, reconstructed on ibm_fez (1024 shots per circuit) under baseline, dynamical decoupling alone, and gate twirling alone, each a single non-interleaved job. Every configuration returned a complete, finite, positive-semidefinite Gram matrix and preserved the centered statevector geometry to a substantial but incomplete descriptive degree (full-matrix centered kernel alignment, CKA, 0.933-0.989). Gate twirling was most faithful on every reported geometry axis, with the only jackknife-resolved improvement over baseline (persisted Spearman, mean absolute error, and full-matrix CKA diagnostics); dynamical decoupling alone was not separated from baseline at the frozen-window scale. Residual hardware distortion, not finite sampling, dominates the discrepancy. Yet fidelity and label alignment were reversed: the most faithful configuration had the lowest centered kernel-target alignment, which sits at or below label-permutation references for statevector and hardware alike. We read the small hardware uplift as a normalization property of the non-affine distortion, not captured signal. These are descriptive results for single jobs on one backend, not causal mitigation-efficacy estimates; no quantum-advantage, hardware-classifier-superiority, or forecasting claim is made. Implementation fidelity and task relevance are distinct axes; hardware quantum machine-learning studies should report both.

Polaritonic architectures seek to engineer molecular properties by hybridizing localized degrees of freedom with delocalized optical cavity fields. However, scaling laws impose a severe bottleneck on N-molecule collective strong coupling: because each molecule contributes only a fractional share to the collective state, localized responses undergo O(1/N) ensemble dilution. We demonstrate a violation of this scaling using fluorescence-encoded infrared spectroscopy of molecular ensembles under vibrational strong coupling, where macroscopically synchronized electronic responses scale as O(1). This scale-invariance reveals a regime of vibronic quantum transduction, where non-local vibrational entanglement is translated into collective electronic entanglement. By demonstrating the generation of macroscopically entangled electronic states from vibro-polaritons without an O(1/N) penalty, these results provide a scalable framework for room-temperature quantum technologies and coherent steering of non-adiabatic chemical pathways.

Let $\mathbb{K}\in\{\mathbb{R},\mathbb{C},\mathbb{H}\}$, put $β=\dim_{\mathbb{R}}\mathbb{K}$, and let $G_n^{\mathbb{K}}$ be an $n\times n$ matrix with i.i.d. standard $\mathbb{K}$-Gaussian entries, namely a standard $\mathbb{K}$-Ginibre matrix. We prove that the normalized row-ordered permanent $W_n^{\mathbb{K}}=\operatorname{per}_{\mathbb{K}}G_n^{\mathbb{K}}/\sqrt{n!}$ has a radial density $p_n^{\mathbb{K}}$ satisfying $\|p_n^{\mathbb{K}}\|_\infty=p_n^{\mathbb{K}}(0)\lesssim_βn^{(β+2)/4}$ and $\sup_{z\in\mathbb{K}}\mathbb{P}(|W_n^{\mathbb{K}}-z|\leq\varepsilon)\lesssim_βn^{(β+2)/4}\varepsilon^β$. In particular, for $\mathbb{K}=\mathbb{C}$, this resolves the Permanent Anticoncentration Conjecture of Aaronson and Arkhipov. The proof compares the squared Gaussian permanent with the squared (Study) determinant in Laplace-transform order.

Quantum-state texture (QST) is an emerging quantum resource that has garnered increasing attention amid advances in quantum theory. In this work, we generalize the QST to quantum-state block texture (QSBT). This generalization provides profound operational interpretations for quantifying the advantages of quantum states in quantum information processing. We pioneer an alternative framework for characterizing and quantifying quantum-state block texture, and propose three types of block texture measures. By comparing these QSBT measures, we investigate their distinctions and interrelationships. We demonstrate that the geometric measure serves as an upper bound for the trace distance-based measure. For a specific family of quantum states, we evaluate the values of two trace distance-based measures. Then we sample four sets of data from this family of states, with each set comprising $5\times 10^4, 10^5, 5\times 10^5$ and $10^6 $ samples, respectively, and present the corresponding distributions. Our results reveal that the QSBT measures constructed via different approaches show distinct characteristics, indicating their potential roles in quantifying the block texture of quantum states.

Sympathetic cooling of data qubits by coolant ions is an essential technique for trapped-ion quantum computing. Conventionally a second ion species is used, requiring additional lasers and complicating optical setups. We propose a scheme for sympathetic cooling using the same species and test it for $^{43}$Ca$^+$ ions. Pulsed sideband cooling and ion addressing are implemented via integrated microwave control, further simplifying optical requirements. We cool a two-ion gate mode close to its ground state ($\bar{n}\approx 0.16$) and benchmark an induced error on the data qubit of $1.7(4)\times 10^{-4}$ per cooling cycle.

The fractional angular momentum of a two-dimensional charge-flux composite is a well-established phenomenon usually derived from a semiclassical Hamiltonian. However, when the composite is treated as an isolated system in free two-dimensional space, the fundamental rotational and reflection symmetries of the $O(2)$ group demand that its total angular momentum is strictly quantized. We address this conceptual discrepancy by applying a full quantum electrodynamic (QED) approach combined with Noether's theorem. We demonstrate that the interaction between the charge and flux, mediated by the vacuum electromagnetic field, generates an intrinsic interaction angular momentum composed of both field momentum and hidden relativistic momentum. This gauge-invariant interaction angular momentum exactly compensates for the fractional part of the kinetic angular momentum. Consequently, the net angular momentum of the composite strictly follows the integer or half-integer quantization rule. Our formalism clarifies that the conventional fractional spin corresponds to the expectation value of the kinetic angular momentum within the perturbed QED ground state. It also elucidates why the standard classical field angular momentum definition fails to capture this in two dimensions, due to non-vanishing boundary terms.

Local unitary equivalence is central to entanglement quantification and classification. Identifying the local unitary equivalence remains a formidable challenge. We address this problem for a class of quantum states with one highly degenerate eigenvalue and the rest non-degenerate simple eigenvalues that are pivotal to structured resources in quantum resource theory. We introduce a ``reduction" procedure that maps each state to a ``reduced state" by nullifying the highest-multiplicity eigenvalue and prove that the local unitary equivalence of the original states is equivalent to that of their reduced counterparts. For the resulting pure or non-degenerate reduced states, we employ the existing invariants or fixed-point subgroup criteria to establish a complete discrimination framework, although the existing criteria can not directly identify the local unitary equivalence of the original states. We also verify the local unitary equivalence of two families of single-parameterized multipartite mixed states constructed by perturbing absolutely maximally entangled states from distinct combinatorial origins, demonstrating the efficacy and generality of our approach.

The fundamental interactions governed by quantum electrodynamics (QED) are intrinsically rich in quantum resources, yet how these resources dynamically redistribute during relativistic scattering is still not fully understood. In this work, we systematically investigate the tree-level Bhabha scattering process (e^- e^+ \rightarrow e^- e^+) within the framework of quantum resource theory, revealing how QED kinematics and Feynman amplitudes strictly dictate resource redistribution. Specifically, we demonstrate a strict anti-correlation between entropic uncertainty and dynamically generated entanglement across diverse initial states. We find that mass-induced single-helicity-flip transitions cause a pronounced geometric symmetry breaking in the non-relativistic regime, whereas the restoration of chiral symmetry in the ultra-relativistic limit ensures strict symmetry about the backward scattering angle. Furthermore, we analytically establish a rigorous equivalence between local wave-particle duality and global bipartite quantum coherence. Finally, evaluating the trade-off between local duality and Bell nonlocality, we show that in the ultra-relativistic limit, transverse scattering of basic factorized states equalizes the s- and t-channel amplitudes to optimize non-local correlations. However, pre-existing local coherence inevitably disrupts this delicate kinematic balance, significantly suppressing the Bell parameter and preventing the maximal violation of local realism. Therefore, we believe the present results provide deeper understanding of the fundamental quantum nature of QED processes.

We study the dynamics of quantum entanglement between two harmonically trapped electrons interacting via the electromagnetic force. Starting from two-mode Gaussian states at thermal equilibrium, we make use of the covariance matrix formalism in order to compute the logarithmic negativity of the evolved state as a quantitative measure of entanglement. We analyze two initial configurations: thermal single-mode and two-mode squeezed states, and describe the time evolution of entanglement in the system for different values of squeezing and temperature, while identifying the parameter regimes accessible to current and near-future single-electron trap experiments.

Coupling phases play a decisive yet often overlooked role in cavity magnonics, particularly in complex multimode systems. Here, we investigate phase-mediated interference effects in a cavity magnonics system comprising a four-post re-entrant microwave cavity coupled to Yttrium Iron Garnet (YIG) spheres. Using an input-output model that explicitly accounts for both internal and external coupling phases, we achieve agreement with experimental microwave transmission measurements. Our results unravel the emergence of a positionally-dependent uncoupled mode due to interference of cavity photon-magnon (internal) coupling phases. Further, we experimentally observed large nonreciprocity at the antiresonance frequencies and show that this feature arises due to the far-detuned modes' odd parity cavity photon-probe (external) coupling phase interfering with the internal coupling phases. Bridging theory, simulation and experiment, these results establish coupling-phase engineering as a key principle for accurately modeling and designing multimode cavity magnonics devices.

Engineering the photonic environment using lattices of coupled resonators, which we refer to as lattice quantum electrodynamics (QED), provides a route to control both the spontaneous emission of individual quantum emitters and the photon-mediated interactions between them. Here we introduce an optical lattice QED platform based on individual dibenzoterrylene (DBT) molecules embedded in anthracene crystals and coupled to lattices of open optical microcavities. This hybrid architecture benefits from narrow-linewidth molecular emitters, site-resolved optical access, engineered coupled-resonator bands, and compatibility with established molecular frequency-tuning techniques. As a proof-of-principle demonstration, we observe emitter-photon bound states formed when the optical transition of a single molecule is tuned to the band gap of a Su-Schrieffer-Heeger (SSH) cavity lattice. These in-gap states display directional localization and photon emission on a single sublattice, inherited from the vacancy-induced topological edge modes of the underlying SSH lattice. Our results establish open-cavity lattices coupled to DBT molecules as a versatile architecture for engineering many-emitter quantum optical systems with controllable photon-mediated interactions.

While combinatorial optimization problems are central to many scientific and engineering applications, their solution remains challenging due to exponentially large search spaces. Variational quantum algorithms offer a promising route for tackling such problems, yet their practical performance is limited by repeated quantum circuit evaluations and classical parameter updates. In this work, we introduce DQAOA-GPT, a hybrid framework that integrates the distributed quantum approximate optimization algorithm (DQAOA), which decomposes a large optimization problem into smaller sub-problems, with GPT-based quantum circuit generation for solving those sub-problems. Rather than relying on iterative variational optimization, the proposed approach uses a trained generative model to directly generate high-quality quantum circuits for the decomposed sub-problems. As a benchmark, we evaluate DQAOA-GPT against conventional DQAOA on dense HUBO optimization problems with up to 100 decision variables. The results demonstrate that DQAOA-GPT significantly reduces computational cost while maintaining competitive solution quality, with larger acceleration observed for larger sub-problem sizes. Although this work focuses on benchmark-scale validation, the framework provides a promising foundation for larger-scale combinatorial optimization in hybrid HPC-QC environments through increased GPU resources and parallel computing capability.

We study redundancy and effectiveness of Variational Quantum Circuits via algebraic and geometric views of Lie groups. Considering unitary transformations acting on Hermitian observables, a stabilizer group decomposition is given. Subsequently, we identify the Hermitian orbit with a quotient space of a symmetric space. Through this connection, we characterize the effective circuit degrees of freedom. Our approach of spectral decompositions and homogeneous spaces yields tractable calculation criteria, which are verified by numerical experiments.

We propose a protocol for preparing mechanical Schrödinger kittens -- mesoscopic quantum superpositions of coherent motional states of an optically levitated nanoparticle -- by adhering single electron time-bin states to its surface. Over short protocol timescales, coherence of the mesoscopic superposition survives the dominant decoherence mechanisms afflicting levitated systems, and can be observed by varying the phase of the time-bin electrons. Interference fringes can be detected with real-time, near-Heisenberg limited interferometry of photons scattered from the particle. This approach eliminates the need for coherent state expansion, dark potentials, and particle release-and-recapture mechanisms, providing a new route to test quantum mechanics in unprecedented scales.

Do quantum kernels improve cross-sectional stock return prediction? We run a controlled horse race on the Chinese A-share market in which a quantum fidelity kernel, a projected quantum kernel, and a classical RBF control share identical training subsamples, solver, and tuning budgets, so that only the kernel is exchanged. On the main evaluation -- a point-in-time universe and 170 walk-forward windows (2012-2025) -- no quantum advantage exists: the fidelity kernel is indistinguishable from its RBF control ($Δ$IC $=+0.005$, $p=0.42$), and a $2\times2$ design crossing kernel type with training budget (a Nystrom extension to the full ~38,000-observation windows) shows quantum kernels matching, but never beating, equal-budget linear models; after family-wise correction no pairwise difference among eleven models is significant, with point estimates favoring penalized linear regressions throughout. We then document how the opposite conclusion arises: a 60-window evaluation on a universe screened with full-sample information makes the same quantum kernel appear dominant on stability criteria and significantly better than neural baselines. Interaction characteristics from the anomalies literature help nothing, quantum or classical; a widened bandwidth grid reveals an interior optimum rather than the near-classical endpoint a coarse grid suggests; and the geometric difference, while large throughout ($g \gg 1$), does not predict out-of-sample gains ($ρ=-0.20$). We propose protocol standards -- kernel-swap controls, budget-equalized comparisons, point-in-time universes, and multiplicity-robust inference -- for empirical claims of quantum advantage in finance.

Qubits with strongly biased noise, in which phase-flip errors are orders of magnitude more frequent than bit-flips, arise both naturally, as in electron and nuclear spins, and by engineering, as in stabilized cat qubits. This noise structure holds the promise of reducing the daunting hardware overhead of fault-tolerant quantum computing, but exploiting it requires physical operations that do not convert frequent phase-flips into rare bit-flips. In this review, we analyze the most prominent fault-tolerant protocols for biased-noise qubits, organized according to the available set of such bias-preserving operations. When this set is restricted to the CZ gate together with preparation and measurement in the X basis, we show that the complexity of the required syndrome extraction gadgets essentially cancels the benefit of the noise bias: at experimentally relevant error rates, one may as well ignore the bias and rely on standard error correction designed for depolarizing noise. The situation changes drastically when a bias-preserving CX gate is available: the hierarchy of errors can then be reflected in the structure of the code, with frequent phase-flips corrected by a dedicated high-threshold code and rare bit-flips by concatenation with a high-rate code. The same hierarchy also enables hardware-efficient preparation of magic states. Finally, as a bias-preserving CX is forbidden in naturally biased platforms and challenging in engineered ones, we present a measurement-based architecture in which a high-fidelity quantum non-demolition readout of multi-qubit Pauli Z operators takes its place, extending these overhead reductions to a much broader range of physical platforms.

Belief-propagation (BP) decoding for quantum low-density parity-check (QLDPC) codes is attractive due to its low complexity, but its performance is often limited by short cycles, degeneracy, and convergence failures. Recently, reinforcement-learning-based sequential variable-node (VN) scheduling (RL-S) was shown to improve BP decoding by learning state-dependent update orders. However, the VN-by-VN nature of that approach offers limited within-iteration parallelism, since only one VN is updated at a time. In this paper, we propose a cluster-based extension of RL-S for QLDPC codes. The VNs are partitioned into fixed clusters, and at each scheduling step the RL agent selects one cluster to update, after which all VNs in that cluster are updated in parallel using the same pre-update incoming messages. To keep the tabular state space practical for large cluster sizes, we introduce a permutation-invariant cluster state based on a normalized histogram of local mismatch weights, followed by quantization. This representation makes the number of cluster states depend on the quantization resolution rather than the cluster size. We also develop the corresponding cluster-level Markov decision process, reward function, and Q-learning update. Numerical results on representative QLDPC codes show that the proposed clustered learned scheduling preserves most of the error-rate benefit of VN-level learned sequential scheduling while substantially reducing the number of scheduling decisions per BP iteration, thereby providing an attractive latency-parallelism tradeoff.

A graviton can be converted into a phonon in a resonant bar detector. First-order perturbation theory predicts a strong enhancement of this conversion for coherent and squeezed graviton states, but the probability can exceed unity when the coherent or squeezing parameter is large. Since a conversion probability must satisfy the unitarity bound, we solve the graviton-phonon quantum dynamics exactly within the rotating-wave approximation. For an initial coherent state, we find that the conversion occurs intermittently through narrow bursts separated by intervals of strong suppression. For an initial squeezed state, the departure from perturbative behavior occurs earlier, and the conversion is strongly suppressed after its initial growth. These effects may provide signatures of quantum graviton-phonon dynamics relevant to single-graviton detection.

The Schrödinger equation can be rewritten as a second-order equation for a single real-valued scalar field. Taken at face value, however, this one-field reduction obscures several local structures of quantum mechanics: the Born density and current, the role of momentum as a generator, and the usual derivation of the uncertainty relation. We argue that these difficulties do not show that real variables fail. They show that the reduced equation is not, by itself, a complete local representation of the theory. Its coherent real form is obtained by restoring the underlying Hamiltonian phase-space structure, where the missing component reappears as a canonical partner. In this real phase-space formulation, the standard structures reappear locally, and minimal magnetic coupling reveals an internal \(SO(2)\) gauge structure. Thus, the symbol \(i\) can be removed, but the symplectic and complex structure it encodes cannot.

We introduce a physics-informed graph neural network decoder for the surface code. A discrete Poisson equation on the syndrome graph acts as a hard inductive bias on which a graph encoder learns syndrome-adaptive edge weights. A differentiable solver returns the node potentials and the associated edge current. Our central observation is that the logical-error signal is not carried by any part of that current, but by how the syndrome sits relative to the two code boundaries. We place a sink on each of the two boundaries linked by the logical operator and read the difference of the currents they drain. We prove that this single number is a topological pairing: it weighs each excited detector by a smooth coordinate that runs from +1 on one boundary to -1 on the other, and sums the votes. The coordinate is fixed by both the code topology and the learned metric, generating an exact and free-parameter readout. On the rotated surface code under circuit-level depolarising noise, this one topological scalar matches the best full-field readout. That parity is itself the result: for one logical qubit the logical signal is one-dimensional, so projecting onto it discards nothing. At larger code distance the picture strengthens indicating that isolating the pairing helps more as the field grows larger and sparser.

Physical noise in near-term quantum hardware is usually treated as a nuisance to suppress. We ask whether it can instead act as a hardware-native regularizer for photonic hybrid quantum-classical neural networks (PHQCNNs), analogous to noise-injection regularization in classical deep learning. Using Quandela's Perceval simulator and the MerLin framework, we build PHQCNNs for Iris, Digits, and MNIST and inject Perceval's seven-parameter physical noise model directly into training. A genetic algorithm searches the six continuous noise dimensions and 1 boolean parameter to find, per dataset, the configuration maximizing validation accuracy, compared against a noiseless baseline across five seeds. GA-tuned noise yields modest accuracy gains on Iris (+0.82pp) and Digits (+1.45pp), but a clear degradation on MNIST (-1.21pp). Per-parameter sweeps show that no individual noise parameter is consistently beneficial, motivating the joint search, while a second-order loss expansion shows that physical noise induces a Tikhonov-like regularization term whose effect is dataset-dependent. Physical photonic noise can thus act as a free regularizer, but not universally.

Quantum annealing (QA) is used to solve combinatorial optimization problems (COPs). When COPs are implemented on quantum annealers, they are typically encoded as quadratic unconstrained binary optimization (QUBO) problems, but constraint encodings often increase the number of qubits and the embedding overhead. This issue is particularly important for COPs with inequality constraints, where standard slack-variable formulations introduce additional binary variables. Unbalanced penalization (UP) avoids slack variables, but the original UP formulation requires tuning two penalty coefficients and contains a squared residual term that can increase the number of quadratic couplings. In this paper, we propose the unbalanced penalization Ohzeki method (UPOM), which combines UP with the Ohzeki method for inequality-constrained COPs. UPOM replaces the two static penalty coefficients of original UP with an auxiliary-variable update and removes the squared residual term from the Hamiltonian used for sampling. We further propose the deep-unfolded unbalanced penalization Ohzeki method (DU-UPOM), which learns the step-size schedule of the UPOM update from training instances. Numerical experiments on random knapsack problems show that UPOM improves over original UP and that DU-UPOM reaches optimal solutions in fewer iterations than fixed-step UPOM and other baseline. These results demonstrate that the proposed framework reduces the tuning and embedding burdens of UP while making the Ohzeki method trainable for inequality constraints.

Matter-wave Bell interferometers provide a sensitive probe of mass-dependent decoherence in entangled quantum systems. The degree of entanglement is obtained from the Bell-correlation amplitude of this interferometer. For observing potential mass-dependent decoherence, a reliable interpretation of any observed reduction in the Bell correlation amplitude is required, which depends on three factors: geometric dephasing, environmental decoherence, and technical dilution from source and detection statistics. In this work, we present a framework based on the Schwinger SU(2) mapping to separate these contributions into local unitaries or dissipative channels. We show that by evaluating the Bell correlation at zero interferometer path difference, it is possible to extract a source-distribution-independent Bell correlation amplitude reduction. When this framework is extended to involve atoms of different mass, we show that the known differential decoherence channels are negligible at current sensitivity. This yields a concrete bound at which a dual-species Bell interferometer would begin to signal differential decoherence beyond the known systematics, opening the way for such systems to probe new physics, such as mass-dependent decoherence mechanisms.

Quantum secret sharing is a fundamental technique in quantum cryptography. However, in practical quantum networks, it still faces several bottlenecks, such as high quantum communication cost and low transmission efficiency. To reduce the communication cost, ramp quantum secret sharing schemes have been proposed in existing studies. Nevertheless, intermediate sets in such schemes may leak partial information about the secret. To address this problem, this paper presents a method for detecting intermediate sets. Based on this method, we further propose a communication-efficient perfect quantum secret sharing scheme with eavesdropping detection capability.We analyze the communication cost under different numbers of participating parties and determine the range of participants that minimizes the reconstruction communication cost. The results verify the communication efficiency and security of the proposed scheme.

In recent years, vortex light, a distinctive form of structured light, has attracted considerable attention owing to its unique properties and the rich physical phenomena arising from its interaction with matter. In this paper, we investigate the propagation dynamics of vortex beams in a symmetry-broken three-level system based on forward and backward three-wave mixing (TWM) processes. We find that both processes enable the transfer of high-gain vortex light, with the associated topological charges obeying identical algebraic relations. The forward process exhibits periodic oscillatory transmission and modulates the transverse spatial profile of the generated signal vortex field, whereas the backward process features stable transmission and produces a signal field with higher gain and improved fidelity. Under the Autler-Townes splitting (ATS) regime, the probe field detuning in both schemes has a negligible influence on the gain. Optical depth influences only the rate at which the gain approaches its maximum, while the peak value remains unchanged. These results constitute a meaningful extension of the work reported in reference [40] and may provide a feasible approach for quantum communication, quantum computation, and the generation of high-gain, high-fidelity vortex light.

We propose a scheme for achieving nonreciprocal phonon blockade in a quadratic optomechanical (QOM) system consisting of two spinning resonators near-field coupled to a nanomechanical oscillator. Due to the Sagnac-Fizeau effect, pump fields propagating in opposite directions experience distinct effective detunings,thereby leading to asymmetric intracavity intensities. Through the optical spring effect, this intensity imbalance gives rise to direction-dependent shifts in the effective mechanical frequency, providing the core mechanism for nonreciprocal phonon blockade. By judiciously setting parameters, single-phonon resonant excitation leads to conventional phonon blockade for one pump direction, whereas two-phonon resonance facilitates phononinduced tunneling (PIT) for the other. The pronounced nonreciprocity is quantified by a contrast ratio in the phonon second-order correlation function exceeding 55 dB. To elucidate the nonreciprocal statistics, the phonon blockade is further analyzed in terms of interference between the coherent component and squeezed fluctuations. Incorporating thermal phonons, we reveal an extended nonreciprocal thermal effect, where increasing thermal noise degrades antibunching toward Poissonian statistics in one direction, yet reverses the statistics from bunching to antibunching in the opposite direction. Our work provides a pathway toward nonreciprocal phonon devices and directional phonon switches, with potential applications in chiral networks and phononic information processing.

The Ising model is ubiquitous in various optimization problems but notoriously difficult to solve due to combinatorial explosion. In view of this, Hamiltonian reduction is a useful preprocessing technique for reducing the effective problem size before applying heuristic solvers. However, existing reduction techniques mainly target second-order Ising models, whereas many pseudo-Boolean formulations naturally contain higher-order interactions. In this work, we generalize the concept of non-separable groups to arbitrary-order Ising-like models and develop a Hamiltonian reduction framework that iteratively detects and merges constrained spin groups into single variables. We benchmark the reduction on synthetic hypergraphs and higher-order network datasets, and evaluate its integration with downstream order-reduction and solver workflows. Our results establish a foundation for Hamiltonian reduction in higher-order Ising-like optimization problems.

We construct a simple model of two particles mutually attracting/repulsing in a one-dimensional lattice and investigate the corresponding dynamics. We show that enforcing reversible unitary evolution on a minimal direct-motion interaction rule necessarily gives rise to emergent boundary-memory and non-trivial dynamics. Remarkably, the resulting boundary-memory leads to event-horizon-like behaviour, entanglement between subsystem, and Page-curve-like entanglement dynamics.

The eigenstate thermalization hypothesis (ETH) provides a statistical description of thermalization in isolated quantum many-body systems, yet the phenomenological smooth function $f_O(\bar{E},ω)$ -- which controls the energy dependence of off-diagonal matrix elements -- lacks a systematic microscopic foundation. We develop a multi-resolvent hierarchy for the correlation corrections entering the ETH smooth function. Using recursive projection identities together with a diagonal closure approximation (DCA), the hierarchy organizes multi-channel interference processes by the number of interacting bath channels, replacing the uncontrolled neglect of higher-order correlations with a systematically improvable expansion. The ETH smooth function is thereby obtained as $f_{ji}^2 = D_{ji} + \sum_{r\ge 2} g_{ji}^{(r)}$, where the diagonal baseline $D_{ji}$ and each correlation level $g_{ji}^{(r)}$ are expressed entirely through diagonal spectral functions and microscopic interaction couplings, providing a unified, closed, and systematically improvable microscopic theory. A rigorous projector sum rule constrains the entire hierarchy: the integrated off-diagonal correlation carries a negative bias of order unity, a consequence of projector idempotency. The hierarchy further reveals a parity structure in which even-$r$ sectors carry even parity under $ω\to-ω$ while the $r=3$ sector generates the first odd-parity (skewness) contribution -- absent from all single-resolvent closures -- suggesting experimentally testable signatures in quantum many-body systems.

In this Letter, we theoretically propose an alternative scheme for generating vortex optical squeezing, based on the Raman scattering process in a coherently prepared medium, distinct from approaches such as parametric down-conversion and four-wave mixing. Our analysis reveals that both the input control field and the generated signal field can exhibit squeezing upon adjusting the relevant system parameters, with the control field exhibiting a greater degree of squeezing under identical conditions. We further demonstrate the existence of optimal squeezing values over a range of tuning parameters, highlighting the flexibility and robustness of the proposed scheme. These findings may offer a new reference for continuous-variable vortex optical squeezing and possess potential applications in domains such as quantum information processing, quantum precision measurement, and quantum sensing.

For Hamiltonian $H = \sum_j h_j$, we prove asymptotically tight lower bounds on the gate and query complexities of simulating time evolution on a quantum computer. Our bounds hold for arbitrary term norms $\|h_j\|$, time $t$, and trace-distance error $ε$. The matching upper bound (known as composite qDRIFT) consists of high-order Trotterization of the large terms and a randomized first-order Trotterization of the small terms. Unlike prior work that chooses worst-case $\|h_j\|$ to encode the computation of parity or other Boolean functions in time evolution, our proof is elementary and based on a local, bounded-degree classical Hamiltonian. Our work suggests that for many physical systems (e.g., power-law interactions), gate count must scale polynomially in $1/ε$, contrary to the complexity suggested by counting coherent oracle queries such as those in the block-encoding model.

Quantum network implementations using single spontaneous parametric downconversion (SPDC)-based broadband entangled photon pair source (EPPS) have been reported recently. Here, leveraging the wavelength-correlation between entangled photon pairs, the traditional wavelength division multiplexing (WDM) method is utilized to route photons based on their wavelengths. From single EPPS, entangled photon pairs are distributed in a centralized way to different node pairs in the network. However, the number of nodes pairs that can be entangled in a network is limited by the number of entangled wavelength pairs that an EPPS can generate. To entangle a higher number of node pairs in a network, multiple EPPSs can be employed. In this work, we present a WDM-based entanglement distribution approach using multiple EPPSs in multi-hop repeaterless mesh optical networks. We experimentally characterize two EPPSs developed in-house and consider multiple such EPPSs in the network to perform network-level simulations. We consider heterogeneous entanglement demands requiring different entanglement bit (ebit) rates and entanglement visibility. For each entanglement demand, EPPS placement/selection, wavelength-pair assignment, and photon pair routing are performed considering the degradation in both ebit rate and visibility with fiber length and hops in the network. Two main findings of this study include: (i) a hybrid approach of one-photon (OP) and both-photon (BP) entanglement distribution provides higher flexibility in multi-EPPS placement and (ii) distributed entanglement distribution using multiple EPPSs enables better entanglement resource utilization and higher entanglement demand acceptance as compared to centralized entanglement distribution.

In addition to electric and magnetic multipoles, the expansion of current density also yields toroidal terms, a lesser-known family of multipoles. A recent proposal, I. Kuprov $\textit{et al.}$, Science Adv. 8 abq6751 (2022), explores the possibility of a direct observation of optical toroidal transitions in hydrogen and alkali atoms in the presence of a large magnetic field that decouples the spin and the angular momentum of the electron. However, the difficulty of observing these transitions against the nearby electric dipole (E1) transitions were underestimated because of extra admixture coming from diamagnetic coupling. Here, we revisit the toroidal coupling in atoms, taking diamagnetic contribution into account, and discuss the technical challenges of observing toroidal coupling in atomic physics. We show that toroidal transition should be searched in transitions with low principal quantum numbers. The remaining strong electric-dipole contribution could be removed using an appropriate differential measurement.

In this paper, we examine the dynamical charge-Kondo-breakdown scenario proposed for cuprate superconductors within the perspective of renormalization group (RG) topology. By analyzing the coupled RG flow equations governing the effective low-energy theory, we determine the fixed-point structure, stability properties, and global organization of the flow. We find that the putative finite-coupling interacting fixed point is unstable against perturbations transverse to an invariant critical manifold. As a result, generic RG trajectories exhibit runaway behavior. To elucidate the global structure of the theory, we combine analytical solutions of the flow equations with numerical phase portraits and Poincaré compactification. This analysis reveals that the interacting fixed point exhibits a marginally relevant instability, generating an exponentially large but finite crossover scale. The resulting flow topology closely resembles anisotropy-driven runaway flows encountered in fluctuation-induced weakly first-order transitions. Within this framework, the apparent quantum-critical regime can be understood as an extended crossover controlled by a near-critical fixed point, rather than by asymptotic scale invariance. The results obtained indicate that the existence of extended scaling behavior does not, by itself, imply the presence of a stable interacting quantum critical state. More generally, our analysis demonstrates how RG topology can provide a powerful diagnostic for distinguishing genuine criticality from pseudo-critical behavior in theories of strongly correlated quantum matter.

Kernel methods are powerful tools in machine learning but commonly used full-Gram kernels face three key limitations: (1) quadratic scaling with training set size; (2) the use of fixed, non-trainable kernels; and (3) the absence of an intrinsic formulation for multiclass classification. We present McQuack, a trainable quantum kernel method for multiclass problems that achieves linear scaling in the number of training samples. This is accomplished by replacing the full training-set Gram matrix with a trainable sample-to-(class-centroid) fidelity matrix. We evaluate the model in simulation and on 124 qubits of two IBM devices, across more than 150 datasets. In simulation, McQuack outperforms existing "pure" quantum baselines, while results from hardware inference -- obtained without training -- achieve performance similar to an RBF kernel. Finally, we study the trainability of the model and observe no evidence of barren plateaus in our experiments with up to 13 qubits, and highlight the importance of parameter initialization for successful optimization.

Quantum teleportation is a key protocol for transmitting quantum information using entanglement and classical communication. Its reliability is constrained by both the availability and fidelity of shared entangled pairs, which are affected by stochastic generation and memory decoherence. In this work, we focus on encoded teleportation, in which quantum information is encoded using a quantum error-correcting code and transmitted as a codeword. We evaluate reliability in terms of logical error probability, considering latency-constrained settings where entanglement is accumulated over time and degrades while in memory. We develop a unified framework that captures the interaction between entanglement availability, decoherence, and coding decisions. Our results show that the benefits of longer codes depend on the availability and fidelity of entangled pairs, as acquiring additional resources introduces delays that can reduce their quality. To address this latency-reliability tradeoff, we leverage code puncturing to enable flexible encoded teleportation, allowing the effective code length to adapt across different latency regimes while preserving a common stabilizer structure. Numerical results show that encoded teleportation can provide substantial reliability gains over uncoded transmission under a common entanglement-acquisition latency constraint, and that selecting appropriate punctured codes improves performance across varying latency budgets. Overall, our results highlight the importance of resource-aware adaptation for reliable quantum networking.

In this work, we investigate the quantum entanglement properties of analog Hawking radiation produced by a moving mirror. Using two detector modes defined through window functions on a quantum field, we quantify the bipartite entanglement established between these modes. Our results reveal that the amount of entanglement accessible to the detectors increases when the mirror follows trajectories with non-monotonic, time-dependent acceleration, which are accompanied by the emission of negative energy flux. This indicates that the negative energy flux acts as a channel through which information can be returned. To substantiate this perspective, we examine how the recovery or reconstruction of the associated partner modes is related to the negative energy flux emitted by the mirror.

We establish a quantitative adiabatic estimate for a class of finite-dimensional non-Hermitian Schrödinger dynamics. The original non-Hermitian Hamiltonian is assumed to be diagonalizable with real spectrum and non-crossing eigenvalues. We then construct a dynamically compatible time-dependent metric operator, and its positive square root defines a Dyson map. The associated Dyson-transformed Hamiltonian is Hermitian. When this Dyson-transformed Hamiltonian satisfies the Hermitian adiabatic assumption, the standard resolvent-projection method gives an explicit adiabatic estimate in the Hermitian representation. Pulling this estimate back through the Dyson map gives an approximation in the original non-Hermitian representation. The resulting Dyson-pulled-back projections are then compared with the spectral projections of the original non-Hermitian Hamiltonian by using a contour-resolvent estimate. The final bound contains two contributions: the pulled-back Hermitian adiabatic error and the projection-comparison error. A two-level non-Hermitian model is presented to illustrate the hypotheses of the theorem and the two contributions appearing in the final estimate.

Incommensurability and elastic reconstruction do not by themselves define a structurally superlubric phase. We define fully sliding and pinned zero-temperature phases by $\limsup_{A\to\infty}τ_{\rm dep}^{\max}(A)=0$ and $\liminf_{A\to\infty}τ_{\rm dep}^{\min}(A)>0$, respectively; $Λ_n=|V_n|G_{n,i}[D_{\rm rel}^{-1}(\mathbf q_n)]_{ij}G_{n,j}$ measures only reconstruction susceptibility. Translational covariance then proves that a clean, smooth, infinite moiré continuum can reconstruct without acquiring a bulk sliding barrier. We restore atomic sampling in a two-dimensional discrete model of graphene/hBN and test both a diffusion quantum Monte Carlo first-star potential and a 15-harmonic Leven potential across three rational approximants and five directions. No physical-coupling equilibrium or metastable barrier is resolved. The Leven spectrum raises the largest tested $Λ$ from $0.142$ to $0.212$, while artificial scaling through $Λ=1$ reaches uncontrolled strain before a size-independent threshold appears. The tested zero-temperature in-plane models are therefore consistent with an elastically relaxed sliding regime; $Λ=1$ is a reconstruction scale, not a static phase criterion.

Quantum nonlocality based on the violation of Bell-like inequalities constitutes a fundamental feature of quantum physics and drives the development of device-independent (DI) quantum information technologies. Existing studies of Bell nonlocality have mainly focused on physical qubit systems, where the observed nonlocal correlations are directly encoded in physical degrees of freedom. The decoherence sensitivity of Bell nonlocality largely limits the performance and security of its DI applications. Here, we investigate the robust logical Bell nonlocality based on quantum error correction codes. We construct the general logical Bell inequality in the stabilizer coding subspace and prove its violation indicates the global nonlocal feature of the logical system. Then, we indicate that the logical Bell nonlocality is robust against decoherence. Comparing with the physical qubit system, the fidelity thresholds for the logical Bell inequality violation based on the [[3,1,1]] and [[7,1,1]] repetition codes under the bit-flip error model can be reduced from 82.8% to 73.10% and 66.35%, increasing DI QKD's bit-flip noise threshold from 10.64% to 14.42% and 23.36%, respectively. Such stabilizer-based framework can be also used to characterize the multipartite logical Bell nonlocality in principle. Finally, a logical Bell test implementation circuit based on the [[3,1,1]] repetition code is presented. This work provides a feasible avenue for unlocking robust Bell nonlocality in scalable logical quantum systems and facilitates its applications in future scalable quantum network.

We propose a minimal quantum-optical scheme for generating hybrid entanglement between photon polarization and electronic orbital angular momentum in a semiconductor quantum disk. A spin--orbit structured two-photon state excites two channels in the same disk: a radiatively recombining zero-orbital-angular-momentum channel and a finite-orbital-angular-momentum channel that stores the electronic orbital qubit. An effective coherent mapping prepares a selected two-excitation state, followed by emission of a photon whose polarization is entangled with the residual electronic orbital state. A master-equation analysis shows that the heralded state conditioned on single-photon occupation of the selected output mode approaches the target entangled state in the ideal coherent limit. We also discuss orbital relaxation and perturbative validity conditions for branch-dependent Coulomb shifts, orbital-angular-momentum mixing, and finite-orbital-angular-momentum radiative leakage. This proof-of-principle effective model suggests a route toward structured-light-mediated photon--electron hybrid entanglement in semiconductor nanostructures.

We study the time evolution of entanglement and quantum discord for a pair of maximally entangled qudits of arbitrary dimension $d$ under non-Markovian pure dephasing, using the exact solution of the independent boson model. Because this solution requires no Born--Markov, Lindblad, or rotating-wave approximation, every result reported here follows directly from the exact dynamics. Exploiting the Toeplitz structure of the resulting density matrix, we obtain a closed-form expression for the negativity as a finite sum, valid for arbitrary dimension and evolution time, together with a corresponding closed-form expression for the quantum discord. For the family of dephased maximally entangled states considered here, we prove that a computational-basis measurement is globally optimal over the entire POVM space, thereby eliminating the numerical optimization otherwise required for evaluating the quantum discord. We further show that both quantities saturate, as the dimension grows, to a dimension-independent limiting value, with a convergence rate of exactly $1/d$. For negativity, this scaling law is established through a rigorous theorem, including a Gaussian-type error bound of order $e^{-αd^2}$, and is confirmed across six independent parameter regimes for two distinct classes of spectral density, Lorentzian and Ohmic; for discord, the same leading-order behavior is found numerically across the six Lorentzian regimes. The analytical results are validated by independent numerical approaches, including reconstruction from the underlying definitions, arbitrary-precision arithmetic, and a complementary pseudomode cross-check.

We develop an analytical procedure to retrieve fundamental material parameters of monolayer transition-metal dichalcogenides from optical and magneto-optical exciton spectra, based on the solvable modified Kratzer model. The proposed retrieval procedure naturally consists of two complementary stages. In the first stage, explicit inversion formulas determine the quasiparticle bandgap, effective screening parameter, and energy scaling factor directly from the experimentally measured energies of the three lowest excitonic states, from which the screening length is subsequently obtained. In the second stage, an analytical expression for the magnetic-field dependence of the exciton energies independently yields the reduced exciton mass, from which the surrounding dielectric constant is then calculated. Once the complete set of material parameters has been retrieved, the framework analytically predicts the diamagnetic coefficients, exciton radii, and complete magnetoexciton spectra without introducing additional fitting parameters or matrix diagonalization. The method is applied to a broad range of experimental samples for WSe$_2$, WS$_2$, MoS$_2$, MoSe$_2$, and MoTe$_2$ monolayers embedded in different dielectric environments. The retrieved material parameters are in good agreement with independent experimental measurements and previous Rytova--Keldysh (RK) calculations, while the predicted excitonic properties accurately reproduce available magneto-optical observations. The proposed analytical theory provides an efficient, physically transparent alternative to conventional numerical fitting procedures and offers an effective tool for the rapid characterization of two-dimensional semiconductors via excitonic spectroscopy.

Nuclear quantum effects are rigorously captured by imaginary-time path integrals, which map the quantum Boltzmann distribution onto a ring polymer of classical replicas. Yet the nuclear masses, the coupling to the environment, and the boundary conditions of the path remain hard-wired in the simulation or the trained model, even though this quantum context enters the path measure only through a quadratic action known in closed form. Here we show that a denoiser trained on classical Boltzmann statistics alone, composed at sampling time with an analytic Gaussian component carrying the entire quantum context, yields the quantum Boltzmann distribution of the nuclei. Such a composition exists and is exact whenever the training noise does not exceed the intrinsic quantum uncertainty of the target ensemble, and it is invariant across all quantum contexts admitted by this bound. We show exact transfer across temperature, isotopic mass, dissipation strength, and the boundary conditions of the path in theory and in numerical experiments, without retraining. The last yields the end-to-end displacement and momentum distributions of a tagged nucleus from open imaginary-time paths. The same invariance extends in principle to the permuted boundary conditions of bosonic exchange, with the identical denoiser. In this view, the noise of generative modeling and the quantum fluctuations of the nuclei are two faces of the same quadratic structure.

We establish the global well-posedness of the Cauchy problem for the reverse space-time nonlocal Fokas-Lenells equation with the weighted Sobolev initial data $q_0(x)\in H^{3}(\mathbb{R}) \cap H^{2,1}(\mathbb{R})$ on the line. We develop the inverse scattering transform formulated via the associated Riemann-Hilbert problems to study this issue. A spectral uniformization transform is introduced to resolve the singular behavior inherent in the KN-type negative flow spectral problem. Owing to the reverse space-time reduction, reflection coefficients no longer satisfy the usual Hermitian conjugation symmetry, and the coercivity of the jump matrix is therefore not available a priori. The quantitative smallness condition on the initial data yields uniform bounds on the reflection coefficients and ensures the uniform positive definiteness of the Hermitian part of the associated jump matrix. The resulting coercivity allows us to establish the bounded invertibility of the associated singular integral operator through a Fredholm and vanishing-lemma argument. Under this condition, we prove an $L^{2}$-Sobolev bijective correspondence between the potential and scattering data, exclude spectral singularities on continuous spectra, and obtain the global existence and uniqueness of solutions. Moreover, the associated solution map is Lipschitz continuous on the admissible initial-data class.

The work presents analytical solutions to the Schrodinger equation for the Killingbeck potential, a Hybrid model combining harmonic, linear and Coulomb terms, and which is also an approximate model of Yukawa-type potentials. The radial Schrodinger equation is solved by means of the series expansion method, thus yielding the exact expressions of both bound-states solutions and eigen-functions for the systems; these systems include quarkonium and confined hydrogen-like atoms in plasma environments. Furthermore, we offer a constructive commentary on the work of Obu et al. (East Eur. J. Phys. 3, 146-157, 2023), with the aim of clarifying a mathematical misstatement used in their analytical treatment of analogous systems.

Natural and engineered classical systems are replete with examples of synchronization, understood as the adjustment of rhythms of physical systems. Such synchronization is at the heart of the stability of several classical technologies, such as mechanical bridges and electrical networks. Given the advent of quantum simulation and computation technologies, it is natural to study a quantum analogue of synchronization and explore novel applications. This review surveys synchronization in few and many-body quantum systems, measures that quantify them, and their applications to quantum technologies.

Many well-motivated dark matter models predict meV-scale energy deposits in interactions with terrestrial experiments, but this regime is challenging to probe due to a lack of mature single-quantum detectors. Here we report results from QUALIPHIDE (QUAntum LImited PHotons In the Dark Experiment), a cryogenic dark matter search using a $41$-pixel array of energy-resolving microwave kinetic inductance detectors with a $13$ meV threshold, simultaneously used to look for both conversion photons from THz wavelength hidden photon dark matter and phonons from particle-like light dark matter interactions. The experimental design, with on- and off-focus pixels for the hidden photon search, allows for a data-driven background model, giving the experiment discovery potential. A blind analysis of $22$ hours of data shows no significant excess, setting the strongest constraints on the hidden photon kinetic mixing parameter $χ$ over the mass range of $13$-$90$ meV/$c^2$, reaching $1.5\times10^{-12}$ at $50$ meV/$c^2$. These data also yield among the first terrestrial limits on dark matter scattering off nuclei and electrons, down to $5$ MeV/$c^2$ and $20$ keV/$c^2$, respectively. The low threshold also enables future study of the low-energy excess limiting cryogenic detectors and, as we project, will allow for a terahertz-scale QCD axion search with a magnetic field.

The Variational Quantum Eigensolver (VQE) is a leading algorithm for estimating molecular ground-state energies on near-term quantum hardware, with applications spanning quantum chemistry, materials science, and drug discovery. As VQE workloads are increasingly deployed through cloud-based ``VQE-as-a-service'' pipelines, they become exposed to adversaries such as compromised service components, malicious co-tenants, or insiders in the transpilation stack, any of which can corrupt results before they reach the user. A range of attacks on variational quantum circuits has been proposed, but each has been studied in isolation: some on quantum classifiers with accuracy-based metrics, others on variational quantum algorithms with energy-error metrics. This lack of a common evaluation setup makes their relative severity difficult to compare and leaves the security of VQE poorly characterized. In this work, we present \textbf{VQE-AdvBench}, the first unified red-teaming benchmark for the Variational Quantum Eigensolver, systematizing these attacks under a single evaluation protocol to rigorously assess VQE's adversarial robustness. We organize attacks along a black-, gray-, and white-box access taxonomy, and evaluate seven representative attack scenarios -- the QTrojan circuit backdoor, the QDoor parameter backdoor, parameter-space adaptations of FGSM and PGD, and three QNBAD noise-induced variants -- over a fixed molecule-ansatz-backend-metric configuration, on H$_2$ and H$_3^+$ across five noise-calibrated IBM backends. Our results reveal a clear severity ordering: noise-induced attacks that manipulate the Zero-Noise Extrapolation (ZNE) pipeline are the most damaging (up to 8.84$\times$ error amplification), followed by the QTrojan circuit-level backdoor (7.52$\times$), while the QDoor parameter-level backdoor is the least effective, yielding only marginal amplification (up to 1.37$\times$).

A Cayley graph $\operatorname{Cay}(Γ,S)$ over a finite group $Γ$ is said to be normal if its connection set $S$ is a union of some conjugacy classes of $Γ$. This paper investigates perfect state transfer in Grover walks on normal Cayley graphs. The Grover walk is a widely studied discrete-time quantum walk. We establish a necessary and sufficient condition for the occurrence of perfect state transfer on normal Cayley graphs. As applications, we derive explicit spectral criteria for perfect state transfer on Cayley graphs over abelian groups, dicyclic groups, and dihedral groups. These results yield several infinite families of Cayley graphs exhibiting perfect state transfer. We further obtain simple combinatorial characterizations of the existence of perfect state transfer on Cayley graphs over dihedral and dicyclic groups. Our general characterization also recovers a number of previously known results as special cases. As a further consequence, we obtain a complete characterization of perfect state transfer on unitary Cayley graphs. In particular, we prove that exactly four graphs in the class of unitary Cayley graphs exhibit perfect state transfer.

We show that informational completeness, while sufficient to have a bijection between ideal measurement probabilities and quantum states, does not guarantee statistically stable reconstruction from finite measurement data. To address this problem, we develop a general estimation theory for continuous-variable systems in which stable reconstructibility is characterized by the POVM effects forming a measurement frame. Informational completeness is therefore necessary, but not sufficient, for stable reconstruction. Our framework is based on measurement frames in a $σ$-regularized operator geometry, where the reference state $σ$ encodes prior information about relevant features of the measured states. For any fixed measurement scheme, observables may be inaccessible, weakly reconstructible only through estimators with divergent variance, or stably reconstructible by finite-variance unbiased estimators. The relevant regime is determined by the range of the POVM synthesis operator. Our framework provides practical methods for constructing estimators and gives an operational interpretation of singular quasiprobability distributions, including the Glauber-Sudarshan $P$ representation: quasiprobabilities act as unbiased estimators for associated observables, and their singularities reflect a pathological feature of the corresponding measurement: its lack of loewr frame bound. We furthermore show how this formalism naturally provides operational regularization procedures tied to prior information. Overall, our framework provides a unified view of continuous-variable tomography, quasiprobability representations, and classical-shadow estimation.

Quantum simulation of open quantum systems offers a pathway towards better understanding various non-equilibrium physics that would otherwise be challenging to study. Most open quantum systems studied are modeled as obeying the Markov approximation, where the bath into which the system dissipates information is assumed to be unaffected by the system-bath interaction. However, real baths are in general influenced by this interaction to some degree, and some systems which exist in structured non-Markovian environments can display novel behavior as a result. Here we utilize a trapped ion quantum simulator to simulate a single spin-$1/2$ driven-dissipative system with a non-Markovian dissipation channel, and experimentally compare steady-states to those from an analogous Markovian bath. We observe that a non-Markovian dissipative channel can dramatically change the steady-state even for a single qubit, to a regime inaccessible for Markovian dissipation. This demonstrates the added richness available to quantum systems in structured environments. The techniques used here are compatible with many-body extensions of the model, which can not be simulated efficiently on a classical computer in general. Our work also opens up new possibilities in quantum reservoir engineering beyond the Markovian regime.

Gaussian Boson Sampling (GBS) provides a native photonic quantum heuristic for sampling dense subgraphs from adjacency matrices, offering a scalable physical approach to combinatorial graph search problems. Simultaneously, correlation matrix clustering algorithms, such as Spectral and SPONGE, have established robust benchmarks for identifying co-moving assets from correlation matrices in statistical arbitrage (StatArb) strategies. In this work, we map S&P 500 residual correlation data into GBS-compatible adjacency matrices. We benchmark those classical clustering algorithms against two quantum clustering algorithms, GBS Boost and our novel GBS Roots, to construct dynamic, market-neutral portfolios over a rolling one-year window. Simulations across distinct macroeconomic regimes reveal that quantum clustering generates superior alpha within large stock universes during periods of high volatility, effectively isolating structural market idiosyncrasies. Crucially, this economic advantage persists under simulated low-loss conditions and extends into high-loss regimes via the application of coherent displacement to compensate for photon loss. Our findings underscore the efficacy of GBS-derived graph clustering in constructing robust StatArb portfolios, establishing a quantum foundation for broader quantitative finance applications.

We propose a mechanism for fast and efficient quantum transport through disordered networks with variable on-site energies, inspired by photosynthetic complexes. The mechanism relies on an interplay between inter-site couplings of the network and driving by external vibrations. Two design principles are shown to ensure close-to-perfect transport despite the disorder, namely a reflection symmetry in Floquet-Hilbert space and the existence of a dominant doublet or triplet of Floquet states.

This letter proves realistic grid properties limit the applicability of quantum computers for power flow. Grids that split into two large regions meeting at only a few buses, common in transmission networks, force the pseudo condition number of the DC susceptance matrix to grow polynomially in the network size, and long chains of lines bridging such regions force quadratic growth, making recent empirical observations rigorous. The bounds also hold with overwhelming probability for arbitrary bounded random line susceptances. Combined with query and tomography lower bounds, this precludes end-to-end quantum advantage for DC power flow at every readout level, and these obstructions persist through AC power flow, optimal power flow, and unit commitment. All proofs are formally verified with accompanying Lean 4 source code.

This paper introduces an interactive music system with quantum musical agents that communicate by teleporting quantum states to one another. Human performers interact in real time with agents whose melodic and rhythmic behaviours are encoded as quantum states using Single Qubit Probability Amplitude Modulation (SQPAM) and structured through Quantum Phase Estimation (QPE). Up to three agents are combined within a single quantum circuit, with directed communication via quantum teleportation. We are interested in supporting ambiguous, transformative interactions reminiscent of free Jazz improvisation. Therefore, rather than treating noise and decoherence as limitations, the system embraces NISQ-era constraints as creative affordances, framing agent communication as quantum whispers, that is, deliberate, musically expressive imperfections in state transfer. We provide demonstrations and analyses based on melodic correlation, pitch-set distance, and state fidelity, where a continuum between imitation and divergence can be observed. We developed a tunable interpretation method to assess how agents reinterpret teleported states. This work positions teleportation as a promising interaction mechanism for agent-based quantum computer music and outlines future directions toward distributed ensembles connected via the Quantum Internet.

We investigate the $n$-time cumulant generating function (or $n$-Full Counting Statistics, $n$-FCS) of extensive $U(1)$ charges following a quantum quench. Exploiting space-time duality we characterise this function when evolving from initial states that are symmetric under the action of the charge. In particular, we show that if the correlations in time are sufficiently weak, e.g.\ the transport is ballistic, the $n$-FCS factorises into a sum of single-time FCS arranged in a time-shell structure. A direct implication of this structure is a drastic simplification of dynamical correlation functions: in the presence of time ordering they only depend on the smallest time entering the correlator. We support these findings with several analytical and numerical tests performed in free and interacting models.

Quantum key distribution (QKD) allows for provably secure key distribution between two trusted parties. Because the security and performance of QKD protocols rely on devices that behave according to specific assumptions, idealized or inaccurate assumptions about device behavior can introduce security loopholes. Real devices can never be perfectly characterized, and their performance metrics are always subject to certain error margins, which must be accounted for in a rigorous theoretical analysis. Only recently have rigorous finite-size results allowed for imperfect characterizations of devices (where device parameter have uncertainty margins) - an advance yet to be considered in experimental implementations of the BB84 protocol. In this work, we prove the security and analyze the performance of an implementation of the BB84 protocol using single photons generated by a semiconductor quantum dot light source in combination with dynamic polarization-state encoding. We consider the presence of incompletely characterized devices by accounting for imperfections in the single-photon source (in terms of finite g(2)(0)) as well as the receiver (non-ideal beam-splitters, finite detector efficiencies, and dark counts), all with error margins. The resulting protocol implementation shows competitive performance, paving the way towards practical and loop-hole free implementations of QKD.

We investigate the bound state properties of the hydrogen-like atoms in the radial screened Coulomb potential (RSCP). using three complementary analytical approaches - expectation values with Coulomb and Kratzer reference states, variational optimization with a scaled Kratzer basis, and the Hellmann-Feynman theorem - we derive approximate energy eigenvalues as function of the screening parameter c. Benchmarked against high-precision generalized pseudospectral data, the expectation value-approach with the Kratzer basis achieves relative errors of 0.63% for the first ten s-states at $c=0.1$, while the variational method improves this further. The formalism extends naturally to Positronium, demonstrating its generality for arbitrary reduced-mass systems. The complementary biases of the methods provide robust error estimation for plasma-embedded atoms.

In weakly anharmonic qubits, coherent control errors take two generic forms -- over/under-rotation and phase errors -- whose suppression normally requires iterated experiments. We show that, for any symmetric $π/2$ pulse in the weak-driving regime, both follow from a single parametrization, $\mathcal{X}(π/2)=Z(δ)X(π/2+ε)Z(δ)$, that ties the rotation error $ε$ and the phase error $δ$ directly to the system parameters. The parametrization enables DRAPE, a Ramsey-type protocol in which sweeping the phase-error correction reveals a crossing point that fixes both corrections at once. The phase correction is estimated with Heisenberg scaling while the rotation error saturates the standard quantum limit. We experimentally demonstrate DRAPE by calibrating a $π/2$ gate on the $|1\rangle\leftrightarrow |2\rangle$ transition of an IBM transmon, reducing the over-rotation from $0.997^\circ$ to $-0.007^\circ$ and the phase error from $2.52^\circ$ to $0.0052^\circ$ per gate, validated independently by phase- and rotation-error amplification protocols.

Information is widely regarded as the resource underlying the thermodynamic advantages enabled by conditional control. We show, however, that informational quantities such as Holevo information and accessible distinguishability, although constraining the achievable advantage, do not uniquely determine its thermodynamic value. The missing ingredient is a passive spectral rearrangement vector that characterizes the effect of conditioning on the ensemble. Specifically, the conditional-control advantage is exactly determined by the geometric pairing between this vector and the Hamiltonian energy-gap structure. This result reveals a thermodynamic geometry of conditional control, explains how informationally equivalent ensembles can possess different thermodynamic values, and identifies the passive spectral rearrangement vector as the minimal operational descriptor required to determine the thermodynamic value of conditional control for a fixed Hamiltonian.

We investigate a class of local quantum quenches in which the conformal boundary condition of a (1+1)-dimensional conformal field theory is abruptly changed. We derive a remarkably simple and universal expression for the time evolution of one-point functions on the half-line. This result provides a direct description of the propagation of the disturbance generated by the quench and, in turn, allows us to determine the dynamics of bipartite entanglement for subsystems adjacent to the boundary. We show that, once the subsystem becomes fully causally connected to the quench event, the entanglement entropy undergoes a sharp finite jump whose magnitude is universally given by the logarithm of the ratio of the boundary g-factors associated with the initial and final boundary conditions. We benchmark these analytical predictions against Matrix Product State simulations of the critical Ising spin chain, finding excellent agreement. The numerical analysis further allows us to investigate the time evolution of the spin-flip entanglement asymmetry, revealing how the symmetry-breaking perturbation emitted from the boundary propagates through the system. Our results uncover universal dynamical signatures of boundary quenches and establish a direct connection between nonequilibrium entanglement dynamics and boundary critical phenomena.

Adaptive agents realise complex reactive behaviours by using a memory of past input stimuli and output actions to guide structured future responses. Quantum adaptive agents can operate while storing less information in memory than optimal classical counterparts; yet, this does not necessarily translate into a reduced dimension of the memory that must be physically realised. We introduce a route-truncate-repair procedure that converts entropic quantum memory advantages into reductions in memory dimension. Routing a reference input process through an agent yields a temporal matrix product state representation whose canonical bond is identified with the agent's memory. Truncating this bond and locally repairing the resulting dynamics produces a smaller, physically-valid agent that remains capable of responding to arbitrary input sequences. A fidelity-divergence certificate quantifies the resulting trade-off between accuracy and memory dimension. Benchmark adaptive processes exhibit substantial dimension reduction whilst preserving the underlying behaviour with high fidelity. These results establish a route from entropic memory advantages to practical, dimension-reduced adaptive quantum agents.

Sublinear optical response, in which the emitted field scales as a fractional power of the driving field, lies beyond the conventional perturbative hierarchy of nonlinear optics. Here, we show that such a response can be engineered in a hydrogen atom using tracking control. Rather than prescribing the driving waveform, the field is determined self-consistently from the evolving quantum state to enforce a chosen relation between the optical response and the applied field. We demonstrate accurate tracking for multiple exponents and scaling strengths, establishing that a single atomic system can be driven to realize a family of distinct sublinear responses. The calculations are enabled by a compact wave-packet continuum discretization that treats bound and continuum states on equal footing and is applied here, to the best of our knowledge, for the first time to strong-field optics and quantum control. These results establish tracking control as a general route to engineering optical responses beyond conventional polynomial nonlinearities.

We propose an explicit quantum circuit for quantum spatial search based on discrete-time quantum walks on $d$-dimensional lattices. In this algorithm, the flip-flop shift operator moves the walker to a neighboring site along the selected spatial direction and reverses the corresponding direction label after the move. By encoding each pair of opposite directions so that they differ only in the least significant qubit of the coin register, we implement the shift using coin-controlled modular increment and decrement operations on the position registers, together with a single $X$ gate that reverses the direction label. We verify that the proposed circuits reproduce the theoretical dynamics on two- and three-dimensional periodic lattices. We further extend the circuit construction to systems with position-dependent shift rules, such as non-periodic boundaries, and validate this extension on a two-dimensional lattice. The resource analysis shows logarithmic growth of the circuit width. For the two-dimensional lattice, the synthesized depth is consistent with $O(\sqrt{N}(\log N)^{3/2})$, while the three-dimensional depth empirically follows an $O(\sqrt{N})$ dependence over the investigated range. Under a CX-gate depolarizing noise model, CX-optimized circuits exhibit improved noise robustness. These results provide a practical framework for implementing quantum spatial search on regular lattices and extending it to defective and other irregular lattice structures.

Quantum mechanics is widely recognised as being incomplete. It is not consistent with the second law of thermodynamics and does not provide a scientifically credible physical account of the measurement process, the means by which coherence is broken and classically observable states are recorded. This had led to many ad hoc assumptions being used to account for various properties of quantum systems, among which is the coherence time of quantum devices that determines their ability to perform computations. Here, we show that all these properties can be accommodated naturally and consistently in the context of quantum systems which exhibit continuous spectra, as arises in the thermodynamic limit of large systems. In particular, for isolated systems we show that the time-reversal symmetry associated with unitary time evolution of the quantum state gives rise to time-symmetry breaking and a semi-group evolution which attains thermodynamic equilibrium at long times. Moreover, the emergence of this non-unitary time-asymmetry leads to microcanonical equilibrium states in which all quantum coherence is lost and is accompanied by the transformation of pure states into mixtures, leading in turn to an increase in entropy. Inclusion of a macroscopic measurement apparatus shows how the outcome of a measurement corresponds to the von Neumann projection postulate, arising with probabilities in conformance with the Born rule. The mathematical structure of the theory which applies to quantum systems with continuous spectra is closely analogous to the classical ergodic theory of dynamical systems and the conditions under which they attain equilibrium states.

Discriminating enantiomer pairs is of central importance in the molecular sciences. The preferential interaction between chiral light and matter is commonly employed in this discrimination, despite fundamental challenges. Here we present quantitative error bounds for classifying the handedness of a chiral, randomly oriented, quantum optical emitter from the perspective of classical and quantum hypothesis testing. Most interestingly, we find that a collective measurement on $N$ photons can provide an orders-of-magnitude improvement in error rate relative to a corresponding separable measurement.

We present a rigorous perturbative analysis of the Szegedy quantum walk search algorithm on the complete graph with marked nodes, when a specific anomaly is present in the graph. This is motivated by the problem of monitoring the integrity of dense trusted communication networks with a quantum-assisted procedure. The topology of these networks is modeled as a complete graph, and the anomaly of interest is the disappearance of a single communication link which represents the minimal and spectrally hardest structural defect to detect. Building on the graph-completeness testing algorithm framework, we quantify how the removal of a single unmarked-unmarked edge propagates through the relevant spectral quantities of the Szegedy quantum walk. Denoting by $n$ the total number of nodes of the graph and by $m$ the number of marked nodes, we prove that the perturbation to the transition matrix has spectral norm $Θ(1/n)$, and that the gap eigenvalue undergoes a strictly negative first-order shift for every $n$ and every number of marked nodes $m$, providing a formal proof of a conjecture from our completeness testing algorithm work; in the regime $m = Θ(n)$ relevant for the search algorithm, this shift has magnitude $Θ(1/n^2)$. The corresponding eigenphase shift satisfies $Δθ_\star = Θ(1/n^2)$ in the same regime. We establish that the rotation angle of the effective subspace under this perturbation is $O(1/n)$ for $m = Θ(n)$. Finally, we bound the change in success probability to $O(1/\sqrt{n})$ in this same regime of marked nodes, and show that this bound is dominated by the geometric misalignment of the effective subspace rather than by the spectral shift of the eigenphase. These results provide both the theoretical foundations and the fundamental scaling limits of quantum walk-based topology integrity monitoring under minimal structural perturbations.

Non-Hermitian quantum walks on lossy lattices with open boundaries can exhibit an anomalous peak of the loss probability at the boundary, known as the non-Hermitian edge burst (NHEB). This phenomenon has been attributed to the combined effect of the non-Hermitian skin effect (NHSE) and a gapless imaginary spectrum. Here we investigate a class of models in which the NHSE is induced by magnetic flux while the loss is spatially nonuniform. We show that the spatial distribution of loss plays a crucial role in determining the emergence and strength of the NHEB. Notably, even in the absence of the NHSE, a weak boundary accumulation of the loss probability persists. We term this effect a quasi-non-Hermitian edge burst (quasi-NHEB). By analyzing the dependence of the loss probability on the initial position, we further demonstrate that the quasi-NHEB obeys a bulk-edge scaling relation distinct from that of conventional NHEB. Our results show that spatially nonuniform loss alone can generate boundary-localized loss anomalies even without the NHSE, providing new insight into non-Hermitian boundary phenomena and a broader platform for their exploration and potential applications.

Proving spectral gaps above the ground space is a central problem in quantum many-body physics. Yet, finding lower bounds on the gap is notoriously difficult. We revisit the martingale method, originally developed by Fannes, Nachtergaele, and Werner [Fannes '92, Nachtergaele '96] to prove the existence of spectral gaps of parent Hamiltonians of Matrix Product States (MPS), and provide improvements to the different steps of the method. Most importantly, we devise a new technique which allows to compute the key quantity in the martingale method -- the overlap of local ground spaces -- exactly and efficiently. This enables a clear improvement of the method, allowing it to outperform other existing techniques to lower bound gaps, which we demonstrate by benchmarking on several models. Remarkably, our -- numerically motivated -- approach at the same time also yields a significantly simplified proof of the fact that parent Hamiltonians of any (well-behaved) MPS are always gapped.

Classically simulable measurements (CSMs) constitute an important class of restricted measurements in the odd-prime-dimensional magic resource theory, referring to those measurements with positive discrete Wigner functions. Since their discrimination power is weaker than that of global measurements, it is necessary to study how to improve the discrimination power of CSMs. In this paper, we consider three methods to improve the discrimination power of CSMs, including adding magic resources, using quantum catalysts, and using quantum memories. Specifically, we relate measurements with positive discrete Wigner functions to completely positive Wigner-preserving measurement channels, thereby transforming the problem of improving the discrimination power of CSMs into the problem of determining how many magic resources are required to simulate quantum channels using free operations. Based on this, we derive the lower and upper bounds of the simulation cost. Moreover, we provide a concrete example for which these bounds coincide and prove that consumable magic resources can enhance the discrimination power of CSMs. Finally, we establish a no-go theorem, which shows that for discriminating a pair of states with positive Wigner functions, neither finite-dimensional quantum catalysts nor finite-dimensional quantum memories can improve the optimal success probability of discrimination using CSMs.

The Bender--Brody--Müller (BBM) Hamiltonian was proposed as a non-Hermitian Hilbert--Pólya operator. We analyze the Hilbert completion induced, on the standard half-line $L^2$ core, by BBM's candidate metric $\hatη=\sin^2(\hat p/2)=Δ^\daggerΔ/4$. The form $η_0=Δ^\daggerΔ$ is positive with trivial kernel but is not coercive. Completing $C_c^\infty(0,\infty)$ in the norm $\|ψ\|_{η_0}=\|Δψ\|$ gives a Hilbert space canonically unitarily equivalent to $L^2(\mathbb R_+)$. Its free self-adjoint realization is the dilation generator, with simple, purely absolutely continuous spectrum $\mathbb R$. The analysis yields two spectral statements of interest beyond the BBM problem. First, no bounded sandwich $Δ^\dagger h(D)Δ$ is boundedly invertible. Second, the transported symmetric operator has deficiency indices $(\infty,\infty)$ and an adjoint with every real point as an eigenvalue of infinite multiplicity, while its free extension is purely continuous. The realization-independent BBM conclusion concerns the candidate eigenfunctions: $Δψ_z=x^{-z}$, so for $\operatorname{Re}z=1/2$ they do not belong to the completed space. Thus the original BBM boundary-condition/eigenfunction mechanism cannot produce point-spectrum Riemann-zero states in this $L^2$-based metric completion.

While entanglement is known to enable exponential improvements in the sample complexity of quantum learning, it remains unclear which properties of entangled resources are responsible for such improvements. We address this question through the reduction criterion, a condition obeyed by all bound-entangled states. In $n$-qubit Pauli-channel learning, we show that restricting either the input states or the measurement effects to satisfy this criterion rules out an exponential advantage for incoherent adaptive protocols. An exponential lower bound persists for the one-sided coherent adaptive protocols considered here, even when the unrestricted side retains quantum correlations across channel uses. Using conditional min-entropy, we further quantify how the sample-complexity lower bounds weaken as larger violations of the reduction criterion are allowed. Finally, we show that the same obstruction appears in conjugate-state learning: restricted joint measurements cannot reproduce the logarithmic-sample advantage of unrestricted joint measurements on $ρ\otimesρ^*$. These results identify violation of the reduction criterion as a necessary condition for an exponential advantage in the learning tasks considered here.

Four-spin ring (cyclic) exchange $J_{ring}$ is an essential ingredient of the Heisenberg spin Hamiltonian of cuprates and other square-lattice magnets, yet it has lacked the kind of direct, local first-principles extraction that the four-state method provides for bilinear exchange, $J$. We supply it by generalizing that method to a sixteen-state ($2^4$) scheme. Symmetry reduces the sixteen configurations to six or eight inequivalent energies, so the cost is modest. The derivation also shows that the conventional four-state magnetic coupling, $J$, is itself ring-renormalized, by $\pm 2 J_{ring} S^2$ with the sign set by the reference state. T-La$_2$CuO$_4$ confirms this quantitatively: three independent routes agree on $J_{ring}$ to $0.2\%$, giving $J_{ring}/J_1 = 0.25$, and a four-state $J_1$ quoted without naming its reference is wrong by $12\%$ in this material. The direct sixteen-state extraction itself proves reference-dependent, the Néel and ferromagnetic baths bracketing the mapping value: a fourth-order fingerprint of interactions beyond the pair-plus-ring model, which additional reference baths resolve into a bare $J_{ring}$ and a converging tower of six- and eight-spin loop couplings. SrFeO$_2$ ($S = 2$), with the same plaquette yet $J_{ring}/J = 0.006$, provides the negative control: a plaquette is necessary for ring exchange, far from sufficient. The complete workflow, including the band-gap and local-moment diagnostics that certify any such extraction, is implemented in the openly available Mag4 package, so that $J_{ring}$ costs no more effort to obtain than $J$.

While decoherence is known to erode classical hardness in quantum random sampling, the impact of coherent spatial disorder remains an open question. We study a square-lattice instantaneous quantum polynomial-time (IQP) architecture subject to two-qubit gate-angle disorder and single-qubit dephasing using exact tensor-network simulations up to 576 qubits. For finite systems without dephasing, increasing disorder drives two consecutive crossovers toward classical simulability: the output distribution first loses anticoncentration, and then the tensor-network simulation cost drops from exponential to polynomial as entanglement is suppressed. The finite-size scaling collapses are consistent with continuous transitions in the large-system limit. Dephasing further reduces the complexity. We characterize the computationally hard regime through scaling laws that provide quantitative error-budget bounds for realistic near-term devices.

Coherent perfect absorption (CPA) has emerged as a powerful paradigm for controlling classical and quantum light, and has been demonstrated across a broad range of physical platforms. CPA realized in optomechanics relies on interference between the input field and the mechanically scattered field, but is intrinsically confined to the weak-cooperativity regime, resulting in a narrow absorption bandwidth and the mechanical mode remains thermally occupied. Here, we experimentally demonstrate collective interference-induced CPA in a synthetic photon--phonon lattice. By harnessing cavity-reservoir-mediated interactions among Floquet lattice sites, collective interference shifts the CPA condition deep into the high-cooperativity regime. This enables CPA to coexist with ground-state cooling of the mechanical oscillator, together with a broadened non-Lorentzian absorption lineshape and a singular group-delay response. Our results identify collective interference as a route to quantum-compatible perfect absorption and long-lived quantum storage.

Current quantum computers do not yet have the required qubit resources to meet the demands of most practical quantum algorithms. To circumvent this constraint, the practice of dividing these algorithms into parts through quantum circuit cutting has been explored. Many of these works either show exponential scaling or are far from optimal solutions. In this paper, MosaiQC is presented as a novel framework to improve upon existing circuit cutting frameworks. A hybrid warmstart with refinement optimization is used to find cutting solutions, allowing the combination of both wire and gate cuts. Additionally, MosaiQC enables hardware partitions of mixed sizes. Furthermore, the refinement stage incorporates a fast approximate quadratic assignment solver to better place hardware partitions, demonstrating a mean local fidelity improvement of $19.56 \% \pm 6.17\%$ over the baseline algorithm. In runtime and sampling overhead costs, improvements of $2.88 \times$ and an average of $16.84\%$ cut reduction (resulting in an average $5.83 \cdot 10^{11} \times$ overhead reduction) are observed. MosaiQC demonstrates a superior trade-off for run speed and solution quality, while adding fundamental features excluded by most competitors. With this, MosaiQC demonstrates that scalable heuristic optimization can substantially reduce the computational overhead of circuit-cut placement for increasingly large quantum circuits.

Neural quantum states offer expressive representations of quantum many-body wave functions, yet their practical accuracy can be limited by stochastic optimization rather than representational capacity. Here we identify a finite-sample instability, termed subspace trapping, in which physically important configurations become strongly underestimated, remain absent from successive sampling batches and receive insufficient gradient feedback. This self-reinforcing loss of sampled support can confine optimization to an effective subspace and produce apparently stationary states above the true ground state energy. To address this problem, we introduce annealed gradient descent (AGD), a sampling-aware update with annealing factor that temporarily increases the relative contribution of sampled low-probability configurations while limiting the dominance of high-probability ones. We establish the connection between finite-sample support loss and effective subspace optimization, and then evaluate the method across molecular systems, one and two-dimensional $J_1$-$J_2$ models. Annealed gradient descent suppresses metastable trapping, preserves physically relevant configurations and enables compact neural quantum states to attain chemical accuracy and competitive state-of-the-art performance. These results establish AGD as a lightweight complement to expressive neural architectures, improved sampling strategies for scalable quantum many-body optimization.

We present full-dimensional quantum simulations of $H_2^+$ dissociative ionization driven by strong orthogonal laser fields. We consider equal-frequency orthogonal components, which generate elliptical or circular polarization depending on their relative phase and amplitude, as well as orthogonal $800$- and $400$-nm two-color fields. These two-dimensional fields strongly modify the fragmentation dynamics. Most notably, we identify a high-energy peak in the proton kinetic-energy-release (KER) spectrum at approximately $4-5$ eV that is absent from the corresponding single-color, linearly polarized calculations. The yield of this peak can be coherently controlled by varying the relative carrier-envelope phase of the perpendicular field component. The perpendicular field also disrupts the clear electron-proton energy-sharing pattern observed in the main $3-3.5$ eV dissociation channel, indicating more complex multichannel dynamics. Time-dependent state projections and calculations initiated from individual excited states attribute the additional peak to laser-induced vibrational excitation of $H_2^+$. Furthermore, the perpendicular field rotates the fragment angular distributions, causing the most probable proton and electron emission directions to deviate substantially from the principal $z$ axis. These findings demonstrate that the spatial and temporal geometry of orthogonal laser fields provides an additional degree of freedom for controlling ultrafast electron-nuclear dynamics.

Multi-objective combinatorial optimization requires identifying Pareto-optimal trade-off solutions among conflicting objectives, often making it more demanding than its single-objective counterpart. Although quantum multi-objective optimization methods have begun to emerge, most existing quantum optimization workflows are still built around single-objective or fixed-scalarization settings. Building on existing weighted-sum QAOA approaches to quantum multi-objective optimization, we propose QEMOO, a quantum-enhanced multi-objective optimization framework that combines Pareto-based selection and warm-started QAOA sampling in a multi-round protocol under the same total shot budget. We further introduce a PBI-inspired adaptive direction-update scheme to improve coverage in strongly conflicting benchmark regimes. Across three benchmark stages, QEMOO improves Pareto-front hypervolume over the single-pass weighted-sum QAOA baseline under matched shot budgets, suggesting a practical route toward shot-efficient quantum-assisted multi-objective optimization and its future applications.

The Higgs and Nambu-Goldstone modes are paradigmatic collective excitations in superconductors and superfluids. These modes are commonly analyzed within the pseudospin formulation of BCS theory, where the dynamics are obtained from the Heisenberg equations of motion for pseudospins. However, this construction becomes inconsistent when directly extended to non-Hermitian systems. In this work, we develop a consistent pseudospin framework for non-Hermitian fermionic superfluids based on the metricized formulation of non-Hermitian quantum mechanics. We apply this formalism to a driven non-Hermitian BCS-type Hamiltonian with complex pairing interaction and analyze its collective excitation spectrum. We find that, in addition to the conventional Higgs (amplitude) mode, the system hosts a novel phase mode that has no counterpart in Hermitian superfluids. Remarkably, this mode is gapped even in the absence of the Anderson-Higgs mechanism, as is the case in neutral superfluids. Furthermore, the resonance spectrum depends explicitly on the initial nongauge phase of the complex order parameter and the dynamical response remains finite at resonance, in contrast to the divergence characteristic of Hermitian systems. These resonances disappear upon the emergence of exceptional points.

Quantum field theory (QFT) in curved spacetime has led to profound predictions, including the Unruh effect and Hawking radiation, yet their direct observation remains extraordinarily challenging because of their extremely weak signatures. Here, we show that the transverse-field Ising model provides a quantum simulator for Majorana fermions in a Schwarzschild black hole background. Remarkably, different coordinate representations of the same spacetime-Schwarzschild, tortoise, Kruskal, and conformally flat-map onto distinct microscopic Ising spin models. Despite their microscopic differences, these models converge in the continuum limit to the same Majorana field theory, exhibiting an emergent form of general covariance. This provides a rare example of a fundamental symmetry of general relativity arising as an emergent property of a condensed matter system. We further demonstrate how black hole particle production can be simulated and detected through spin correlation measurements, and discuss experimental platforms capable of realizing these models. Our work establishes a practical route for investigating fermionic QFT in curved spacetime using controllable quantum many-body systems and tabletop experiments.

Exceptional-point (EP) sensing has attracted considerable interest because of its anomalous response scaling. However, recent studies have shown that the enhanced response near an EP is inevitably accompanied by amplified quantum noise, fundamentally limiting the achievable signalto-noise ratio (SNR). Here, we propose a fundamentally different route toward non-Hermitian quantum sensing based on symmetry-protected noise suppression rather than response amplification. We develop a fully quantum continuous-variable model that unifies parity-time (PT) and anti-paritytime(APT) symmetries within a single framework. Exploiting the incompatibility between these two symmetries, we uncover a non-Hermitian Dirac eigenspectrum and reveal a hidden symmetryprotected phase transition embedded in the Hamiltonian spectrum. Remarkably, this hidden phasetransition simultaneously constitutes a symmetry-protected vacuum-noise fixed point, where collective three-mode quadratures exhibit suppressed quantum fluctuations despite the absence of any anomalous spectral response. As a consequence, quantum sensing is enhanced through the suppression of excess quantum noise while maintaining a finite response sensitivity, establishing a sensing mechanism fundamentally different from conventional EP-based approaches. These results reveal an unexpected connection between hidden symmetry, quantum fluctuations, and non-Hermitian quantum metrology, and establish noise suppression as an alternative paradigm for non-Hermitian quantum sensing.

Rydberg atoms have emerged as a versatile and efficient platform for high-sensitivity quantum sensing of free-space electric fields, with remarkable progress in detecting low-frequency signals. To date, low-frequency Rydberg receivers have relied on a constant bias field, typically realized via intra-cell electrodes or Rydberg plasmas generated by photoelectric effects or inter-atomic interactions. While these approaches improve sensitivity, they suffer from inherent challenges in calibration, long-term stability, and robustness, hindering practical deployment. Here, we propose, design, and experimentally demonstrate a quantum sensing scheme for low-frequency electric signals using modulated auxiliary fields in Rydberg atoms. Unlike conventional methods that employ external DC electric fields that are often fully shielded by adsorbed atom layers on the cell walls, we introduce an AC-field modulation strategy. The incoming low-frequency signal mixes with the auxiliary field, and together they induce Stark shifts of the Rydberg level. These shifts are mapped onto the probe laser via electromagnetically induced transparency (EIT), in a manner analogous to heterodyne detection. We demonstrate a sensitivity of $7.5 \pm 2.6~\mathrm{μV/(cm\cdot Hz^{1/2})}$ at 5 kHz and a minimal detectable field of $0.26 \pm 0.04~\mathrm{μV/cm}$ with an integration time of 1000 s. Furthermore, we extend this approach to systematically analyze the performance of generalized auxiliary fields containing multiple frequency components. By virtue of modulated auxiliary field and quantum frequency mixing, our results establish a robust and systematic framework for quantum sensing of low-frequency electric fields with Rydberg atoms, offering improved sensitivity, stability, and immunity to environmental drifts.

The complementarity principle is a cornerstone of quantum mechanics. In this work, we investigate a complementarity relation between the predictability and quantum coherence, respectively, representing the particle-like and wave-like behaviour in wave--particle duality, in a multi-path setup. We introduce a basis-dependent predictability defined by the Bures distance between the state dephased in the chosen basis and the maximally mixed state. The predictability depends only on the observed basis statistics and admits a closed form in terms of the Bhattacharyya overlap. We derive a trade-off relation between the predictability and a coherence measure defined based on the nonclassicality of the Kirkwood--Dirac quasiprobability. For pure states, the trade-off relation is an exact equality. Remarkably, this wave--particle duality relation endows the coherence measure with an operational interpretation as the classically irreducible part of measurement randomness, yielding a tight worst-case bound on the guessing probability in source-independent QRNG.

Modern information systems increasingly require memory architectures capable of storing not only static data but also the evolution of information over time. While continuous-variable photonic platforms have been extensively studied for quantum communication and computation, their potential as dynamically evolving memory systems remains largely unexplored. In this work, we introduce a metadata-assisted continuous-variable photonic memory architecture in which information is represented by latent vectors encoded across multimode coherent states and updated through reversible displacement operations. The framework combines multimode storage with metadata-based indexing, enabling navigation and reconstruction of historical memory states through rollback retrieval. Unlike conventional approaches that focus on preserving a single quantum state, the proposed framework treats memory as a continuously evolving trajectory in continuous-variable phase space. This perspective naturally extends beyond image storage to temporal data streams, machine-learning latent representations, scientific simulations, and other forms of dynamically changing information. Although presented as a theoretical proof-of-concept, the results suggest that continuous-variable photonic systems may provide a promising foundation for future metadata-aware memory architectures capable of storing, tracking, and reconstructing the history of evolving information.

The monogamy relations characterize the distribution of quantum correlations among the multipartite quantum systems. We study the monogamy relations of the entanglement of assistance in $2\otimes 2\otimes d$ systems. We present explicitly the relations satisfied by the concurrence, the tangle and the concurrence of assistance, which can be used to derive rigorous monogamy relations. Detailed examples are given to illustrate our results.

We derive the form of the one-photon state of the electromagnetic field resulting from spontaneous optical emission of a randomly oriented chiral quantum source, including electric dipole, magnetic dipole, and electric quadrupole contributions to the radiation. We describe how spatial coherence in the emission can be exploited to reveal hidden information about the emitter. This work serves as a prelude and companion piece to our concurrently submitted work \cite{Backlund2026Letter} in which we present the classical and quantum error bounds associated with assigning the handedness of such an emitter.

We challenge the notion that a stoquastic binary governs fundamental computational boundaries in quantum computing and classical simulation of quantum systems. We argue that vanishing geometric phase (VGP), a geometric condition on the Hamiltonian's transition graph, more adequately captures these boundaries. To distinguish VGP from stoquasticity, we construct VGP 3-local Hamiltonians that are formally hard to stoquastize, yet belong to a family admitting polynomial-time recognition of the VGP property. Without constructing a stoquastizing unitary, we prove that the local Hamiltonian problem is $\mathsf{StoqMA}$-complete under the promise that the input Hamiltonian has VGP, and that a frustration-free variant is in $\mathsf{MA}$ under the same promise. We use this result to argue that non-VGP is necessary for any claimed adiabatic advantage justified by escaping the $\mathsf{StoqMA}$ regime. Further, we identify natural settings where the VGP property can be recognized in polynomial time. In contrast, we show that recognition of VGP is $\mathsf{PSPACE}$-complete in general for geometrically local Hamiltonians. Our results show that the computational boundaries $\mathsf{MA} \subseteq \mathsf{StoqMA} \subseteq \mathsf{QMA}$ traditionally attributed to stoquasticity are better understood as boundaries between vanishing and non-vanishing geometric phase structure.

Schrödinger cat states - quantum superpositions of classically or macroscopically distinct states - constitute a powerful resource for quantum computing, enhanced metrology, and probing coherence on large scales. Encoding such states in the phase space of an oscillator requires a nonlinearity, typically inherited from an auxiliary degree of freedom such as atomic spin or a Josephson junction. Neutral atoms trapped in reconfigurable optical tweezer arrays - a leading platform for quantum science and computing - provide an intrinsic nonlinearity via the motion of a single atom in a tightly focused trap. However, this self-Kerr mechanism has not previously been exploited for cat-state generation, and remains largely unexplored as a resource for motional-state control. Here we realize Schrödinger cat states in the quantized motion of a single neutral atom trapped in an optical tweezer. By modulating the depth and position, we demonstrate parity control of both Kerr-cat and Fock states alongside tunable nonlinearity, establishing a spin- and species-independent framework for controlling motion. We further show that the cat-state encoding is intrinsically robust against trap-frequency fluctuations that otherwise limit the fidelity of direct Fock-state transitions. These results establish Kerr-based control of neutral-atom motion as a new paradigm for cat-state and bosonic-state engineering in optical tweezers, providing a route toward quantum-error-correcting codes such as grid states, and toward quantum-enhanced sensing with arrays of non-Gaussian states.

In recent years, chiral quantum optics has emerged as an active research area due to the promising applications in quantum information processing as well as nonlinear optics. We present results on the properties of the incoherent component of the transmitted light after transmons chirally coupled to a waveguide. The well-known resonance fluorescence of one chiral transmon resembles nonlinear quantum optics as it can convert the coherent light, with photons having spatially extensive coherence and Poisson distribution, into a field with spatially localized coherence and bunching photon statistics. However, another chiral transmon can undo the effect of the first transmon regardless of the Rabi frequency under the idealization involved in this work. A full wavefunction calculation shows that, in the weak driving limit, this incoherent light mainly comes from two-photon processes - one chiral transmon converts two independent photons into a photon pair with opposite momentum shift. In addition to the driving through the waveguide, a local driving with independently tunable amplitude and phase can address each transmon individually. The interplay between the waveguide driving and local driving modulates the contribution of the incoherent transmission and hence enables the engineering of the quantum statistics of the transmitted field, with tunable $g^{(2)}(0)$ spanning anti-bunched, coherent, and strongly bunched regimes.

Quantum reservoir computing (QRC) uses the dynamics of a fixed or weakly tuned quantum system to transform temporal and sequential inputs into measured features, while training is typically confined to a classical readout. This separation reduces reliance on repeated quantum parameter updates and avoids the barren plateaus associated with variational circuit training. Its computational power is often attributed to the exponentially large Hilbert space of the quantum system. However, the memory, nonlinearity, and expressivity that determine what a reservoir can actually compute depend jointly on the input encoding, quantum evolution, observables, measurement, and readout, not on Hilbert space dimension alone. On hardware, these capabilities are further constrained by finite sampling, hardware noise, measurement backaction, and the cost of estimating observables, so a large state space alone does not guarantee useful computation. In this survey, we develop a common system model that connects these components and use it to organize QRC foundations, computational properties, reservoir architectures, operating protocols, and physical implementations. We examine spin, photonic, superconducting, bosonic, neutral atom, and other analog platforms, together with applications, software and high performance computing support, benchmarking, and reproducibility. The analysis distinguishes hardware demonstrations from simulations and identifies the assumptions and resources that govern comparisons across implementations. Current results do not establish a broad quantum advantage over well matched classical reservoirs. We therefore specify the resource accounting, benchmark standards, and theoretical criteria needed to evaluate claims of quantum advantage.

The Dicke model provides a fundamental description of collective light-matter interactions and has long served as a testbed for exploring a wide range of physical phenomena in quantum optics and condensed matter physics. In this work, we develop a variational framework for investigating the finite-size Dicke model on both fully qubit-based (digital) and hybrid qubit boson based (digital-analogue) quantum computing platforms. We show that the resulting model reproduces the characteristic critical behavior of the Dicke model in the appropriate large-spin limit while remaining suitable for implementation on both classical emulators of quantum computers and actual trapped ion quantum computers, albeit in the case of latter somewhat limited by noise. Finally, we introduce a complementary hybrid qubit-bosonic variational ansatz that directly exploits the bosonic degree of freedom to reduce quantum resources and discuss its potential implementation on hybrid quantum hardware. Our results establish a scalable, symmetry-aware framework for variational quantum simulations of collective light-matter systems and provide a pathway toward efficient simulations of more general spin-boson models on near-term quantum devices.

We investigate the dissipative dynamics of a generalized Lipkin-Meshkov-Glick (LMG) model coupled to a thermal environment. In this generalized model, in addition to the conventional quadratic interaction, one considers quartic interactions between spin-$1/2$'s coupled all-to-all and evolving in presence of a transverse field. Employing the usual linear Lindblad master equation with thermally-balanced jump processes, we derive magnetisation evolution equations, and demonstrate that the corresponding stationary solution reproduces the canonical equilibrium phase diagram of the model. We then extend our analysis to a nonlinear Lindblad equation that incorporates imperfect quantum-jump processes in terms of jump-retention parameters. Here, remarkably, the system relaxes to a genuine nonequilibrium stationary state whose properties differ qualitatively from those obtained in the linear case. The jump-retention parameters provide tunable knobs that shift the phase boundaries and even modify the nature of the phase transitions with respect to the linear case. Our exact results establish a direct connection between dissipative relaxation dynamics and stationary-state behavior, while identifying controlled quantum-jump retention as a mechanism for engineering nonequilibrium phases in long-range interacting open quantum systems.

We study the generation of state $k$-designs from time evolution under a fixed Hamiltonian. Specifically, we consider the ensemble $\mathcal{E}=\left\{e^{-iHt}|ψ_0\rangle | \ t\sim \mathrm{Unif}[0,T],\, |ψ_0\rangle\sim \mathcal{E}'\right\}$, where the initial states are sampled from an ensemble $\mathcal{E}'$. For Hamiltonians drawn from the Gaussian unitary ensemble, we derive a simple relation between the frame potential of the evolved ensemble $\mathcal{E}$ and that of the initial ensemble $\mathcal{E}'$ in the large evolution time limit. This relation shows that $\mathcal{E}$ forms an exact state $k$-design in the thermodynamic limit as long as $\mathcal{E}'$ forms a state 1-design. Remarkably, we further show, both analytically and numerically, that time evolution under a simple nonintegrable mixed-field Ising Hamiltonian can generate approximate state $k$-designs with high precision, starting from product states in an appropriately chosen Pauli basis. We also analyze the finite-$T$ correction and find it scales as $O(1/T)$. To reduce the evolution time, we propose an $M$-step quench protocol that suppresses this correction to $O(1/T^M)$, which is also verified numerically. We then extend our analysis to unitary ensembles, deriving an analogous recursion relation for the unitary frame potential. Our results elucidate the mechanisms underlying recent proposals for generating unitary $k$-designs through sequential quantum quenches in a unified manner.

A driven qubit exchanges energy with the propagating modes that drive it. When two spatially separated modes drive a single qubit with opposite amplitudes, their net action on the qubit cancels. Yet the qubit can still transfer power from one mode to the other through stimulated emission. The directionality originates from opposite stimulated emission powers into each line. We realize this situation with a superconducting transmon qubit coupled to two transmission lines and show that the direction of the power flow is set by the phase $φ$ of the qubit superposition between its ground and excited states, rather than by any classical control parameter. From a time-resolved measurement of the output power in one line, we observe a transfer that varies as $\cosφ$ and hence changes direction between $φ=0$ and $φ=π$. The directionality of the total power flow is limited by the phase independent contributions of the reflected drive and of spontaneous emission, which sets a routing efficiency that we measure as a function of the input power. For an equal superposition of ground and excited qubit states (maximal coherence), the efficiency reaches $63\%$, close to the bound of $69\%$ expected from the measured qubit coherence times.

Non-Abelian gauge fields play a key role in describing the behavior of particles whose motion is coupled to internal degrees of freedom, such as their spin. Here, we experimentally realize a tuneable non-Abelian gauge field in an active mechanical lattice by using pairs of oscillators to encode a local pseudo-spin for each site, with inter-site spin-dependent couplings engineered via real-time measurement and feedback. We experimentally extract Wilson-loop observables in our set-up and hence demonstrate that we can create a genuinely non-Abelian gauge field. We then exploit the controllability of our mechanical lattice to engineer non-reciprocal hoppings to explore non-Hermitian non-Abelian gauge potentials. For a two-dimensional (2D) lattice, we demonstrate that the non-Hermiticity can manifest in direction-dependent Wilson loops for a single plaquette, while for a one-dimensional (1D) system, we show that a non-Abelian gauge potential can switch the localization of non-Hermitian skin modes between opposite ends of a chain. Our work establishes active mechanical lattices as a flexible and programmable platform for probing non-Abelian gauge fields and exploring their interplay with non-Hermitian dynamics.

Real-time decoding is a critical bottleneck for large-scale fault-tolerant quantum computing. AI-based neural pre-decoders locally correct most physical errors before passing residual syndromes to a global decoder, enabling sub-microsecond latencies. However, existing architectures carry significant overhead from dense 3D convolutions. We present QuantiSpect, a lightweight 3D convolutional neural network (CNN) pre-decoder for the rotated surface code, built on the decoding pipeline of Chamberland et al. The key idea is to replace the dense 3D convolutions with three parallel branches in each residual block: a depthwise spatial branch, a depthwise temporal branch, and a grouped spatio-temporal branch, followed by a squeeze-and-excitation channel gate. This reflects the structure of surface code errors, where spatial and temporal syndrome correlations are partially separable. On a unified 4xA100 GPU benchmark, QuantiSpect matches the receptive field of the Accurate baseline at R=13 while using ~2.71x fewer parameters (0.663M vs 1.80M) and ~2.84x fewer per-voxel convolutional MACs. It matches Accurate's circuit-level threshold and accuracy at moderate and large code distances, reduces the logical error rate by up to ~1.85x relative to uncorrelated PyMatching at d=13, p=0.5%, and speeds up the PyMatching decode by up to 3.11x at d=23. We also explored enlarging the receptive field by adding blocks. Even at R=21, the model uses only 1.18M parameters, fewer than both the R=13 Accurate baseline (1.80M) and the R=17 dense model (4.22M), despite its larger receptive field. This expanded variant significantly outperforms the Accurate model, raising the circuit-level threshold to ~0.80% and further reducing the logical error rate. Together, both variants show that a structure-aware factorized design is an effective, parameter-efficient alternative to a dense one for decoding the surface code.

Sample-based Quantum Diagonalization (SQD) is a hybrid quantum-classical method that replaces variational optimization with a self-consistent recovery loop over QPU samples. Although SQD is considered robust to noisy samples and imperfect classical inputs, its robustness across practical deployment choices has not been systematically analyzed. As a result, shot budgets, qubit layouts, noise mitigation strategies, and the coupled-cluster singles and doubles (CCSD) amplitudes that initialize the ansatz are often chosen without clear empirical guidance. We analyze SQD robustness on IBM Heron hardware across these dimensions. Structured CCSD-amplitude perturbations, including complete zeroing, produce only modest energy shifts from the clean baseline. Differences across layouts and noise-mitigation settings are large in the first recovery iteration but narrow within a few iterations. Accuracy saturates at moderate shot budgets, while very large budgets slightly worsen recovered energies, likely because working-set selection limits the value of additional samples. These results identify where SQD provides genuine deployment robustness and where its limits remain.

We study a quantum particle hopping on an infinite Cayley tree with nearest-neighbor hopping amplitudes drawn from a distribution singular as $|t|^{-a}$ near weak links and no on-site disorder. Because the graph is bipartite, the model has chiral symmetry, which strongly affects the statistics of eigenstates at the center of the spectrum. Using population dynamics to solve the cavity equations for the propagator, we analyze the distribution of the local density of states and show that it develops broad power-law tails. These tails imply an unusual form of wave-function statistics, which we call semi-fractality: the eigenstates occupy an extensive fraction of the system, but their higher moments behave as in a multifractal state. We find that the symmetry properties of the local-density-of-states distribution are not fixed only by the symmetry class, but vary continuously with the exponent controlling the power-law hopping distribution. As this exponent is changed, the system crosses from a semi-fractal regime to a localized one. At the transition, the wave functions realize an extreme intermediate form that we call semi-localized, simultaneously extended in their support but localized according to higher moments.

We construct and experimentally implement compact gate-native circuits that simulate the state-transfer interference underlying three- and four-level chiral-resolution protocols. Both models are encoded in a two-qubit register, with the enantiomer-dependent sign of one of the couplings simulated by a conditional-phase operation in the four-level circuit and by the sign of a final rotation in the three-level circuit. On an IBM quantum processor, the two circuits produce the expected enantiomer-dependent output states with probabilities of nearly $98\%$. We then use these circuits as physically motivated, phase-sensitive benchmarks for composite quantum gates. We introduce rotation-angle error to the single-qubit operations and replace them by several composite gates, including B5, SK1, BB1, H5s, and X5. The comparison demonstrates that single-gate robustness does not translate to equivalent whole-circuit robustness. In particular, variable-rotation sequences do not preserve the required relative phases, making them unsuitable for error correction in circuits. By contrast, the H5s/X5 sequences maintain high target-state populations for relative errors as large as $50\%$, whereas elementary rotations reach the same threshold only for approximately $8\%$. The three-level circuit exhibits a similar enhancement and additionally reveals an error-cancellation symmetry whose protection under composite replacement is exact only when the relevant full propagators satisfy an inverse relation.

Variational Quantum Algorithms (VQAs) are a leading paradigm for near-term quantum computing, combining parameterized quantum circuits with classical optimization across quantum chemistry, combinatorial optimization, and quantum machine learning. Since real-world VQA deployments routinely require circuits that exceed available hardware capacity, quantum circuit cutting has become an indispensable execution strategy, and pre-trained parameters are increasingly distributed through public repositories, introducing supply-chain security risks that have received little attention. Prior quantum backdoor attacks either introduce detectable circuit modifications or depend on device-specific noise, and none consider circuit cutting as an attack surface. We present CutBackdoor, the first parameter-supply-chain backdoor that uses cut circuit execution from CutQC as the deployment-time trigger against VQAs. Under noisy finite-shot circuit-cut execution, poisoned parameters preserve full-circuit validation performance while substantially increasing cut-path reconstruction error, without any circuit modification. The trigger activates when a resource-limited victim responds to a qubit-capacity mismatch by invoking the cutting workflow, requiring no attacker presence at deployment. We provide a theoretical analysis and empirically validate it across varying shot budgets. Evaluation across multiple VQA benchmarks on IBM quantum backends demonstrates cut-path energy amplification of $1.3\times$ to $2.9\times$ \revA{over clean baselines on the VQE and VQD benchmarks while maintaining small stealthiness error on the full-circuit path. The cut-path gap persists across the evaluated backends and cut placements under matched compilation; Zero-Noise Extrapolation provides only partial mitigation, and the diagonal-cost QAOA benchmark delineates the attack's structural boundary

Can a quantum PDE algorithm avoid the polynomial cost of resolving a fine spatial mesh? For standard fixed-order discretizations, direct classical methods require work polynomial in $h^{-1}$, or equivalently in the number of spatial degrees of freedom $N_h=Θ(h^{-d})$. Direct quantum implementations of a parabolic semigroup still have coherent complexity $\widetilde{\mathcal O}(\sqrt{T}/h)$, and gradient-dependent observables such as heat flux and dissipation introduce additional mesh dependence. Decay of the solution norm will further suppress the postselection probability for preparing a normalized final state. We develop a multilevel quantum algorithm that estimates linear and quadratic observables $directly$ and places the fine--coarse cancellation inside the circuit before measurement. A contour-based LCU reconstructs each target-time correction from a coherent family of shifted resolvent differences. Rather than block encoding the fine and coarse inverses separately, we encode their difference through a shifted Ritz--Schur factorization, exposing its $\mathcal O(h_\ell^2)$ two-grid normalization. For Fourier hierarchies, the corresponding SELECT oracle consists of a quantum Fourier or sine transform, a spectral-band selector, and reversible diagonal arithmetic. We also give a non-Fourier realization based on energy-orthogonal dyadic midpoint details in one dimension, together with structured tensor-product extensions under fixed-rank coefficient and access assumptions. For readouts with derivative order $0\leχ\le2$, optimized amplitude estimation removes $all$ polynomial dependence on the finest mesh size. Under the stated access assumptions, both linear and quadratic observables can be estimated with complexity $\widetilde{\mathcal O}(1+(Tε)^{-1})$, with only polylogarithmic dependence on $h^{-1}$.

We investigate the topology of the set $\mathsf E$ of entangled bipartite density operators acting on $\mathbb{C}^{n_1}\otimes\mathbb{C}^{n_2}$. We start by showing that $\mathsf E$ is path-connected, and even simply connected except in the two-qubit case. In this exceptional case $\mathsf E$ turns out to be homotopy equivalent to the set of maximally entangled states, which itself is homeomorphic to $\mathbb{RP}^3$. Here we also compute the complete homology of the closure and interior of $\mathsf E$. In all larger dimensions, we show that the homology and homotopy groups of $\mathsf E$ vanish in degrees $1\leq k\leq 2(n_1-1)(n_2-1)-2$, and all homology groups of degree $k\geq (n_1n_2)^2-3$ also vanish. This range is controlled by the space $\mathsf W$ of entanglement witnesses, which we show is highly connected beyond two qubits and homotopy equivalent to $\mathsf E$. By computing the Euler characteristic, using a torus-action fixed point argument together with Alexander duality, we show that $\mathsf E$ nevertheless has non-trivial reduced homology over every field for all $n_1, n_2 \geq 2$.

Quantum materials experiments increasingly rely on microwave, electrical, thermal, optical, and structural probes, but these capabilities are typically assembled from custom hardware that limits reproducibility and scalability. Here we show that a commercial 65-nm CMOS process can be repurposed as a passive, foundry-manufacturable characterization platform by functionally partitioning its metal stack into microwave, thermal, and electrical subsystems within a 1 mm2 footprint. The integrated RF architecture enables cryogenic magnetic susceptibility measurements of Fe3GeTe2 heterostructures at 1.75 K without sample-specific fabrication. We further demonstrate NV-center optically detected magnetic resonance (ODMR) with >20% contrast at 4-9 dBm microwave power, reducing power requirements by 20-25 dB relative to conventional antenna-based approaches while maintaining sensitivities of 2-3 uT/sqrt(Hz). We additionally confirm compatibility with in-situ electron-beam imaging, showing no measurable degradation in image quality upon device operation. These results establish a scalable, foundry-manufacturable platform for multimodal quantum sensing and materials characterization.

In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers $S_{1},S_{2}\geq1$ of generalized quantum measurements at two sites. In the present article, we find analytically a new general condition sufficient for a nonseparable Werner state with a dimension $d\leq\min\{S_{1},S_{2}\}$ to satisfy all Bell inequalities under every $S_{1}\times S_{2}$-setting correlation scenario with outcomes of an arbitrary spectral type, discrete or continuous $-$ that is, to be $S_{1}\times S_{2}$-setting Bell local, for short. For a variety of $S_{1},S_{2}\geq1$ values, this new general locality condition is beyond Werner's and Barrett's locality conditions for a nonseparable Werner state. We also prove explicitly in the operator terms the optimization result by Terhal et. el. [Phys. Rev. Lett. \textbf{90,} 157903 (2003)] via semi-programming that every nonseparable Werner state with a dimension $d>\min\{S_{1},S_{2}\}$ is $S_{1}\times S_{2}$ -setting Bell local. The new results of the present article are important both for Bell nonlocality theory and for quantum applications based on Bell nonlocality.

We revisit the problem of \textit{real-time} quantum dynamics of the paradigmatic two dimensional transverse-field Ising model using the recently developed fuzzy sphere regularization scheme. By linearly ramping the transverse field from the paramagnetic phase to criticality, we study the finite-time scaling behavior of the squared order parameter $\langle m_z^2 \rangle$, the excitation energy density $Q$, and the two-point correlation function of $m_z$. We establish numerically that, at intermediate quench rate, $\langle m_z^2 \rangle$ follows the conventional Kibble-Zurek prediction set by the critical exponents of the $3$D Ising universality class, and the correlation function exhibits the expected exponential decay whose correlation length can be used to estimate the non-universal scaling coefficient in the freeze-out time/length. In contrast, the excitation energy density $Q$ does not reach the same scaling regime at available system sizes due to large effective finite-size gap from symmetry-enforced level sparsity in the energy spectrum. At slow quench rates the universal quasi-adiabatic scaling for both $\langle m_z^2 \rangle$ and $Q$ is recovered. Since the fuzzy sphere construction can realize not only the Ising conformal field theory (CFT), but a broad family of $(2+1)d$ CFTs, our results establish a route to the real-time critical dynamics of strongly coupled CFTs that are otherwise computationally challenging to study.

Can a many-body state relax faster because it is blind to the slowest decay channel? We show that this mechanism gives rise to a robust strong quantum Mpemba effect in locally dephased constrained Rydberg chains. The key observation is that, for constrained single-spin-flip Hamiltonians, local dephasing turns the Hamiltonian itself into an exact left Liouvillian slow mode, $\mathcal L^\dagger(H)=-γH$. A thermal state generically retains this slow channel, whereas translationally invariant states with vanishing energy expectation remove it and are forced to relax through faster visible modes. This exact selection rule produces a strong quantum Mpemba effect in the locally dephased PXP chain, including for a zero-energy scar eigenstate, the $|0\cdots0\rangle$ product state, and a translation-invariant $Z_2$ cat state. We further show that the same mechanism persists in the $(2,3)$ model and in the longer-range blockade family. Our results identify exact slow-mode selection, rather than special scar wave functions, as a general organizing principle for anomalously fast relaxation in constrained open quantum systems.

Fourier-transform infrared (FTIR) spectroscopy is a well-established technique for qualitative and quantitative chemical analysis. Classical FTIR systems rely, however, on direct mid-infrared (mid-IR) scan-based time-domain measurements of coherence functions; thus, the signal-to-noise ratio and measurement speed are constrained by design. In this paper, we demonstrate a scanless quantum FTIR (sQFTIR) technique that exploits principles of metrology with entangled photons to circumvent the limitations inherent to classical FTIR systems. The approach exploits the interferometric nature of the sensing paradigm and relies on frequency-domain measurements performed with a static, low-gain nonlinear interferometer. A robust reconstruction algorithm is used to retrieve time-domain signals and reconstruct respective mid-infrared (mid-IR) spectra (3000$~$cm$^{-1}$ to 2380$~$cm$^{-1}$) from near-IR measurements (approx. 780$~$nm to 820$~$nm). The suggested sQFTIR protocol eliminates the need for optical delay scanning and leverages inherent mapping between the related domains. In the theoretical section, we evaluate the intrinsic signal-to-noise advantage of the proposed method over conventional scan-based time-domain measurements; a difference of 26.8 dB (factor of 21.8) is demonstrated. Building on the enhanced sensitivity of the scheme, we demonstrate rapid sQFTIR-based hyperspectral imaging with a spatial resolution of 12.3$~μ$m and a spectral resolution down to 8$~$cm$^{-1}$. Hyperspectral mapping of human colon tissue, microplastics, and multilayer polymer samples composed of polypropylene and ethylene vinyl alcohol yield high-quality single-pixel spectra with acquisition times down to 10$~$ms.

High-speed LDPC decoding is a major bottleneck in CV-QKD and motivates hardware acceleration with fixed-point arithmetic. This work compares SPA, MSA, and NMS under a unified low-SNR fixed-point framework using common graph, matrix, and quantization settings. Multiple formats are evaluated through FER, and average iterations. The results show that performance depends strongly on the interaction between decoder rule and numerical precision. SPA achieved the best overall performance. For reduced-complexity decoders, Q16.8 was the lowest consistent precision, with NMS outperforming MSA. Practically, SPA with Q8.4 offered the best balance between reliability and hardware efficiency for large-scale implementations.

We analyze fixed-depth Trotter simulation as a method for structuring hardware noise in digital many-body dynamics. The number of layers is chosen using the largest endpoint time and is then kept fixed throughout the time scan, making the total noise dose approximately independent of the endpoint time. For local stochastic faults, we show that, once propagated faults lose memory of their insertion layer, the noisy circuit factorizes into ideal evolution followed by a stationary finite-depth binomial channel. In the dilute-layer limit, this channel reduces to a Poissonian exponential. The memory time of a single fault is related to a Loschmidt echo. An important consequence is observable-level depolarization: for selected macroscopic observables at low to moderate noise levels, the stationary channel can act as an almost time-independent affine contrast correction, even though the full channel need not be depolarizing, which is crusial for error mitigation purposes. At short times, the same protocol produces a digital Zeno-like transient, in which a fixed number of noise opportunities competes with a vanishing coherent angle per layer. Our results also reveal limitations of naive zero-noise extrapolatin strategies based on oversimplified functions.

We apply a hybrid variational framework to interacting spin-boson Hamiltonians, targeting regimes where simulations are limited by the unbounded bosonic Hilbert space and strong many-body correlations. The bosonic sector and spin-boson correlations are captured within a compact non-Gaussian variational manifold, while the minimized spin sector is obtained as the solution to an effective spin Hamiltonian. Minimization is carried out inside a self-consistent energy-minimization loop, where variational parameters are minimized and the effective Hamiltonian is solved via DMRG. The results are obtained without eliminating or truncating the photonic field. We benchmark the method on the Dicke and Dicke-Ising models by comparison to converged spin-boson DMRG, finding accurate ground-state solutions with reduced bond dimension.

We develop a framework for minimally perturbing local measurements in relativistic quantum field theory, with the aim to sense local properties of the field in a non-destructive manner. The field properties are sensed by weakly coupled pointers and encapsulated in conditional expectation values dependent on a postselection of the field state. Our operational protocol uses causally admissible Kraus updates for the field, in line with recent relativistic measurement theories, keeping in mind restrictions related to ``impossible measurements''. We illustrate our approach with three applications: a spacelikeness detector for causal-structure sensing, counting particle-creation densities in a supercritical potential and non-destructive discrimination between entangled states of the field and mixtures.

Bell proved that no theory of pre-existing local values can reproduce the predictions of quantum mechanics, but his proof leaves the culprit ambiguous: one may reject either of two independence conditions, Outcome Independence or Parameter Independence, and most commentators have found Outcome Independence the safer sacrifice. The first part of this paper presents, in a form adapted to spin-1/2 particles in the singlet state, an argument (Forster 2014) that removes the ambiguity: using a chained family of experiments in which quantum mechanics predicts an extreme pattern of correlations -- the quantum Sorites phenomenon -- a contradiction is derived without ever assuming Outcome Independence. Under the resulting theorem, anyone who holds that hidden variables could improve on the quantum probabilities must give up Parameter Independence itself. That looks like a heavy price, because Parameter Independence appears to be protected twice over: rejecting it seems to put superluminal influences into spacetime, and its statistical shadow -- the No-Signaling condition -- is experimentally beyond reproach The second part of the paper shows that the price is payable. In the random-matrix collapse dynamics proposed by Kryukov, measurement is a random walk of the quantum state, and the hidden variable is not a stock of values fixed at the source but the random stream that drives the walk -- like the stored random numbers of a computer simulation, with the measurement settings playing the role of seeds. In that framework Parameter Independence is false while Outcome Independence and No-Signaling are both true, and one can say exactly how the Sorites argument is blocked, why the violation involves no process propagating in spacetime, and why the influence of one wing's setting on the other wing's outcome -- demonstrated here in a simulation -- can never be used to send a message.

Charge-learnability transitions in monitored symmetric quantum circuits reveal how local measurement records acquire sufficient information to infer a conserved charge. Here we extend charge learnability to probabilistic weak measurements, for which the measurement probability and measurement strength are independently tunable. We find that the learnability phase boundary is organized by the informational power of local measurement. We further introduce cross entropy as a label-sensitive diagnostic that distinguishes unbiased, biased, and antibiased decoder variants. Finally, the exact record--label mutual information provides a decoder-independent benchmark for the information fundamentally available for charge inference. Our results establish informational power of local measurement as a unifying principle for charge learnability under general monitoring protocols.

Circuit cutting promises to scale quantum computations beyond current hardware, but variational quantum advantage also requires low cutting overhead, classical hardness, and trainability. We show that these properties are strongly constrained by entanglement geometry. Matrix product state (MPS) and tree tensor network (TTN) circuits with constant seam bond dimension can be cut with \(O(1/\varepsilon^2)\) sampling overhead, but remain efficiently classically simulable, ruling out asymptotic quantum advantage within these families. By independently controlling seam and intra-block entanglement, we construct a two-block circuit family that remains cheaply cuttable while requiring a super-polynomial global MPS bond dimension, as supported numerically up to \(n=100\). However, MPS hardness and trainability require incompatible depth regimes, \(d=ω(\log n)\) and \(d=O(\log n)\), respectively. Using magic rather than entanglement as the hardness resource avoids this conflict: shallow Clifford+\(T\) circuits remain cuttable and trainable while their stabiliser-simulation cost grows exponentially with the \(T\)-count.

We show that the Belopol'skaya-Daletskii formulation of stochastic differential equations on a Riemann manifold offers an elementary way to construct equivariant representations of finite-dimensional approximations to the path measure of a diffusion. The key ingredient is the use of the exponential map to describe increments of the diffusion.

Here we propose a general protocol for dual-channel lock-in detection of high-frequency ac signals. We find that the effect of a high-frequency target signal can be modulated through the application of rapidly oscillating driving fields. Based on this mechanism, we develop a quantum dual-channel lock-in detection protocol for high-frequency signals, which not only extends the accessible frequency range of quantum sensing but also enables the simultaneous estimation of the signal amplitude and initial phase. Furthermore, we present a feasible implementation scheme of the protocol based on nitrogen-vacancy centers in diamond. Numerical simulations demonstrate that the proposed protocol can effectively filter out background noise and significantly improve the signal-to-noise ratio. Our results provide a promising approach for realizing noise-resistant detection of weak signals in the high-frequency regime.

Pauli-based simulators offer a promising route to large-scale classical simulation of quantum circuits in the low-magic regime. Yet their applicability remains largely limited to forward simulation, making them inadequate for optimization-driven quantum tasks such as variational state preparation and parameter initialization. Existing approaches either lack native support for gradient-based optimization or suffer from severe gradient bias. Here we propose the stochastic Pauli-path simulator (SPPS), a computational framework for large-scale quantum optimization that enables unbiased stochastic gradient estimation via Pauli-path sampling across optimization iterations. Our theoretical analysis shows that the proposed simulator yields unbiased gradient estimates and admits provable convergence guarantees. We systematically evaluate our proposal, including quantum eigensolver benchmarks with up to 100 qubits and quantum neural network benchmarks with up to 40 qubits. Across these tasks, SPPS faithfully tracks optimization dynamics, converges within minutes, and broadens the role of Pauli-based simulation from forward estimation to large-scale quantum optimization.

Common-mode metrics of a high-$Q$ helical resonator do not determine the residual ion-side field in a dual-electrode drive. We combine a two-node differential RF model with single-electrode finite-element bases to obtain a computation-only, geometry-resolved projection for a same-phase blade trap. For a 3.5 pF external load per branch, the model gives a total effective branch capacitance of 7.640 pF and an HWHM-equivalent full branch-difference scale of 12.7 fF at $Q_{\mathrm{loaded}}=600$. The seven-segment geometry gives center and axial-RMS differential field coefficients of 640 V m$^{-1}$ and 635 V m$^{-1}$ per differential peak volt. A representative 10 fF mismatch with an effective 0.1 pF balance scale projects to 44.5/44.1 nm center/RMS $^{171}\mathrm{Yb}^{+}$ micromotion at 100 V common peak voltage. Supplementary thermal, bypass-admittance, and tested numerical cases characterize model sensitivity. All reported displacements are projections; no RF-bench or ion-side validation is claimed.

Randomized measurements provide an efficient way to extract physical properties of an unknown quantum state from limited data. On near-term hardware, gate and readout errors bias the reconstructed observables. Here we develop a microscopic description of this bias for locally scrambled shallow circuits. Independent local twirling reduces local implementation noise to stochastic Pauli damping, and a noise event contributes only when it overlaps the Heisenberg evolution of the measured Pauli operator. This gives an activated path-average formula for the noisy Pauli coefficient. In one-dimensional shallow circuits, the activated noise volume grows linearly with the size of a contiguous observable, leading to an exponential damping ratio. We verify this scaling for two-qubit random Clifford and locally scrambled iSWAP circuits with two-qubit Pauli noise, including spatial fluctuations and temporal drift. The scaling supports a small-string calibration protocol that predicts larger string observables without learning the full noisy measurement channel. Our result relates the noise bias of shallow-shadow protocols directly to operator-evolving dynamics.

Quantitative quantum sensing with shallow electron spins, such as those hosted by nitrogen-vacancy (NV) centers in diamond, requires accurate knowledge of the spin's depth below the host material's surface. A widely used approach infers this depth from the 1H nuclear magnetic resonance (NMR) signal of immersion oil on the diamond surface that can be detected using dynamical decoupling sequences such as XY8. However, finite-width pulses make XY8 sensitive to subharmonic responses, including unwanted contributions from nearby 13C spins, and its instrument-limited spectral resolution provides only sparse sampling of the narrow 1H NMR lineshape. Here, we introduce Spin-Lock NMR as an alternative approach to single-NV depth determination. By tuning the Spin-Lock Rabi frequency to the 1H Larmor frequency, the NV probes the 1H NMR signal through the Hartmann-Hahn resonance without the harmonic ambiguities of pulsed decoupling sequences and with substantially higher instrument-limited spectral resolution. We derive a quantitative Spin-Lock NMR fit function from a Markovian master equation that directly relates the measured spectrum to the NV depth. Our approach yields NV depth estimates in excellent agreement with the established XY8-based protocol across multiple NV centers and establishes Spin-Lock NMR as a robust alternative for quantitative single-NV depth determination. To demonstrate its applicability, we employ our method to investigate the 1H nuclear spin signal that is regularly reported to be present on diamond, even in the absence of immersion oil.

We provide a formal framework for Continuous-Variable Quantum Computing (CQC). While CQC is supported by photonic quantum hardware, we are not aware of a formal semantics for continuous-variable quantum programs nor of a unary Hoare logic for their verification. There are several technical obstacles to extending to CQC any of the formal frameworks available for Discrete-Variable Quantum Computing (DQC). Most importantly, continuous-variable quantum programs act on {\em infinite-dimensional} Hilbert spaces; their measurement outcomes are often {\em unbounded} and have expected values that are defined by an improper integral (or an infinite series), which may not converge. We overcome these challenges to give a formal semantics to a universal programming language for CQC and to provide the first Hoare logic for CQC. The assertions of our logic are built from polynomials over canonical observables. Besides proving relative completeness, we implement a symbolic weakest-precondition calculator for CQC based on our logic. Our tool has successfully verified CQC algorithms from textbooks and calculated their approximation errors for physically realizable implementations, proved the correctness (i.e., equivalence) of gate decompositions for CQC hardware, and computed the resource requirements (i.e., number of photon-number states) for achieving a desired accuracy in the classical simulation of continuous-variable quantum programs.

Quantum machine learning on real noisy intermediate-scale quantum (NISQ) hardware has remained largely confined to binary or few-class tasks, limited by the cost of on-hardware training and the underuse of large devices at inference. We present a unified framework that classifies ten-class MNIST end-to-end on a $127$-qubit IBM Eagle processor, with three central contributions. First, a two-phase protocol decouples a gradient-based classical optimization of the encoder and readout from a gradient-free optimization of the quantum parameters, removing the parameter-shift gradient cost that makes on-hardware training impractical. Second, we introduce Quantum Multi-Programming to a trained quantum classifier for the first time, packing multiple circuit copies onto one device to deliver parallel inference at no mean-accuracy cost while cutting quantum-processor job submissions proportionally. Third, a controlled comparison shows that on-hardware fine-tuning yields no measurable accuracy gain, motivating a practical NISQ workflow: train on a classical simulator and reserve the hardware for inference only. Benchmarked against a matched-capacity classical network, the quantum module shows no per-parameter accuracy advantage at this scale; we therefore frame the work as a feasibility-and-workflow demonstration for multi-class quantum image classification on current hardware.

Quantum key distribution (QKD) over non-stationary channels, such as satellite links, is characterized by short, high-loss, and strongly fluctuating transmission windows that produce sparse detection events. In many QKD protocols, these data must be analyzed using non-IID statistical inequalities, yet existing methods either become loose for small sample sizes or heavily rely on fine-tuning, yielding poor estimates when the optical channel is mis-modeled. Using mixture martingale techniques, we introduce tight concentration inequalities that retain sharpness when the channel model is accurate, while remaining robust to model mismatch. In realistic simulations of satellite QKD with fluctuating loss, the resulting bounds can reduce the minimum required number of transmitted signals by more than $70\%$.

Monte-Carlo trajectory (quantum-jump) methods are the practical route to simulating noisy quantum circuits once the exact density-matrix method is precluded by its $4^n$ memory cost. Their bottleneck is estimator variance: resolving one expectation value can demand thousands of trajectories. Recent tensor-network work shows that \emph{variance-reduced unravelings} -- projector and analog sampling -- sharply cut this variance, but only on CPU matrix-product-state backends, with no path into production tooling. We implement both unravelings on a \emph{GPU dense-statevector} trajectory engine and validate them against the exact density matrix (ideal-circuit fidelity $1-2.2\times10^{-16}$; $1/\sqrt{N}$ convergence; all unravelings unbiased to trace distance $<0.01$). On a single consumer GPU, projector unraveling reaches a target standard error with $20.8\times$ fewer trajectories than Qiskit-Aer's \texttt{batched\_shots\_gpu} at $n=10$, a factor that holds at $19$--$26\times$ across $n=8$--$20$. A regime map places analog sampling optimal at weak noise and projector at strong noise, crossing near $γt\approx0.35$. We further report a systems finding: Qiskit-Aer applies noise at the \emph{channel} level and reconstructs a canonical Kraus decomposition at apply time, discarding any user-supplied unraveling, so variance-reduced unravelings cannot be delivered through its public API. Because Aer's Born-rule collapse machinery already exists, we specify a minimal change that would unlock the technique in production.

Superradiant emission from long-lived excited states of an atomic ensemble confined in an optical cavity constitutes a practical source of light with narrow linewidth. In the pulsed regime, however, superradiance implies rapid emission and a broadening of the spectrum. Recent experiments have demonstrated constructive and destructive interference of superradiant emission by different strontium atomic transitions. In this article, we show that by modulating the atomic transition frequencies with a magnetic field, it is possible to control the release of the atomic excitation energy as a prolonged pulse or a train of superradiant pulses. By simulations, we show that heterodyne detection of the prolonged superradiance shows extremely sharp spectral features, which leads to significantly reduced frequency uncertainty and fluctuation.

We investigate a fully-connected three-mode squeezed vacuum (FC-C3MSV) state, where all three modes are pairwise coupled through nonlinear interactions in a triangle ($K_3$) topology. Using the integration-within-ordered-product technique, we derive the normal product form of the squeezing operator and obtain the covariance matrix directly from the Bogoliubov transformation. Under symmetric coupling, the physical state is genuinely tripartite entangled for any nonzero squeezing, while the three Armstrong-type witnesses provide a finite-window sufficient experimental test; in the chain-type C3MSV only one of these witnesses is violated. We find that, despite two-mode entanglement, the fully-connected topology admits \emph{no} two-mode Gaussian steering ($\mathcal{G}^{i\to j}=0$) between any pair of physical modes; the steering resource is instead collective one-mode-versus-two steering $\mathcal{G}^{i\to jk}$, which is $θ$-independent and grows with $r$. We analyze independent vacuum losses and obtain critical transmittances for steering survival: under full symmetric loss at $r=0.5$, one-to-two collective steering disappears at $η\approx0.58$, whereas reverse two-to-one collective steering survives down to $η\approx0.502$ and the underlying two-mode entanglement persists for all $η>0$. Finally, we revisit photon subtraction using a normalized phase-space derivation. A photon subtraction on a single physical mode does not generate Wigner negativity on another single mode, consistent with the absence of two-mode steering. Wigner negativity can instead be generated when Bob subtracts from the collective mode $(b+c)/\sqrt{2}$, with a loss threshold $η_c\approx0.667$ at $r=0.5$. These results distinguish pairwise and collective nonclassical resources in the FC-C3MSV and clarify the operational role of the complete-graph topology.

Bell nonlocality is both a defining signature of entanglement and a key quantum information resource. However, visualizing and certifying nonlocal correlations across a spatially multimode photonic field remains challenging due to the rapidly growing measurement cost of spatially resolved projective tests. To address this issue, we build a spatial nonlocality imaging scheme that directly reveals the spatial distribution of quantum nonlocality by integrating a metasurface that performs parallel polarization projections with a quantum-adaptive neural network. Spatially resolved Clauser--Horne--Shimony--Holt (CHSH) tests are realized over a 400-pixel biphoton field using an average of only 1.7 detected coincidence pairs per pixel per basis. This approach yields a nonlocality image that maps the two-dimensional spatial distribution of Bell violations across the optical field and reveals the target-state-dependent spatial evolution of Bell violations. It provides a highly resource-efficient route to large-scale Bell certification and opens new possibilities for exploiting spatially multimode entanglement in quantum imaging, quantum networking, and scalable photonic quantum technologies.

Precision measurement of low-frequency electric field (LFEF) signals with frequency from 30 kHz to 300 kHz is crucial for advancing both fundamental science and practical applications, owing to their unique frequency regime. For conventional electromagnetic antennas, the long wavelength (i.e., several kilometers) of the LFEF leads to a severe size constraint that efficient radiation becomes challenging to achieve when the antenna size is much smaller than the long wavelength of the LFEF signals, which in turn results in a reduction of measurement sensitivity and compromises antenna's performance. By exploiting the high intrinsic sensitivity of cold trapped ions to weak alternating electric signals via Coulomb interaction, we demonstrate a single-ion phonon laser sensor acted by an injection-locked 40Ca+ ion confined in a surface-electrode trap. Combining the beat frequency technique with the injection-locked phonon laser oscillation, we demonstrate a practical and efficient approach for simultaneous extraction of the frequency, phase, and amplitude from a single measurement, without the need for sideband cooling. This approach achieves precision detection for LFEF signals with the sensitivity of 404 uV/(m * Hz1/2) and the detection limit of 61.5 uV/m. Besides, this approach also shows remarkable robustness against noise. Our study helps realizing practical single-atom sensors in the low-frequency regime, opening avenues for applications in subsurface communication, precision metrology, mass spectrometry, and biomedical monitoring.

Parametric frequency modulation is a standard tool in superconducting circuits for activating tunable interactions and implementing quantum gates. Here, we engineer dissipation in a flux-tunable transmon qubit by using sideband modulation to bring it into resonance with a lossy resonator, opening an on-demand Purcell decay channel. We find that pulsing this channel on and off does not simply lower the time-averaged decay rate; instead, it reorganizes the dissipation spectrum into a structured interference pattern. A Chebyshev-propagator model for the repeated on/off block reproduces the measured spectra and reveals a close structural correspondence to N-slit Fraunhofer diffraction, with each on-window acting as a temporal aperture. By varying the pulse duration and duty cycle, we demonstrate control over the spacing, contrast, and envelope of the dissipation spectrum. These results establish pulsed parametric modulation as a direct method for shaping engineered dissipation in superconducting circuits and provide a new control knob for open quantum system dynamics.

Mode connectivity has been widely studied in classical machine learning as a geometric property of low-loss regions in parameter space. In quantum machine learning (QML), however, the physically relevant object is not the parameter vector itself but the unitary transformation implemented by a parameterized quantum circuit. In this study, we formulate mode connectivity on the reachable unitary Lie group generated by the dynamical Lie algebra of the generators. We show that, under a near-minimum connectedness assumption and the absence of critical values in a low-loss band, the corresponding low-loss sublevel set on the reachable Lie group is path-connected. This provides a geometric interpretation of mode connectivity in QML that is independent of a particular parameterization. We further discuss how overparameterization can enable the lifting of Lie-group paths to parameter space, thereby making Lie-group connectivity observable in parameter-space experiments. Finally, we present toy numerical experiments in which geodesic interpolations between trained unitaries exhibit nearly zero loss barriers, consistent with the proposed interpretation.

Simulating the nonequilibrium dynamics of interacting open quantum systems remains challenging beyond small system sizes. Quantum phase-space representations provide a scalable approach, but their useful simulation time can be limited by broad distribution tails and the associated boundary terms. We introduce the neural gauge-$P$ representation for open bosonic systems, in which stochastic gauges are parameterized by neural networks and optimized using exact moment equation residuals. For the driven-dissipative Bose--Hubbard model in both single-site and square-lattice settings, the neural gauge-$P$ representation remains accurate during long-time evolution toward the steady state, whereas the corresponding ungauged representation becomes unreliable at substantially earlier times. These results demonstrate the potential of the neural gauge-$P$ representation for accurate simulations of nonequilibrium open quantum many-body dynamics.

Quantum optimal control (QOC) underpins adiabatic quantum computation, quantum annealing, and quantum state engineering, yet practical deployment is fundamentally bottlenecked by strict hardware constraints and substantial expert effort required to design protocols for each problem instance. To overcome this, we introduce QOC-Workbench, an auditable, large language model (LLM)-driven workflow that acts as an automated quantum co-scientist for cross-paradigm protocol design. Going beyond traditional numerical optimizers that merely tune parameters within a fixed formula, the LLM autonomously parses physics literature, proposes structural hypotheses, and writes code to validate them by direct simulation. This workflow supports cross-paradigm design by accumulating control motifs across tasks. We demonstrate this approach across three distinct settings: Case 1, Rydberg-atom maximum-independent-set arrays; Case 2, interacting XXZ spin chains; and Case 3, random transverse-field Ising models. In Cases 1 and 2, the workflow autonomously discovers hardware-compliant auxiliary controls, target catalysts, and schedule deformations that outperform literature baselines. In Case 3, it addresses the computational bottleneck of variational counterdiabatic driving by escalating from per-instance optimization to an amortized graph-neural-network generator, successfully transferring learned coefficient paths to larger unseen systems. By actively bridging the gap between theoretical algorithms and experimental restrictions across distinct control paradigms and Hamiltonian families, QOC-Workbench establishes a continuously evolving, cross-paradigm methodology for autonomous quantum control.

By applying the framework of entropic uncertainty relation (EUR) and the Quantum Leftover Hash Lemma (QLHL), we introduce a security-proof method for variable-length side-channel-secure (SCS) quantum key distribution (QKD) against coherent attacks. This method reframes composable security as a statistical fluctuation problem of phase errors, enabling direct proofs against coherent attacks through observables and virtual observables. It yields tight key rates for the SCS protocol and reduces pulse requirements by over two orders of magnitude compared to prior works that employ the post-selection technique. We prove that the secure key length for the SCS protocol can be determined after error correction by exploiting the fact that untagged bits are free from bit-flip errors, using the actual information leakage during error correction and the post-error-correction statistics of each state to calculate the final key rate. We further identify sufficient conditions under which the final key length may be determined after error correction in a broader class of QKD protocols. Under the framework of EUR and QLHL, we clarify the applicability of several commonly used concentration bounds to variable-length QKD and the appropriate manner of their implementation. This work enhances the practical value of the SCS protocol and clarifies the security justification of key-rate formulas used in practical variable-length QKD implementations.

We develop a sparse operator-centric realization of $n$-qubit variational quantum algorithms in the complex Clifford algebra $\mathrm{Cl}(2n,\mathbb{C}) \cong M(2^n,\mathbb{C})$. Density operators, gates, observables, channels, fermionic modes, and adaptive-selection observables are represented in one Pauli-word algebra, with the Jordan--Wigner map providing the exact bridge to anticommuting Clifford generators. We distinguish general Pauli-word rotations from Spin-group rotors and derive an exact transpose-parity rule: for real Hamiltonians and real states, every candidate Pauli word containing an even number of $Y$ factors has zero ADAPT gradient, while odd-$Y$ rotations preserve the real sector. For the critical open transverse-field Ising chain, a depth-three Hamiltonian variational ansatz gives relative energy errors $4.84\times10^{-5}$, $2.19\times10^{-3}$, and $3.67\times10^{-3}$ for $n=4,5,6$. A compact local ADAPT pool is exact at $n=4$ but leaves residual errors at larger sizes; a systematic contiguous three-local odd-$Y$ pool reaches relative errors below $1.3\times10^{-12}$ for $n\leq6$. In 100-seed finite-shot tests at $n=4$, fixed-shot selection succeeds in $0/100$ runs, whereas uniform escalation and confidence-bound racing each succeed in $84/100$ runs; racing lowers median shots by $34\%$. We claim no asymptotic speedup over matrix methods. The contribution is a corrected algebraic formulation, an exact pool-pruning rule, and a reproducible study of measurement-limited adaptive selection.