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Wednesday, 4 November 2026: 68 new papers, 22 cross-lists and 88 replacements in Quantum Physics (quant-ph), in arXiv's order, with full abstracts. The same papers as arXiv's own listing, set as a newspaper; every title links to arXiv.
A quantum-secure withdrawal framework is presented by replacing reproducible classical credentials with quantum tokens for authentication. The protocol integrates token generation, authentication, and verification into the existing banking workflow using experimentally motivated quantum control techniques. This mitigates card cloning, credential theft, and counterfeiting.
Entanglement-based quantum key distribution from ground to satellite has been proposed as a scalable primitive for global quantum networks and will be demonstrated as part of the imminent QEYSSat mission. Both theoretical studies and experimental emulations have shown that a significant asymptotic key rate can be expected. In this work we investigate this scenario with a more rigorous security analysis taking into account the finite size effects that arise from short block lengths common in satellite transmission. Our findings suggest a slight alteration of the optimal source operation when informed by finite statistics as opposed to the asymptotic regime, notably that the pump power should be slightly lowered. We quantify the annual key rate based on a dynamically optimised source operation for the Heriot-Watt ground station and several satellite parameters. We find an improved annual key rate when accumulating all raw key material before extracting a secure key instead of doing so for each overpass. We ultimately show that QEYSSat will be able to generate a significant secure annual key with both strategies.
We find that coherent error can induce a phase transition from the clean surface code phase into an extended long-range entangled critical regime with diverging Markov length. To demonstrate this, we establish two general results of independent interest. The first relates topology and quantum information to mixed-state entanglement: we show that when a noise channel acting on a topological code preserves a higher-form symmetry and nonzero coherent information, the noisy state for generic logical input is long-range entangled. The second generalizes the local recovery construction based on finite Markov length to any locally parameterized family, thus encompassing local Lindbladian evolution, coherent errors followed by syndrome dephasing, and thermal states. We apply these results to the honeycomb surface code, in which we find an extended long-range entangled critical regime that is a quasi-long-ranged counterpart of 1-form strong-to-weak spontaneous symmetry breaking. As a byproduct of these studies, we relate the conditional mutual information to conductance in a Majorana network model.
We introduce a scalable framework for globally optimal quantum-circuit partitioning and entanglement-aware block resynthesis. The partitioning problem is formulated as an integer linear program over qubit-feasible convex subcircuits, supporting objectives such as minimizing the number of partitions or a weighted execution cost. The resulting partition selection is exact over the enumerated feasible candidates and their computed costs when the ILP is solved to proven optimality. The selected partitions are resynthesized using an operator-Schmidt rank (OSR) based synthesis technique, which exploits their internal entanglement structure. We compare the end-to-end integer linear programming (ILP)--OSR workflow with BQSKit while identifying their different routing methods, and separately compare local OSR and BQSKit synthesis on matched three- and four-qubit unitaries. On the frozen sample of 772 local unitary targets, OSR produces 741 verified syntheses versus 617 for BQSKit, and matches or improves the CNOT count in all 617 jointly verified pairs. These results demonstrate that globally optimal partition selection combined with entanglement-aware resynthesis improves circuit quality and extends block-based optimization to problem sizes that are impractical for existing optimization workflows.
We propose a physics-informed neural network (PINN) approach for high-fidelity quantum gate learning in both one- and two-qubit systems. We train a PINN using the time-dependent Schr\"{o}dinger equation, where smooth control fields with fixed boundary conditions are obtained by minimizing a loss function that considers model dynamics, gate error, physical constraints, regularization terms, and multiple initial conditions. Training considers pairs of mutually unbiased bases, while independent validation combines Haar-random input states with the average gate fidelity. Unitary simulations yield an average gate infidelity of $8.49\times10^{-8}$ for Hadamard and values between $3.39\times10^{-7}$ and $4.96\times10^{-6}$ for controlled-NOT under $XX$, $YY$, and $ZZ$ interactions. We examine how the learned control fields depend on the coupling, training configuration, and available local fields, including five exchange-type dipolar scenarios. We test the learned control fields under the Lindblad master equation with dephasing and amplitude damping, theoretically reproducing the expected first-order fidelity loss in the weak-dissipation regime. Finally, boundary-adapted Chebyshev expansions represent 139 learned controls with a minimum common count of $K_\ast=24$ coefficients per control for all eleven family-averaged mean squared errors to fall below $10^{-6}$. Separately, square-pulse and Strang propagation at $K=30$ preserve all 31 continuous polynomial references within infidelity $10^{-5}$ at $N=128$ and all larger tested resolutions, under both sampling rules. These results connect multi-state gate synthesis, control-resource characterization, and compact square-pulse playback.
Quantum reservoir computing (QRC) processes temporal information through quantum dynamics, but it remains unclear whether small QRC models can forecast real data competitively with classical models and whether their predictions survive the transfer from ideal simulation to noisy hardware. We address both questions for a six-qubit gate-based reservoir that forecasts next-day motor-insurance claim counts. Five reservoir candidates were selected and frozen using hardware-native interaction graphs, Trotterized Ising dynamics, memory and measurement-robustness criteria, circuit cost, and calibrated-noise screening. On 232 held-out test days, the ideal candidates reached root-mean-square errors (RMSEs) of 5.66-6.12 claims/day, compared with 5.36 for ridge regression. For four of the five, the difference from ridge was not significant under a 95% block bootstrap, and their accuracy was comparable with classical recurrent and reservoir baselines. On the 156-qubit IBM Kingston processor, we ran 63 evaluations in 21 paired rounds, comparing hardware-aware, random-native, and Qiskit optimization level 1 layouts. Hardware-aware placement gave lower RMSE than Qiskit in every round, with a maximum transfer distortion of 7.59 claims/day (11.84 for Qiskit), and avoided the severe transfer failures seen for some random layouts. Most of the hardware distortion appeared as a systematic forecast shift, which a short hardware probe on training inputs detected before the test runs. Longer replay windows raised circuit cost without a consistent gain in forecasting accuracy or hardware transfer. Small QRC models can thus reach competitive accuracy on this task, and hardware-aware layout selection makes their transfer to IBM Kingston more consistent.
The algebraic and environmental characteristics of mixed unitary quantum operations are investigated. It is established that the composition of two uniformly n-mixed unitary channels is itself n-noisy, and this n-noisy property is shown to be an invariant under unitary equivalence. Furthermore, by utilizing majorization and the divisibility of Kraus rank-four unital qubit channels, we demonstrate that any unital qubit channel can be physically simulated using a three-dimensional maximally mixed environment. Together, these results advance the classification and physical realization of noisy quantum channels.
Bosonic and fermionic quantum statistics describe all known elementary and emergent particles in three dimensions, although many attempts have been made to discover other valid quantum statistical frameworks. One recent formulation proposes "$R$-paraparticles," indistinguishable particles with nonlocal internal degrees of freedom governed by generalized exchange rules [Wang and Hazzard, Nature 637, 314 (2025)]. Here, we emulate a species of paraparticle that exhibits a generalized Pauli exclusion principle using a superconducting qubit lattice. We confirm its unique quantum statistics by measuring a $180^\circ$ phase shift under paraparticle exchange, observing antibunching independent of internal degrees of freedom under two-particle interference at a beamsplitter, and finding a thermal occupation inconsistent with both Bose-Einstein and Fermi-Dirac statistics. These results demonstrate that parastatistics are observable on quantum simulation platforms, further motivating their use to explore theorized new phases of matter.
Multiple seemingly distinct frameworks are commonly proposed to explain the emergence of effective non-Hermitian dynamics in quantum systems coupled to an environment. Furthermore, it remains contested how to properly calculate expectation values or whether thermal equilibrium states exist in non-Hermitian systems. In this work, we show that Feshbach projection, the Lindblad master equation, and the ancilla approach can all be understood through the Kraus map formalism, leading to non-Hermitian time evolution if an appropriate post-selection procedure is enforced. After first deriving an exact expression for the conditional system dynamics, we discuss the approximations employed in each approach and the classes of non-Hermitian Hamiltonians that can be obtained. Within this framework, we physically justify the consistency of the right-right formalism (as opposed to the biorthogonal one) for calculating expectation values. Finally, we demonstrate that the traditional notion of thermodynamic equilibrium is not applicable to general non-Hermitian systems. Consequently, stationary states are characterized as non-equilibrium steady states, which should not be conflated with system-projected thermal states of the system-environment composite.
Standard analyses of quantum phase sensing often neglect the overhead of generating squeezed-light by treating the pump as an undepleted classical resource. Realistically, the pump is a quantum object that undergoes significant depletion and entangles with the produced squeezed light, raising the question of how the crossover from a classical to a quantum pump limits the quantum advantage in sensing. Contrary to prior analyses, we show that quantum advantage persists despite pump quantization, but depends critically on the nonlinear $(\chi^{(2)})$ source dynamics. In particular, we demonstrate that Heisenberg scaling emerges in the regime of strong pump depletion, rather than maximum signal squeezing. At maximum squeezing, the quantum Fisher information (QFI) for interferometric sensing of an unknown phase scales as $N^{3/2}$, where $N$ is the pump photon number, surpassing the shot-noise limit but establishing that squeezing itself is insufficient to attain Heisenberg scaling of $N^2$. At maximal pump depletion, where the signal flux is maximized, the QFI scales as $N^2$. In this regime, standard photon counting is suboptimal, while a joint nonlinear measurement of the entire pump-signal system is shown to achieve Heisenberg scaling. Our work shows that pump quantization changes both the optimal operating point and the measurement strategies required to preserve a realistic quantum advantage in phase estimation and, more broadly, many-body quantum dynamics.
Nitrogen-vacancy (NV) center spin ensembles are a promising platform for accurate vector magnetometry, as they offer measurements referenced to a spin Hamiltonian in an anisotropic crystal with native vector sensing capabilities. However, charged dopants within the diamond produce random internal electric fields (RIEFs) that shift NV spin-transition frequencies, and their impact on the accuracy of NV magnetometry has not been investigated. Here, we characterize RIEFs' effect on NV spin-transition spectra and propose an analytical fitting function to improve accuracy in their presence. We build a Monte Carlo RIEF model that reproduces the asymmetric lineshapes observed in experimental optically detected magnetic resonance (ODMR) spectra, and use it as a testbed to quantify RIEF-induced errors by simulating ODMR spectra including RIEFs and comparing reconstructed magnetic fields to the known model input. With standard analysis approaches, we observe systematic errors exceeding the g-factor uncertainty in fields below $\sim$ 5 mT, while the proposed fitting function reduces the error by nearly an order of magnitude. Our results demonstrate that RIEFs can play a significant role in the systematic error budget for NV magnetometry, and offer a path towards improved accuracy in NV quantum sensing.
Optimizing continuous-variable functions on qubit-based quantum hardware requires a finite representation of the search space and a solver-compatible representation of the objective function. Fixed-grid discretizations provide a direct encoding, but restrict the search to a predefined range and resolution; at the same time, constructing a compact Hamiltonian for a general continuous-variable objective can be impractical. Here, we introduce a framework for continuous-variable optimization tailored to qubit-based quantum architectures. The method combines an adaptive discretization with an iterative local mapping of the objective function onto an effective spin-glass Hamiltonian. We assess the approach on unconstrained and constrained instances of the $n$-dimensional Gramacy-Lee benchmark, and on a proof-of-concept inverse-planning problem in intensity-modulated radiotherapy (IMRT) for cancer treatment. The results show that this framework can produce competitive solutions, supporting its use as a flexible mapping strategy for continuous-variable optimization in qubit-based quantum and quantum-inspired pipelines.
It was conjectured by Wehrl and proven by Lieb that the Shannon differential entropy of the Husimi function of a continuous-variable quantum state is lower bounded by the value it takes on coherent states. This corroborates the intuition, familiar from Heisenberg's uncertainty relations, that coherent states are minimal uncertainty states. The analogous statement for the Wigner function would be that the Wigner differential entropy of states with a positive Wigner function is bounded below by the entropy of pure Gaussian states. This was conjectured a decade ago, but recently disproven. Here, we prove the analogous statement for Kirkwood-Dirac distributions with mutually unbiased bases and for the Gross-Wigner distributions. For these discrete systems, the entropy-minimizing role is played by the pure states with positive quasiprobability distributions. Further, we prove that Kirkwood-Dirac distributions with large nonpositivity have large uncertainty.
We consider a quantum integrated sensing and communication problem over an optical link in which a low-power transmitter simultaneously communicates with a receiver and identifies the range of a defect producing a backscattered signal. We model the system as a lossy thermal-noise bosonic channel, in which the target, modeled as a beamsplitter, affects the timing of the backscattered signal through its location. Motivated by the envisioned deployment of entanglement-enabled quantum networks, we develop two protocols that allow the transmitter to leverage shared Gaussian entanglement, in the form of independent two-mode squeezed vacuum states or coupled three-mode squeezed vacuum states, to assist both sensing and communication. Since entanglement is known to enhance sensing, as demonstrated in quantum illumination, and to increase communication rates through entanglement-assisted communication, the transmitter faces a trade-off in allocating its entanglement resources between the two tasks. Our main results characterize these trade-offs under the proposed protocols in terms of achievable communication rate/sensing error-exponent regions, which outperform time-sharing schemes and demonstrate a quantum advantage.
In Fault-Tolerant Quantum Computing (FTQC) using surface codes, reducing $T$-count is critical for efficient computation due to the high cost of $T$-state distillation. Probabilistic Quantum Circuit with Fallback (PQF) synthesis significantly lowers $T$-counts compared to standard protocols like Gridsynth, but introduces high circuit dynamism through extra gates inserted at runtime. This dynamism invalidates static compile-time routing, as these new $T$ gates require dynamic lattice surgery routing to establish non-intersecting ancilla paths to $T$-state factories while minimizing total execution time. To address this, we introduce $\text{R}^2$-PQF, a Runtime Routing protocol for PQF-synthesized quantum circuits. $\text{R}^2$-PQF dynamically routes gates layer-by-layer, computing paths during the execution of the previous logical timestep. To satisfy the strict computational window of $\sim t_{lattice\_surgery} + t_{reaction}$ and non-intersectionality constraints, we implement a Wavefront Breadth-First Search (W-BFS) and synthesise it on a 500MHz FPGA and 2 GHz ASIC. For a clock cycle of 2GHz, we achieve a median logical time-step of $1.51 \mu s$ for a 300 qubit Ising Hamiltonian circuit, demonstrating that $\text{R}^2$-PQF successfully resolves the vast majority of paths (with rare exceptions) within the execution window and enables the $T$-count benefits of PQF without latency penalties. Compared to a baseline stalling-based solution (the only no-runtime-recomputation solution), $\text{R}^2$-PQF speeds up circuit execution by $1.34\times$ on average and up to $1.76 \times$.
We study single-query perfect anti-distinguishability/exclusion tasks of finite quantum channel ensembles, primarily using associated Choi operators and process POVMs. Weak perfect anti-distinguishability requires each measurement outcome to exclude an ensemble candidate with certainty, whereas the strong form additionally requires every candidate to have an exclusion outcome occurring with non-zero probability. For pairs of channels, both coincide with perfect distinguishability, whereas larger ensembles exhibit separations. We derive Choi-operator-support-based obstructions: weak exclusion requires at least two rank-deficient Choi operators, while strong exclusion requires the support of every candidate Choi operator to be strictly contained in the joint Choi support. The common Choi support must also lie in the kernel of the PPOVM normalisation. For commuting Choi operators, this condition is sufficient for weak exclusion when the normalisation also commutes with them. Conversely, a nonzero admixture of the same noise channel into every candidate precludes weak exclusion for any probe. We apply these results to measure-and-prepare, state-space contraction, Pauli, and replacer channels. In particular, the full permutation-channel ensemble of an unlabeled POVM is strongly anti-distinguishable exactly when some POVM effect is rank-deficient, while replacer-channel exclusion reduces to state exclusion. A Choi-commuting ensemble exhibits strong exclusion with an unassisted probe although no positive-definite PPOVM normalisation permits even weak exclusion. In contrast, commuting qubit phase gates, whose Choi operators need not commute, admit exact convex-hull criteria for weak and strong exclusion, both attainable without assistance.
Jointly supporting communication and distributed sensing over a shared, limited pool of entanglement resources is an attractive prospect for future quantum networks. We develop a network-level quantum integrated sensing and communication (Q-ISAC) framework in which a quantum base station dynamically allocates elementary Bell pairs between communication users and distributed sensing. Sensing resources are adaptively partitioned among multiple GHZ probes with dynamically selected sizes and sensing-node assignments. We derive an effective quantum Fisher information model accounting for probabilistic fusion, transmission loss, and memory decoherence, and formulate a finite-horizon allocation problem subject to communication QoS, expected sensing-information, sensing-reliability, and hardware constraints. A hierarchical constrained proximal policy optimization (HC-PPO) framework combines learned discrete sensing allocation with analytical continuous communication allocation. Numerical results show that GHZ probing requires approximately $27$--30% fewer sensing qubits than separable probing under modest probe-size caps and 65-67% fewer at the highest considered target under the same sensing requirements. Adaptive multi-GHZ partitioning provides greater robustness than single-GHZ sensing, while adaptive communication--sensing sharing outperforms the evaluated fixed splits. The proposed HC-PPO framework satisfies the joint requirements in at least 99.9% of test instances across the considered sensing targets and fusion probabilities. Monte Carlo evaluation separately shows that realized terminal information reached its target in 96-98% of realizations, distinguishing expected-information satisfaction from realized sensing performance.
Quantum identity authentication is an effective solution for establishing mutual trust between communicating parties in the post-quantum era. To address the risk of partial secret information leakage under special measurements, this paper designs a quantum identity authentication protocol based on perturbed probability amplitudes. The protocol first proposes a method of encoding a random sequence onto the probability amplitudes of quantum entangled states, forming perturbed probability amplitudes, thereby reducing the involvement of shared information between the sender and receiver. Furthermore, it presents a method for generating n-bit random authentication information based on the n-bit pre-shared information, enhancing the randomness of the authentication information relative to an attacker. The proposed protocol can resist impersonation attack, CNOT attack, and entanglement measurement attack, and ensures backward security. Under equivalent security conditions, the amount of shared information is 1/n that in Chen et al.'s scheme and half that in Dutta et al.'s scheme. And each bit of the secret message has no risk of leakage under special measurements. It can also be extended to a bi-directional quantum identity authentication protocol.
We study deep variational circuits for a periodic Heisenberg chain under local gate depolarization, at depths where noiseless training is coherently exact. Full-width initializations reach low coherent error faster than circuits with confined transverse generators, but incur a larger noise shift and need an order of magnitude more updates for noisy convergence. In many-body-localization-inspired initialization, bounding the initial transverse generator amplitudes keeps the operator support localized and suffices for low-fragility optimization, so longitudinal disorder and Floquet layer repetition are unnecessary. The fault-erasure fraction, the mean fraction of coherent energy removed per fault, sets the effective visibility through a parameter-free exponential model. Full-width circuits start with delocalized operator support, and once coherent energy builds up, each fault erases nearly all of it. Initially, their noise-induced gradient almost uniformly attenuates the coherent gradient, so coherent descent proceeds at the noiseless rate. They then stall on a high-noise force-balance plateau, where finite coherent and noise-induced gradients cancel to first order. At late times all initializations reach the same fault-erasure fraction and noisy-error band, but operator support contracts more slowly, at a rate set by the plateau residence time.
Building on our earlier results for closed quantum systems, we investigate the dynamical evolution of quantum fluctuations and their connections to Fisher information and the quantum operations describing open-system dynamics. Starting from a general expression for the time derivative of an observable's uncertainty, we derive an alternative upper bound on fluctuation growth in an open quantum system using the Cauchy-Schwarz inequality. The resulting bound separates contributions from the evolution of the quantum state and the explicit time dependence of the observable, reducing to a known result for closed-system dynamics. We then establish a connection between fluctuation dynamics and quantum Fisher information by decomposing the density operator and the symmetric logarithmic derivative (SLD) into coherent and incoherent contributions, which leads to a bound relating the evolution of observable uncertainty to the coherent and incoherent components of the Fisher information, providing an information-geometric interpretation of fluctuation growth. To connect fluctuation dynamics with quantum operations governing open-system evolutions, we derive the time evolution of the eigenvalues of the density operator in terms of Kraus operators. Using the infinitesimal-time relation between Kraus and Lindblad operators, we obtain a corresponding expression for the eigenvalue dynamics in terms of Lindblad operators. This formulation directly relates changes in the density operator eigenvalues to the quantum processes acting on the system. We then study the results using some examples. Our results provide a framework connecting observable fluctuation growth, Fisher information, and the Kraus and Lindblad descriptions of quantum evolution, offering a route toward understanding how specific quantum channels influence the information and fluctuations available in an evolving quantum system.
In this paper, we develop a semantic model for the parallel execution of quantum circuits, providing a formal foundation for studying shared-qubit concurrency in quantum computing. As in classical shared-memory concurrency, parallel quantum circuits may interfere with one another through operations on shared qubits. However, quantum entanglement and the noncommutativity of quantum operations introduce additional challenges for reasoning about their correctness. To address these challenges, we generalise the classical Owicki-Gries method to quantum computing at the level of quantum circuits. Our approach enables compositional reasoning about parallel quantum circuits by separating the verification of individual components from the analysis of interference between them. We formulate proof rules for establishing the correctness of parallel quantum circuits and prove their soundness with respect to the proposed semantic model.
We construct a universal quantum computational encoding via braiding in Links--Gould fusion spaces associated to $U_q^H(\mathfrak{sl}(2|1))$ where $q$ is on the unit circle and is not a root of unity. The construction uses only neglectons and is realized in the morphism spaces $\mathrm{Hom}_{U_q^H}(V(0,\alpha),V(0,-\frac{1}{2})^{\otimes 2N}\otimes V(0,\alpha)).$ Under explicit positivity and arithmetic constraints these spaces admit a $2^N$-dimensional computational subspace with a positive definite Hermitian form. We prove single-qubit density in $\mathrm{U}(2,1)$ and approximate arbitrary unitary operators on $N$-qubit computational subspaces with arbitrarily small leakage. The calculations use explicit inclusions, projections, and Hermitian pairings without requiring $F$-matrices.
How can noncommuting quantum observables retain the geometry of a classical phase space? Motivated by Mumford's question on approximately macroscopically unique (AMU) states and the work of Lin and Wang, we study synthetic spectra of position--momentum and angular-momentum systems. Under the hypotheses of their AMU theorems, nonempty synthetic spectra yield AMU states. For sufficiently small $\hbar$, the position--momentum spectrum fills the plane, while the angular-momentum spectrum contains any prescribed ball. The latter calculation leads to compact Lie groups: we prove that highest-weight coadjoint orbits lie in regional synthetic spectra under an explicit variance bound. Function-space representations of $SU(n)$, $SO(n)$, and $Sp(n)$ provide further examples.
We establish a conditional quantum Kac-Bernstein theorem for mixing of two independent, finite-mode bosonic inputs with quantum memories. We characterize exactly when the outputs are conditionally independent given both memories. Each input then decomposes into orthogonal memory sectors sharing a common Gaussian state on the physical system and a bosonic memory factor, up to sector-dependent physical displacements. In particular, triviality of the common bosonic factor implies separability of the inputs, as occurs whenever either memory has finite-dimensional support.
Quantum circuit optimization is an indispensable component of the quantum software stack, used to reduce noise, maximize performance, alleviate costs of quantum error correction, or target specific hardware. A related problem is approximate membership: for a fixed set of unitaries $S$, decide whether a given circuit $C$ is within distance $\varepsilon$ of a unitary in $S$ under some metric $m$. Membership is a special case of optimization, where $S$ is a set of unitaries implementable at no cost (e.g., with noise-minimal circuits, or without magic states). Janzing, Wocjan, and Beth (Int. J. Quantum Inf., 2005) showed that, for the operator metric, the case $S=\{I\}$ (approximate identity) is QMA-complete when $C$ is promised to be either close to the identity or far from it. We generalize this setting in three directions: (i) promise-free inputs, (ii) besides $S=\{I\}$, sets $S$ containing only Clifford unitaries, or only generalized permutation matrices (i.e., no superposition), and (iii) the trace-based, spectral, and operator metrics. We show that, in all cases, approximate membership is PP-hard for wide ranges of $\varepsilon$, provided $C$'s gate-set can implement Clifford+T, as the gate-sets of standard hardware do. If $S=\{I\}$, or if $S$ contains only generalized permutation matrices, $I\in S$, and $m$ is a trace-based distance, PP-hardness holds for all non-trivial $\varepsilon$. If $S=\{I\}$ and $m$ is a trace-based distance, PP-hardness holds even for circuits over classical-reversible gate-sets. Our results indicate that approximate membership is harder over promise-free inputs than the QMA-complete promise version, and that this hardness persists across quantum resources (any gates, non-Clifford, superposition) and distance metrics. They directly imply PP-hardness of circuit optimization when minimizing total, non-Clifford, or superposition gate depth or count.
Quantum amplitude estimation can estimate expected discounted payoffs with quadratically fewer oracle calls than Monte Carlo, but each call requires coherent computation. We use language-model-assisted circuit design to reduce reversible payoff arithmetic for a three-asset worst-of autocallable and a target accrual redemption forward (TARF). The constructions retain compact integer representations of market paths alongside contract history, reconstructing quantities temporarily for contract decisions and payoff-angle evaluation. Relative to matched internal references, the factor-sum autocallable and windowed TARF circuits reduce the product of Toffoli count and peak logical qubits $(N_{Tof} Q_{max})$ by factors of 2.39 and 4.84, respectively. At a second autocallable setting, fresh search recovers a 1.35-fold saving after the tested fixed adaptation loses its advantage. For the factor-sum circuit, we prove exact coherent execution of its integer specification for every input, incoming accumulator and measurement record, with clean workspace and phase cancellation. A separate lattice calculation gives a numerical angle-tolerance-violation probability of 6.248e-8 and evaluates pricing bias under the declared loading law, with bounded omission but no certified numerical enclosure. The results connect compact representations to lower-cost payoff arithmetic and separately assessed logical and financial correctness. Their resource scope excludes loading, payoff rotation and estimation.
Advances in free-electron quantum optics are establishing free electrons as a versatile quantum resource. Photon-induced near-field electron microscopy (PINEM) interactions and free drift provide elementary operations for shaping the longitudinal electron wavefunction, yet their full control capabilities remain unexplored. Here, we prove that a finite sequence of alternating monochromatic PINEM interactions and free drifts can approximate any prescribed inner-product-preserving map from a finite-dimensional input subspace into the full ideal electron-sideband Hilbert space to arbitrary accuracy. We therefore call the protocol PINEMAD (PINEM And Drift). This framework encompasses state preparation, unitary gates, and isometric encoding. We further show numerically that parameter optimization enables high-fidelity state preparation at finite electron energy spreads, using experimentally accessible coupling strengths and tabletop-scale total drift lengths. These results establish electron energy sidebands as a programmable quantum resource.
We introduce the Pauli-Correlator Autoencoder (PCAE), a hybrid quantum--classical architecture for image reconstruction. PCAE splits an image into patches and compresses each patch as a matrix product state (MPS). A small quantum circuit turns each compressed patch into a few measured numbers, and a classical neural network rebuilds the patch from these numbers and the patch position. A learnable energy term, taken from physics, is added to training and tracked as training proceeds. Two versions place the six qubits on a line (PCAE1D) or on a grid (PCAE2D). An averaging step makes the PCAE2D features follow rotations and reflections of the image exactly. Trained on one image at a time, PCAE2D rebuilds images from six public datasets with a peak signal-to-noise ratio of 25.8 to 41.6 decibels. On CIFAR-10 images not used in training, a formula-based stand-in for the PCAE2D features performs within 1 decibel of several simpler classical methods. Five trained models also run on real IBM quantum computers without retraining, and rebuild images at 25.90 to 31.52 decibels. A short argument and a synthetic test show that, with a linear final layer, measuring qubits in pairs is needed for targets built from products of inputs. These results show that PCAE works as a hybrid model that rebuilds varied images and runs on today's quantum hardware at the six-qubit scale.
Sample-based quantum diagonalization (SQD) accuracy remains limited for strongly correlated systems like iron-sulfur clusters. This accuracy heavily depends on the mean-field reference state, which determines the sampling ansatz and configuration-recovery target. We extend the qcsc-prefect workflow to support a broken-symmetry unrestricted Hartree-Fock (BS-UHF) starting point, derived from atom-localized antiferromagnetic initial guesses. For the $[Fe_4S_4(SCH_3)_4]^{2-}$ cubane (54 electrons, 36 orbitals, 72 data qubits; 88 total qubits), this lowers the mean-field reference by $\approx 534$ mHa relative to the Restricted Hartree-Fock (RHF) solution (-327.0809 vs. -326.5474 Ha). Combined with deep multi-step configuration recovery on ROQUO GPU nodes at subspace dimension $d = 3 \times 10^{10}$, we reach $E = -327.235076$ Ha. This is 4.3 mHa above the finite-$D = 4000$ DMRG value (-327.2393952 Ha) and $\sim 512-517$ mHa below a previous same-active-space RHF-reference SQD calculation. Extrapolating to the $d \to \infty$ limit via a Gaussian-in-log $d$ fitting ansatz gives an asymptotic estimate $E_\infty = -327.244468$ Ha $\pm 1.05$ mHa, just 0.33 mHa above our discarded-weight-extrapolated DMRG estimate ($E_{D\to\infty} = -327.244797$ Ha $\pm 0.46$ mHa), well within their combined $1\sigma$ uncertainty. We characterize the determinant-subspace composition driving convergence, show matching validation on $[Fe_2S_2(SCH_3)_4]^{2-}$, and report multi-HPC execution on Fugaku, Miyabi-G, and ROQUO. We conclude that reference-state preparation, rather than subspace size alone, is a key driver of SQD energy accuracy under strong electronic correlation.
We consider a massive object, such as a neutral atom or an Unruh-DeWitt detector, moving at constant speed in a quantum field and investigate how motion affects the quantum coherence of its internal degrees of freedom, manifesting as quantum dispersion in the absence of a quantum field, and decoherence in its presence. Our investigation aims to serve two purposes: One is to obtain the correct results for these effects, which are essential for the design of quantum information processing schemes where the quantum coherence of an atom's internal degrees of freedom is of major concern. The other is to expose the fallacies in commonplace approaches, which start with a non-relativistic calculation and then add on relativistic ``corrections". We first show a fully relativistic calculation of the internal dynamics based on covariance principles, and then one which ignores these principles, often justified by the atom's slow motion. By a direct comparison of results from these two approaches, we identify {significant discrepancies} in a non-relativistic treatment, even at low atomic speeds. The proper procedure, and a much safer one in terms of accuracy, is recommended here: first derive the dynamics and the necessary regularizations within a fully covariant relativistic framework. Only after the exact, internally consistent equations of motion are established should low-velocity limits be extracted from them. Only in this way can all the relativistic effects which matter: time dilation, aberration, non-inertial mass shifts, be systematically preserved, and accurate results obtained.
Quantum memory is a core enabling device for large-scale quantum networks, serving as the fundamental building block for quantum repeaters and transportable quantum memories. Among various physical platforms, rare-earth-ion-doped crystals stand out as one of the most promising solid-state candidates for long-lived photonic quantum memories, owing to their exceptionally long spin coherence time and their compatibility with integration. In this review, we first introduce the physical mechanisms underlying long-lived spin coherence in rare-earth systems, with particular emphasis on the zero-first-order-Zeeman transition and dynamical decoupling techniques. We then review the experimental progress in this field, highlighting three distinct lifetimes--the spin coherence time, the light storage time, and the quantum storage time--and covering experiments that have achieved hour-scale spin coherence, minute- to hour-scale light storage, and minute-scale single-photon-level quantum storage. Finally, we discuss the remaining challenges that hinder the realization of practical long-lived quantum memories, explore potential strategies to overcome these obstacles, and outline the prospects for their future applications in quantum networks.
We prove the security of phase-encoded decoy-state BB84 quantum key distribution for a Mach-Zehnder receiver with imbalanced beam splitters and two threshold detectors that leak fine-grained information about the detection patterns. For this, we derive a lower bound on Bob's single-photon contributions and combine it with the decoy-state method and a recent phase-error framework for leaky receivers. The leakage-induced correction to the phase-error rate is independent of channel loss, providing a loss-tolerant treatment of receiver leakage even in the presence of beam-splitter imbalance. Our results provide a practical route toward loss-tolerant security proofs for imperfect QKD receivers in the presence of receiver leakage.
We investigate the emission profiles of singly excited collective states and propose a matched-mode witnessing protocol in a mirror-terminated waveguide quantum electrodynamics system. The amplitudes and relative phases of the initial collective excitation are encoded in the temporal mode of the emitted single-photon wavepacket, providing a route to state verification through the common waveguide output. We identify the emission mode associated with a chosen target state and employ an auxiliary virtual-cavity representation to evaluate the quantum state of this selected output mode. For a matched initial state, the selected mode contains the emitted single photon, whose Wigner function exhibits a pronounced non-classical negative dip, serving as a distinct fingerprint of the target many-body state. With the reference mode held fixed, different initial configurations yield different photon occupations and phase-space distributions, demonstrating the state selectivity of the protocol. These results connect collective-state verification with temporal-mode analysis of the emitted radiation, offering access to collective coherence with reduced reliance on qubit-resolved correlation measurements.
We study the entanglement dynamics of two qutrits under collective dephasing for a family of states obtained by mixing a maximally entangled state that lives in the decoherence-free subspace with three nonstationary two-term states sharing a common amplitude ratio $r$. We obtain exact PPT and separability regions along the whole trajectory, a specialization of known results on cyclic sign invariant states, and we supply explicit certificates: a finite product decomposition, three fixed positive-map witnesses, and a closed realignment formula that detects every PPT-entangled state, so that no state is left undecided. The negativity is computed in closed form. It shows that the entanglement is time-invariant, positive and constant from the initial time although the state changes, exactly when the weight of the maximally entangled state exceeds the threshold $U_r=r/(1+r+r^2)$. To our knowledge, this is the first demonstration of time-invariant entanglement for qutrit--qutrit systems under collective dephasing. For smaller weights the entanglement decays and vanishes at a finite time: the state either becomes separable (entanglement sudden death) or, for $r\neq1$ in an intermediate range, loses distillability suddenly and remains bound entangled at all later times. Every state with negative partial transpose is one-copy distillable by a fixed local projection. The same trajectories arise from the global dephasing map and from a correlated local random-unitary semigroup, although the two channels differ on product inputs. Exact rational benchmarks and embeddings of the Horodecki and Ha--Kye--Park families are provided.
Acorn tricks turn weak quantum resources into stronger "randomized" ones. A recent example is the random purification channel, which turns $t$ copies of a mixed state into $t$ copies of a random purification. We ask whether analogous techniques can turn queries to an isometry into queries to a random unitary completion, or queries to a quantum channel into queries to a random isometry dilation. For an isometry from dimension $N$ to dimension $M$, we give an efficient, stateful simulator for $T$ sequential, forward queries to a fixed Haar random unitary completion. It uses at most one forward isometry query per simulated call, with total trace-distance error $O(T\sqrt{N/(M-T)})$. This lifts isometry query lower bounds to arbitrary unitary completions, and copy complexity lower bounds to forward access to state preparation unitaries, with dimension-dependent loss that can be made arbitrarily small for most applications. Conversely, we construct two distributions on quantum channels distinguishable exactly with two queries to an arbitrary dilation, but requiring exponentially many channel queries for nonnegligible advantage. This rules out efficient simulation of random channel dilations. Our technique also shows that approximating the quantum switch to any constant error below $1/2$ requires exponentially many channel queries, even for identical channels, giving an exponential query advantage for indefinite causal order and improving on Bavaresco et al. (2025). Finally, we show how to "decontrol" controlled forward access to an isometry: any algorithm making controlled queries to $\phi V$ for a random phase $\phi$ can be transformed into one using the same number of uncontrolled forward queries to $V$, generalizing the analogous result for unitaries.
Implicit neural representations (INRs) model signals as continuous functions from coordinates to values, but their performance depends strongly on how spectral capacity is allocated. Yet most Quantum INR (QINR) architectures treat spectral components as independent outputs of separate quantum blocks. We introduce the Spectral Quantum Memory Model (SQMM), a memory coupled quantum INR in which sequential hybrid data reuploading layers (bands) communicate through a shared coherent quantum memory register. Each band reads the memory, computes on its own coordinate upload, and writes part of its state back, so later bands can build on the computation of earlier ones. When memory read and write layers are input independent, we prove that the memory state forms an operator valued Fourier series whose support is contained in the Minkowski sum of the initial memory spectrum and the local band spectra. Downstream bands then condition their Fourier coefficients on the spectral content stored by earlier bands, and the memory coupling creates no new primitive frequencies. This theory motivates a spectral memory alignment loss that encourages memory to encode the spectrum expressed by the deployed prefix of the model. Across audio and image reconstruction benchmarks, SQMM improves over compact QINR and INR baselines.
Nitrogen-vacancy (NV) centers in diamond have attracted considerable attention for micro- and nanoscale thermometry owing to their high precision and spatial resolution. However, achieving sufficient electron spin polarization and signal-to-noise ratio (SNR) typically requires high-power or long-duration laser excitation, which introduces heating and degrades measurement accuracy and stability. To address this trade-off, a reinforcement learning (RL)-based approach is proposed to optimize spin polarization under low-heating constraints. First, a physical model integrating five-level optical pumping rates and NV spin polarization dynamics is established. A temperature-rise constraint model is then developed based on pulsed optically detected magnetic resonance (P-ODMR) measurements under varying laser powers and pulse widths in an external magnetic field. Subsequently, a Progressive Action-Space Q-learning (PAS-Q) algorithm is employed to explore the parameter space and identify optimal laser power and pulse-width combinations. The agent is trained through numerical simulations and the resulting strategy is implemented in a hardware system. Experimental results demonstrate a 44% reduction in laser-induced heating, a 33% increase in spin polarization rate based on T1 relaxation analysis, and a 71% reduction in optimization time compared with traditional methods. This approach enables efficient spin polarization with reduced laser heating and improved optimization efficiency, and may be extended to other heat-sensitive quantum spin sensors, including silicon-vacancy centers in diamond and divacancy defects in silicon carbide.
We apply the numerically accurate multiple Davydov Ansatz (multi-$\rm D_2$) method to investigate the nonequilibrium dynamics of an open molecular cavity system using an extended driven-dissipative Holstein-Tavis-Cummings model incorporating Kerr nonlinearity. Our results reveal that the synergy between Kerr nonlinearity and exciton-phonon coupling induces an anharmonic level structure, imposing a stringent energy penalty that isolates the one-excitation manifold. This establishes a robust single-excitation-dominated regime that dynamically manifests photon blockade, characterized by suppression of the pure two-photon state and isolation of the one-excitation manifold. While strong coherent driving induces power broadening that overcomes the nonlinear barrier and opens multiphoton channels, cavity dissipation counteracts this process by acting as a highly selective manifold filter. By preferentially depleting fragile multi-photon states while sheltering single excitations within dissipation-free dark states, the cavity mode decay rate actively cooperates with Kerr nonlinearity to restore and reinforce the photon blockade effect. These findings elucidate the intricate interplay among nonlinearity, driving, and dissipation, offering a theoretical blueprint for engineering robust single-photon sources in open molecular cavity platforms.
Exploring interactions between quantum emitters and guided photons, waveguide quantum electrodynamics (wQED) offers a versatile platform for quantum simulation and quantum interconnect. To simplify the quantized light-matter interactions, a linearized dispersion approximation (LDA) was widely used in wQED under the conditions of weak coupling and narrow photonic bandwidth. However, a growing number of strong-coupling wQED experiments have called the validity of LDA into question. Here, by investigating giant atoms coupled to a semi-infinite waveguide, we propose a principle to judge the validity of LDA. We find that the decoherence of the atoms exhibits rich dynamical behaviors determined by different numbers of bound states in and out of the continuum (BICs and BOCs) formed in the energy spectrum of the total atom-photon system. Based on this, we show that despite the LDA can partially preserve some of BICs, it completely erases BOCs. This causes the dominant role of LDA in the atomic dynamics to break down. Providing a physical insight into the validity of LDA, our results lay a firm foundation for exploring fundamental physics and its application frontier in strong-coupling wQED platforms.
Quantum simulations of molecular electronic structure hold the potential for computational advantage but are inherently limited by the linear scaling of qubit requirements with respect to system size. Quantum Density Functional Theory (Q-DFT) addresses this constraint by reformulating the interacting many-body problem in terms of a non-interacting Kohn--Sham reference system. Here, we present and experimentally validate a Q-DFT algorithm that requires only $\mathcal{O}(\log_2(N))$ qubits to simulate a system of $N$ orbitals, thereby reducing resource overhead. More precisely, we solve the Kohn--Sham problem for the lithium hydride (LiH) molecule using the ensemble extension of the variational quantum eigensolver paradigm that minimizes the energy of the system in the subspace spanned by the ground and first excited states. To execute this task, we encode the problem with qubits on a quantum photonic platform, utilizing an architecture that combines a deterministic quantum dot single-photon source with a programmable integrated photonic circuit. By evaluating the molecular ground- and first excited-state properties, this work establishes a pathway for simulating larger molecular systems, demonstrating the viability of integrating qubit-efficient algorithms with advanced reconfigurable photonic hardware for near-term quantum chemistry applications.
Spectral bandwidth and frequency mismatch between quantum light emitters and quantum components is a common problem in the realization of hybrid quantum information networks. Here we propose a simultaneous solution to both of these problems by using a free-space cavity with an embedded nonlinear crystal that, through frequency conversion, facilitates perfect coupling into a cavity mode. The slow leakage of the cavity effectively stretches the photon pulse, resulting in a much longer photon pulse at a different wavelength. We show that the amount of stretching is strictly limited by the finesse and length of the cavity. Including realistic internal losses in the cavity, we show that it is possible to stretch a photon by at least two orders of magnitude with high efficiency. The proposed setup can thus constitute a valuable addition to the toolbox of quantum information technologies.
We study the one- and two-boson energy subspaces of finite open Bose--Hubbard chains with Fibonacci-modulated hopping and zero on-site potential. Their spectra exhibit a hierarchy of bands and gaps, and a critical zero-energy mode for odd lengths, in agreement with prior research. For the singe-excitation subspace we find two families of length-invariant finite-energy states localized at the left cluster boundary. For the two-boson subspace, we report both doublon and separated-pair excitations in the form of Tamm/Shockley states localized near either end. In particular, the right-edge doublon states occur across all Fibonacci generations whereas the left-side states appear every second generation. We check numerically that the second-order perturbation theory accounts well for the structure of the spectrum and the edge states in the doublon subspace in the strong-coupling regime. The results are useful for future explorations of many-body physics beyond numerical tractability, specifically using near-term Josephson quantum simulators.
The introduction of $XX-$interactions, typically in the form of an additional catalyst Hamiltonian, has shown promise as a tool for gap enhancement in quantum annealing, allowing the algorithm to obtain optimal solutions with shorter run-times. However, the optimal placements of these couplings within the problem graph has been found to be highly setting-dependent. In this work, we propose an iterative catalyst-construction protocol for the removal of a common quantum annealing bottleneck known as perturbative crossings. The method utilises the measurements returned by successive annealing runs to effectively steer the algorithm away from the local optima in which it becomes trapped. First, we motivate a framework for $XX-$term selection based on perturbation theory and establish its effectiveness at removing perturbative crossings on scalable toy instances with up to $39$ spins, demonstrating a consistent performance both with increasing system size and number of local optima. We then simulate the recursive catalyst-construction method on a test set of $18-$spin maximum-weight independent set problems that are generated to produce annealing spectra with multiple perturbative crossings. We find that the protocol significantly outperforms both catalyst-free annealing and annealing with catalysts containing randomly selected $XX-$terms.
Quantum error correction becomes more hardware efficient when physical noise is strongly biased towards one error channel. Cat qubits realize such a bias by encoding information in two opposite coherent states of a superconducting oscillator, so that bit flips are exponentially suppressed with photon number while phase-flip rates increase only linearly. In Kerr-cat qubits, a driven double-well potential confines these states and enables fast coherent control, but excitations can induce interwell switching, limiting bit-flip times to milliseconds. Here we show that the nonlinear interaction generating the confinement can also cool these excitations. When an intra-well transition becomes resonant with a lossy readout mode, excitations are transferred out of the qubit and dissipated, as established by spectroscopy and relaxation measurements. We observe the predicted exponential scaling of Kerr-cat bit-flip times with photon number, reaching 450 s, over five orders of magnitude beyond previous demonstrations. Phase-flip rates remain consistent with intrinsic photon loss at operating points with seconds-long bit-flip times. We further demonstrate fast Z gates without measurable degradation of bit-flip protection and single-shot readout with a bit-flip probability below $10^{-6}$ per measurement. Autonomous cooling thus brings minutes-long bit-flip protection to Kerr-cat qubits while retaining fast coherent control, without additional cooling drives or circuit elements.
Neural networks that predict chaotic dynamics can reproduce short trajectories while misrepresenting statistics over long times. Quantum priors represent selected dynamical statistics through quantum generative models and provide statistical constraints for classical neural networks. Training a separate prior for each value of a system parameter, such as the Reynolds number, does not explicitly model how these statistics vary with that parameter. We learn a conditional quantum prior that approximates selected statistics of an invariant measure at unseen parameter values within the training range, without retraining. For Lorenz-63, the prior reduces mean Jensen-Shannon divergence by 56.9% relative to a classical multilayer perceptron with a comparable number of weights across 96 unseen parameter values. Across 101 values of the same parameter, the shared prior uses 84.7% fewer trainable weights than would be required by a separate quantum neural network at each value. We then use the learned prior to regularize classical neural networks, encouraging their autoregressive rollouts to better reproduce long-term statistics. For Kolmogorov flow at Reynolds number $Re=1000$, prior regularization reduces forecast mean squared error by 66.0% over 318 steps relative to the classical baseline without prior regularization. We also implement a photonic quantum prior for noisy intermediate-scale quantum (NISQ) devices, achieving a mean Jensen-Shannon divergence of $4.58\times10^{-3}$ for Lorenz-63 and $2.59\times10^{-3}$ for Kolmogorov flow at unseen parameter values.
We have constructed a quantum sensing system composed of two quantum van der Pol (vdP) oscillators. Coherent and dissipative couplings are combined to establish a generic nonreciprocal coupling between the two vdP subsystems. A weak driving signal to be measured is applied to an oscillator (probe system) and then transferred via non-reciprocal coupling to another oscillator (measurement system) that is easier to measure. This allows for the acquisition of information about the driving strength of the signal being measured. For the classic cascaded dual vdP oscillators, complete non-reciprocal coupling yields a much higher susceptibility than a single classical vdP oscillator alone. For the quantum vdP system, the sensitivity generally does not diverge at the zero driving force point. When only dissipative coupling and two-particle loss are present, the system will have a dark mode at the zero driving force point, which enables the measurement precision to ultimately reach the Heisenberg limit in the time domain. Enhancing incoherent driving can effectively resist dissipation and thereby improve measurement precision. Moreover, in the strong incoherent driving regime, the improvement factor of non-reciprocal coupling over reciprocal coupling in terms of measurement precision tends to infinity as the two-particle loss rate of the measurement system approaches zero.
Magic state preparation is often among the most expensive operations in a fault tolerant quantum computation. One obstacle to coming up with better magic state preparation circuits lies in verifying their fault tolerance properties, as it is difficult to verify either by hand or in software that a very large number of combinations of faults do not give rise to high-weight or logical errors, especially in a non-Clifford circuit. In this work, we propose the use of the CNOT + T gate set to fault-tolerantly prepare a large class of magic states. We consider the propagation of Pauli faults within CNOT + T circuits and derive properties similar to those of Pauli faults within Clifford circuits, with a view to verifying fault tolerance as efficiently as possible. We present Comb, a library that can verify the fault tolerance of CNOT + T magic state preparation circuits, and demonstrate its use in verifying the fault tolerance of distance three and distance five magic state preparation circuits in minutes on a laptop. We present a distance five magic state preparation circuit that was discovered using Comb. As an independent confirmation of Comb's correctness we compare its findings to circuit-level noisy simulations for several magic state preparation circuits.
Open quantum systems naturally relax toward steady states that underpin diverse nonequilibrium phenomena and quantum technologies. We independently control the coherent and dissipative constituents of a Lindblad generator to construct a variational product formula, termed the Lindblad variational ansatz (LVA), that accelerates steady-state preparation over natural relaxation through an optimized preparation path. The protocol consists of small-system learning, continuation to greater depth, and transfer to larger systems, followed when needed by reference-free post-training on quantum simulators. We demonstrate LVA in a bulk-dissipative Ising chain and a boundary-driven Heisenberg chain, where transferred protocols achieve matched preparation accuracies with fewer generator blocks than time-optimized first- and second-order Trotter formulas. The acceleration arises from coordinated endpoint preparation: earlier controls shape the dissipative-mode amplitudes so that the final dissipative step brings multiple components simultaneously close to their target values. Our results suggest a route to open-system quantum simulation that combines classical training on small systems with deployment and optional refinement on larger quantum devices.
An important ingredient in fault-tolerant quantum computation is asymptotically good codes with fully addressable transversal non-Clifford gates. Existing constructions, however, provide only small explicit guarantees for rate and relative distance. Here, we substantially improve these guarantees for fully addressable transversal phase gates at every fixed level $h\ge3$ of the Clifford hierarchy, using a cyclic encoding beyond the binary CSS framework. The encoding separates logical phase control from the joint design of rate and distance, enabling two constructions with different computational costs. A deterministic polynomial-time algebraic-geometric construction gives a common asymptotic lower bound of $52/(675h)$ on both quantities. A counting argument gives an exponential-time construction with exact verification, improving this bound by a factor of approximately $2.86$. We further establish a universal upper bound for codes supporting fully addressable transversal single-qubit phase gates. Within our cyclic encoding framework, we obtain a stronger upper bound that is approximately $1.28$ times the lower bound achieved by our exponential-time construction. As concrete examples, we construct codes with $48$ and $90$ physical qubits supporting fully addressable transversal $T$ gates. These results narrow the gap between achievable code parameters and addressability bounds, providing quantitative targets for further improvements in efficient code constructions.
We introduce the synchronization Mpemba effect, in which a less synchronized initial state overtakes a more synchronized one, and demonstrate it in dissipatively coupled quantum van der Pol oscillators. Within a graph-Laplacian framework, we show that for two oscillators, the mechanism is a competition between a slowly decaying collective background and a fast transverse transient, equivalently an exchange between relative-mode displacement and phase-fluctuation errors. The same decomposition extends to networks: the synchronization error splits into transverse Laplacian modes, yielding closed-form crossing times from eigenvalue separations and initial mode weights, and a sufficient screening criterion. With only these eigenvalues entering, the rule is topology independent: crossing times of different networks collapse onto a single spectral-gap line. Thus, quantum many-body dynamics can be designed and controlled at low dimension without constructing the exponentially large Liouvillian, opening a route to quantum synchronization as a resource.
Quantum batteries can exploit quantum resources to enhance energy storage and work extraction, and recent experimental progress has brought their implementation closer to reality. In realistic settings, however, environmental dissipation is unavoidable, making dissipative charging a physically relevant operating regime. Here we investigate ergotropy in dissipatively charged quantum batteries, focusing on interaction-induced work extraction. For two coupled two-level systems (TLSs), we derive exact analytical expressions for the total, coherent, and incoherent ergotropy in both resonant and detuned configurations. We show that, in the resonant case, ergotropy is activated only above a critical coupling associated with an interaction-induced energy-level crossing, whereas detuning enables ergotropy already in the weak-coupling regime. Moreover, quantum coherence, although necessary for coherent work extraction, is not by itself sufficient to guarantee nonzero coherent ergotropy. In the strong-coupling regime, the resonant setup reaches the maximum ergotropy at a finite coupling strength, whereas the detuned setup approaches the same limit only asymptotically. Extending the analysis to a periodic XX spin chain of $N$ TLSs, we analytically derive the finite-temperature coupling threshold for ergotropy activation and show that it scales as $1/N$ in the large-$N$ limit. These results identify frequency detuning, interaction strength, and system size as key control parameters for ergotropy generation in open quantum batteries.
Modern unit commitment (UC) scenarios, particularly those involving uncertainties from demand fluctuations and renewable energy sources, pose significant challenges to traditional optimization methods due to the large search spaces they encompass. This paper proposes a quantum computing-ready optimization pipeline for deterministic and stochastic UC, integrating classical, quantum-inspired, quantum annealing, and hybrid quantum-classical solvers across test systems, including the IEEE 118-bus system. A novel Quadratic Unconstrained Binary Optimization (QUBO) reformulation accommodates generator scaling and 24-hour scheduling horizons with compact Boolean logic penalties for startup, cooldown, and spinning reserve constraints. A divide-and-conquer strategy and Quantum Computing Monte Carlo (QCMC) simulation address scalability across 27,730 uncertainty scenarios, reducing compilation time by up to two orders of magnitude. Experimental results demonstrate the pipeline's ability to achieve efficient, scalable, and accurate UC optimization under uncertainty: the hybrid quantum method approach matches the classical baseline, reduces stochastic UC runtime from 40.76 to 14.79 hours, and characterizes pure quantum annealing as limited to small systems with 0.22% to 2.18% encoding errors and constraint violations. These results provide an analysis of the scalability and computational practicality of hybrid quantum optimization for generator scheduling in UC.
Decoherence can make gravitationally generated entanglement arbitrarily small, or even vanishing, without necessarily rendering the effective matter dynamics separable. We ask whether this hidden non-separability can be revealed using strictly local quantum error correction. For Newtonian gravity supplemented by physically relevant localization noise, including environmental noise, and noise from collapse models such as GRW, CSL, and Di\'osi--Penrose, we analyze when the underlying entangling resource is locally recoverable. For GRW- and CSL-type noise, we analytically establish that strictly local quantum error correction can make the ratio of the effective gravitational interaction strength to the residual decoherence rate arbitrarily large for any parametrization of the collapse model, even in regimes where the unencoded entanglement signal approaches zero. By contrast, the Di\'osi--Penrose model does not exhibit the same enhancement under bipartite protocol considered here, revealing a qualitative difference. These results show that the loss of detectable entanglement is not equivalent to the loss of a recoverable non-separable resource, and open a route toward practical recovery protocols.
In his 2005 list of semi-grand challenges for quantum computing theory, Scott Aaronson asked whether a quantum computer that is always in a separable mixed state can be simulated by a classical computer in polynomial time. An affirmative answer was claimed for the one clean qubit model of quantum computation. The supporting mathematical arguments relied on an exhaustive characterization of circuits that stay in separable states. Here, we give a counterexample where one pure qubit, known as the clean qubit, controls a sequence of three gates that act on a maximally mixed three-qubit register. The overall unitary that accumulates as these gates are applied has the properties that ensure the state of all four qubits remains fully separable. Crucially, we show that the final unitary cannot be put into the form required by the claimed simulation result. We also give a continuous-time implementation of the same circuit that keeps the qubits fully separable throughout and ends at the same unitary. We extend our counterexamples to a uniform family, and pinpoint the gap in the earlier proof. Since our circuits are themselves efficient to simulate classically, this work does not settle Aaronson's question. It does, however, reopen the semi-grand challenge for an actively researched model of quantum computation.
Quantum error correction provides the mathematical basis for protecting quantum information against noise. Existing formalizations have established foundations for stabilizer codes and code verification. However, a systematic formal treatment of the asymptotic constructions and fundamental limitations that underpin scalable quantum error correction is still needed. We present QECert, a Lean library providing reusable formal foundations for these theoretical questions. It connects quantum error-correction criteria, stabilizer and Calderbank-Shor-Steane codes, and algebraic and homological constructions within a common framework. Asymptotically good quantum low density parity check codes provide the principal case study. We formalize constructions and asymptotic parameter theorems spanning hypergraph products, balanced products, lifted products, and quantum Tanner codes. Further developments cover Bravyi-Poulin-Terhal bounds and related locality restrictions, constant overhead magic state distillation, and energy barriers and storage errors for quantum memories. QECert establishes a reusable formal foundation for studying the capabilities, resource requirements, and fundamental limitations of quantum error correction, supporting systematic verification and further development of its theory.
Quantum networks distribute entanglement between distant nodes by combining many short entangled links using local quantum operations. These operations only succeed probabilistically, yet existing percolation-based theories of entanglement transmission treat them as perfect. We approach the problem through statistical physics, using a stochastic generalization of concurrence percolation to determine how reliable local operations must be for long-range entanglement to remain possible. On hierarchical $(U,V)$-flower networks, which permit full analytical control across network scales, we derive an exact renormalization recursion for the probability that an end-to-end entangled connection survives. For the $(2,2)$-flower this yields a closed-form operational phase boundary, $\eta_p = 2 - \frac{32}{27}\eta_s$, where $\eta_s$ and $\eta_p$ are the success probabilities of the series (entanglement swapping) and parallel (purification) operations, respectively. At this boundary the survival probability jumps discontinuously from $0$ to $S_\infty = 3/(4\eta_s)$. Numerically propagating the full distribution of end-to-end concurrence yields a second threshold in the initial link quality, which varies continuously with operational reliability. Above both thresholds the large-network state is binary: the connection either fails outright or approaches a perfect Bell pair. Our results thus reveal a two-threshold structure for long-range entanglement, in which operational reliability and initial link quality can compensate one another. Operational success rates therefore emerge alongside initial link quality as a primary design constraint for scalable quantum networks.
Choosing a variational quantum circuit (VQC) usually means searching over ansatze and depths, and training each candidate. We give three rules that fix these choices from the data and the gate set alone, before any training. First, a circuit without entangling gates has a rank-one Fourier coefficient tensor on every subset of qubits. A singular value decomposition of a dataset's Fourier coefficients therefore indicates whether entanglement is needed, which qubits it connects, and a lower bound on the error of omitting it. Second, the rank of the quantum Fisher information matrix grows by $p_0$ per layer, after a first-layer deficit $d_0$, until it reaches a ceiling set by the dynamical Lie algebra. This law fixes the depth. Third, reading out all $2^N - 1$ Pauli-Z products from one batch of shots resolves half of the state's directions, the most any single-basis readout can. A single-qubit readout resolves an exponentially small fraction. For the Madelon dataset, the rules prescribe 7 blocks of 3 qubits at depth 3: a 239-parameter classifier with 78.5% test accuracy, found without a grid search. Ablations confirm three predicted effects: shallower circuits, smaller blocks and dropping reuploading all lower accuracy.
We discuss the relationship between quantum Hamiltonian embeddings (arXiv:2610.26833) and prior developments in Quantum Cognition Machine Learning (QCML), including QCML's earlier implementation on IBM quantum hardware. We consider the novelty claims and the computational role of encoding an entire dataset in a single ground state.
We prove a quantum analogue of the classical moment matching method, a popular framework used to prove lower bounds in property testing. For two random variables $X_0$ and $X_1$ whose moments match up to the first $r-1$ moments, the classical moment matching method says that no classical algorithm can reliably distinguish between input instances of length $N$ constructed from $X_0$ and $X_1$, respectively, unless it performs at least $\Omega(N^{1-1/r})$ queries. While this method has been widely explored since its inception in the seminal work of Raskhodnikova, Ron, Shpilka, and Smith (STOC 2007) to prove lower bounds for symmetric properties, it has remained an open question whether a quantum analogue of it could be proved. We prove two variants of this quantum moment matching method, which are incomparable. Our first quantum query lower bound scales as $\Omega(N^{1/2-1/(2r)})$, while our second moment matching theorem yields a sharper lower bound of $\Omega(N^{1/2-1/(2(2^r-1))})$, albeit for smaller parameter ranges. Our results combine a new continuous hybrid argument with the polynomial method. The continuous hybrid argument compares two hard input distributions generated from i.i.d. samples by continuously varying both distributions, keeping them identically distributed at every intermediate stage. It reduces the comparison to the effect of changing the distribution of a single sample. The polynomial method then cancels the terms determined by the matched moments. We apply these moment matching theorems to prove new optimal lower bounds on $k$-distinctness, $k$-star-freeness, planarity and outerplanarity testing, as well as to improve prior lower bounds on image size testing and $K$-junta testing by logarithmic factors. A key advantage of our framework is its simplicity: it reduces quantum lower bound proofs to the construction of suitable moment-matching distributions.
Fault-tolerant quantum computers run millions of logical cycles to perform quantum error correction (QEC). As logical operations span entire logical cycles, the logical cycle time (LCT) dictates program runtime. Qubit measurements, critical to extract parity information for QEC, are the slowest operations and account for 43-86% of LCT. Measurement latencies impact fidelity: fast measurements lower our ability to correctly classify quantum states, whereas slow measurements increase the likelihood of decoherence. Hardware providers thus calibrate measurement latencies that maximize readout fidelity per qubit and use them to schedule all measurements during program execution. However, calibrated latencies are sub-optimal for logical performance because logical cycles span multiple QEC rounds, during which data qubits are not measured. This increases LCT and logical error rates (LERs) due to decoherence at the logical level. We propose DynaMite, a lightweight real-time measurement latency selection policy built on two key insights. First, logical cycles must use a measurement latency that is fast enough to reduce both LCT and LER for the QEC code, instead of the calibrated latency that only maximizes readout fidelity. Second, not all logical cycles are equal; many do not fully utilize the error budget of the QEC code, i.e., the number of failed parity checks it can tolerate without compromising LER. These cycles could use even faster measurements but do not, because latencies are chosen statically, whereas error information is only available at runtime. DynaMite exploits the fact that a logical cycle comprises multiple QEC rounds and selects the fastest latency for an upcoming round based on the error budget left and rounds remaining. Our evaluations show that DynaMite reduces LCT by 1.69x on average and up to 2.29x, and reduces LER to 0.46x on average and up to 0.13x of baseline.
Every realistic quantum system is coupled to an environment. Including the environment restores a closed, Hermitian description, but at the cost of an intractably large Hilbert space. The Feshbach--L\"owdin projection eliminates the unwanted degrees of freedom exactly, yielding an effective Hamiltonian $H_{\rm eff}$ on the relevant subspace alone---which \new{generically becomes non-Hermitian when the eliminated subspace contains an energetically accessible continuum and outgoing boundary conditions are imposed}. We illustrate this through a minimal model: a particle in a box with a delta barrier at its center. Direct elimination of one half-well reduces all information about the discarded sector to a single \new{boundary parameter} $\beta$; the same result is then rederived via the Green's function and Dyson equation, offering a pedagogical illustration of how boundary data enter the Green's-function formalism and relating $\beta$ to a self-energy term. Whether $\beta$ is real or complex determines whether $H_{\rm eff}$ is Hermitian or not, and the full range of behavior---from Hermitian dynamics through finite-width resonances to the counterintuitive quantum Zeno effect---follows from this single parameter.
The complete statistical characterization of defects generated in a quantum phase transition has mostly been studied in exactly solvable models, and remains little explored in nonintegrable systems such as long-range interacting spin chains. We characterize the full defect counting statistics in a nonintegrable long-range spin chain, the fractional Ising model, by time-dependent variational-principle simulations within the matrix-product-state and matrix-product-operator formalism. Fractional interactions capture emergent multiscale correlations and long-range effects in nature, governed by the order of the underlying fractional derivative. Such couplings can be approximated on existing quantum simulation platforms, where the full defect statistics can be measured. The defect number cumulants follow power laws in the driving time, with exponents that vary continuously with the fractional order. At low fractional order, deep in the long-range regime, the mean defect number decays more slowly than predicted by the Kibble-Zurek mechanism (KZM), while at intermediate order the KZM holds with the numerically extracted many-body critical exponents. At large fractional order, the exactly solvable free-fermion limit of the model becomes progressively more accurate towards the short-range limit. We derive exact bounds on the kink-number cumulants and on the kink-kink correlations, implying an exact Gaussian limiting distribution for large system sizes. In the many-body simulations, however, kinks are more correlated, consistent with the confinement of domain walls, and these bounds are violated in the long-range regime, also in the bulk of the chain. Nevertheless, the kink distribution still approaches a Gaussian for large defect numbers, with proportionality partially broken between the cumulants.
We consider the complexity implications of proofs of quantumness and (quantum verifier) oblivious state preparation. We show that both of these objects can coexist with the easiness of nondeterministic computation. That is, we give evidence that proofs of quantumness can exist when $\mathsf{P} = \mathsf{NP}$ and that (quantum verifier) oblivious state preparation can exist when $\mathsf{BQP} = \mathsf{QCMA}$. In particular, we give a classical oracle relative to which (1) $\mathsf{P}^\mathcal{O} = \mathsf{NP}^\mathcal{O}$ (2) $\mathsf{BQP}^\mathcal{O} = \mathsf{PSPACE}^\mathcal{O}$ (3) Proofs of quantumness exist. In particular, there exists a language in $\mathsf{IP}^\mathcal{O} \subseteq \mathsf{BQP}^\mathcal{O}$ which is hard on average against $\mathsf{P}^\mathcal{O}/poly$. We give a unitary oracle such that (1) $\mathsf{BQP}^\mathcal{O} = \mathsf{QCMA}^\mathcal{O}$ (2) Quantum verifier oblivious state preparation exists. These oracle separations directly imply a number of related consequences. For example, our first result implies that proofs of quantumness cannot be used to construct classical or quantum cryptography with a relativizing proof. Our second result implies that quantum computation/classical communication oblivious transfer cannot be used to construct post-quantum one-way functions with a relativizing proof.
For deterministic state verification by separable measurements, the Schmidt rank of an entangled resource must be at least that of the state being verified [N. Yu, R. Duan, and M. Ying, IEEE Trans. Inf. Theory 60, 2069 (2014)], and if the two are equal, the resource must be maximally entangled [S. Akibue, J. Miyazaki, and H. Osaka, Lett. Math. Phys. 116, 110 (2026)]. The latter was derived from a general theorem proved using algebraic geometry. In this paper, we give a simple, self-contained proof of both statements using only linear algebra. We then use these results to show that among pure entangled resources of local dimension at most $d$, a maximally entangled state of $\mathbb{C}^d\otimes\mathbb{C}^d$ is necessary and sufficient for perfect local discrimination of a generic orthogonal basis of $\mathbb{C}^d\otimes\mathbb{C}^d$, however weakly entangled. The same holds for local implementation of a generic orthogonal measurement.
We propose a physical generative model for learning correlated multivariate data based on homodyne detection of photonic continuous-variable (CV) circuits. We use an $N$-mode photonic circuit in which two-mode squeezing provides correlations, local phase shifts tune the strength and sign of these correlations, and an adjustable interferometer redistributes them across modes. We train the circuit by matching its Pearson correlation matrix to the one obtained from data. We apply affine post-processing to adjust the marginals independently while keeping the relations intact. We test the model on the multivariate distribution of standardized log returns of financial assets, showing that the photonic model can represent rich correlation structures. We reproduce empirical correlations with residuals below $10^{-4}$ for five variables and recover the correct correlation signs for $94\% \pm 1\%$ of 190 correlation pairs at twenty variables, with $86\%$ of the residuals below $0.1$. As a separate technical contribution, we develop an approach for simulating Kerr gates with small nonlinearity via a Hubbard-Stratonovich expansion, making them suitable for CV-based simulators. Our results establish CV photonic circuits as a platform for interpretable generative learning, suitable for representing and fast sampling of distributions across different application domains.
When a language model answers, we can usually only estimate why. We build a transformer in which every step is a Born measurement - attention $|\langle q|k\rangle|^4$ normalised over each row, a measured product in place of the feed-forward nonlinearity, and a Born readout. With its denominators held at their values for the input, each class probability is a polynomial in the word amplitudes, so its integrated-gradient evidence is computed by a finite quadrature with no quadrature error: the words' contributions sum to the class probability above its no-information share, to $10^{-11}$ or better. On e-SNLI natural language inference, with about 98k parameters outside the embedding, the model reaches $76.98 \pm 0.17$% test accuracy, level with a softmax transformer of the same size ($76.62 \pm 0.36$%). Deleting the word its evidence ranks first changes the answer in 45% of test pairs, out of the 53% any single deletion can change, against 32% for the softmax model explained the same way and 40% by its attention x gradient. Attention can look more like the words annotators highlighted, yet accounts for the answer less well: deleting the word it ranks first changes the Born Transformer's answer in 32% of pairs. The same weights compile exactly to optoelectronic optics and to qubits, and a coherent attention layer becomes one circuit equal to the model (852 CNOTs on 23 qubits). On IBM's ibm_kingston, reading only the attention overlaps by Hadamard tests, the device gave the model's answers on two short test pairs and kept or changed them under deletion as the model does; the evidence itself did not yet survive the device, and we work out the shots and calibration that measuring it on hardware would need.
In the graph collision problem, the task is to decide whether a known graph on $n$ vertices contains an edge with both endpoints marked, given query access to the input bits specifying the marked vertices. We first refute the conjectured $\Omega(n^{2/3})$ query lower bound with a bounded error quantum algorithm using $\widetilde O(n^{92/139})$ queries. We then refine this approach to obtain a $\widetilde O(n^{11/17})$ query algorithm. We also obtain a $\widetilde O((nq)^{11/17})$ query bound for all (partial) Boolean output functions with positive certificate complexity at most 2 and alphabet size $q$, contrasting a known $\Omega(n^{2/3})$ lower bound for such problems with large alphabet sizes. We complement these algorithms with an $\Omega(\sqrt{n\log n})$ quantum query lower bound for graph collision, exceeding the $O(\sqrt n)$ certificate complexity barrier for the positive adversary method.
The Pointwise Dimension is a diagnostic that reveals the effective dimensionality of classical trajectories in a $2N$-dimensional phase space. The essence of this diagnostic is to find a scaling according to which density changes with radius $r$ around a point of interest in phase space. Particularly, regular trajectories are confined to an $N$-dimensional invariant torus, while chaotic trajectories explore a $(2N-1)$-dimensional energy surface. In classical mechanics, this trajectory density can be found by counting recurrences to within the sphere of radius $r$. In quantum mechanics, probability density is intrinsic, making the Pointwise Dimension compelling, but surprisingly this has not been studied in the quantum regime. In this work, we implement the Pointwise Dimension in the quantum regime using the Husimi representation of the quantum wavepacket. This implementation entails a long-time average of the time-dependent Husimi representation to obtain a stationary phase space density, and a radial spatial integration of this density over a sphere of radius $r$. The classical-quantum correspondence is excellent for both autonomous and non-autonomous systems, adding a new diagnostic to the study of quantum chaos. Finally, we explore the possibility, both classically and quantum mechanically, of obtaining the Pointwise Dimension from a time correlation function.
An important physical quantity that is part of the Saha ionisation equation is the partition function of the neutral hydrogen atoms. An immense uncertainty is caused by the divergency of the neutral atom partition function arising due to the fast growing degeneracy factor of its excited n-state. We suggested a regularisation and renormalisation procedure for the partition function of the neutral hydrogen atoms. The renormalised partition function is well defined and allows to calculate the population of the energy levels and the ionisation state of the hydrogen plasma as a function of its temperature and pressure. In the low-temperature limit the behaviour of these functions smoothly transforms to the Saha equation, which is used in the description of the low-temperature plasma. At higher temperatures the renormalised ionisation equation describes the deviation from the Saha equation. The application of the renormalised ionisation equation to the solar core and atmosphere is considered.
Recently, we found a method to reconstruct the dilatation operator (sphere Hamiltonian) from a regulated conformal field theory groundstate. In this paper, we explore methods to construct the whole global conformal algebra, and test our construction using fuzzy sphere regularization. Starting from a groundstate of the same Hamiltonian, these methods perform better than constructions of the conformal generators based on a Hamiltonian density, are model-independent, require no additional tuning, and improve with system size. One purpose of reconstructing the conformal algebra is to identify conformal primary states, which we do with some success. We also find further evidence supporting the model of the short-distance corrections to the entanglement Hamiltonian proposed earlier and use it to make systematic improvements.
We present a preconditioning pipeline that accelerates Tensor Train (TT) linear solvers for symmetric positive-definite problems. Extending the Factorized Sparse Approximate Inverse framework to tensor networks, we construct a preconditioner as the product of a TT operator and its transpose. This formulation is positive semidefinite for any bond dimension and truncation, and definite whenever the factor is non-singular, satisfying the mathematical requirements of the Conjugate Gradient method. We detail the construction of this preconditioner and its integration into Density Matrix Renormalization Group (DMRG)-like linear solvers. Performance evaluations show consistent iteration reductions for anisotropic diffusion and Poisson problems across various configurations, leading to net speedups of up to 25% in ill-conditioned settings of time stepping schemes that can reuse the approximate inverses. These benchmarks were performed with the open-source Julia library DifferenTT.jl, which we also introduce in this work to provide out-of-the-box access to these preconditioned pipelines.
The Kramers theorem generally guarantees the spectral degeneracy of time-reversal-invariant Hamiltonian operators with half-integer spin, underlying a variety of physical phenomena. Despite its fundamental significance, the Kramers degeneracy has been argued to be absent in Liouvillian superoperators acting on mixed states because of the double structure of the Hilbert space. Here, we instead demonstrate that the interplay of time-reversal symmetry$^{\dag}$ and parity symmetry enforces the Kramers degeneracy in Liouvillians. We explicitly construct dissipative many-body models of interacting fermions and spins exhibiting the Kramers degeneracy and show that their complex spectral statistics follow those of non-Hermitian random matrices in the corresponding symplectic symmetry classes. Of the three fundamental universality classes of non-Hermitian random matrices, the symplectic class has never been realized in symmetry-resolved many-body Liouvillians. Our constructions provide its explicit realizations and spectral signatures of nonintegrability in symplectic open quantum systems.
None of the $S$-matrix representations used in analyses of nucleon-nucleon ($NN$) scattering above the inelastic threshold is implicitly unitary, general, and connected to low-energy (Stapp) parameters, and hence correspondingly related to the physical properties of the scattering. Such a representation is also needed to solve the corresponding inverse scattering problem. I present an $S$-matrix representation which satisfies these requirements. As a by-product, I derive a parametrization of an $n$-dimensional unitary matrix.
We propose a scheme to realize Weyl superfluidity from topologically trivial bands in the strongly correlated regime of a three-dimensional optical Raman lattice. The scheme builds on a pairing mechanism arising from the interplay between a large Zeeman splitting and strong Hubbard interaction. Spin-flip hopping suppressed by the large Zeeman detuning is resonantly restored when the attractive Hubbard interaction compensates the energy mismatch, yielding a correlated spin-orbit coupling that depends on the local particle configuration. Combining this density-dependent in-plane spin-orbit coupling with density-dependent spin-conserving interlayer tunneling extends the pairing mechanism to three dimensions. A self-consistent mean-field treatment of the microscopic model yields Weyl superfluids with two, four, or eight nodes, together with fully gapped weak topological superfluids. Tuning the interaction strength and particle filling drives transitions between these phases and controls the number of Weyl nodes. We further propose an experimental implementation with ultracold $^{40}\mathrm{K}$ atoms. Our results highlight density-assisted spin-orbit coupling as a mechanism for realizing Weyl superfluidity in strongly correlated systems.
Quantum low-density parity-check (QLDPC) codes are promising for fault-tolerant quantum computing, but their decoding algorithms present significant hardware implementation challenges. Reinforcement-learned sequential belief propagation (RL-S) improves the error-correction performance of conventional belief propagation (BP) through adaptive variable-node scheduling. However, its heap-based priority management introduces substantial hardware overhead. This paper presents hardware implementations of BP, RL-S, and bucket-based reinforcement-learned BP (BRL-S) for the [[288,12,18]] bivariate bicycle QLDPC code. The BRL-S architectures employ quantized priorities and first-in, first-out (FIFO) buckets to simplify scheduling. Three configurations with two, four, and eight priority levels are evaluated. FPGA synthesis results demonstrate that BRL-S reduces lookup-table utilization by approximately 68--72% compared with RL-S. ASIC synthesis further shows reductions of 63--67% in area and 64--69% in estimated power consumption. These results demonstrate that bucket-based scheduling substantially improves the hardware efficiency of reinforcement-learned QLDPC decoders.
A three-region junction in a free real relativistic scalar vacuum in $2+1$ dimensions yields a strictly negative logarithmic contribution to genuine tripartite R\'enyi multi-entropy for every integer $n\geq3$ and all nondegenerate sector angles. The replica subtraction exactly removes loop classes associated with a single interface. Surviving loops have positive, scale-independent weight, yielding a logarithm whose sign is fixed by the negative R\'enyi prefactor. The selector is empty at $n=2$. The flat-sheet Friedrichs prescription fixes the scalar operator at the nonmanifold replica apex. It yields a convergent angular spectral formula for the coefficient.
Strong coupling between collective excitations provides a route to controlling quantum states of matter, yet its evolution under thermal fluctuations remains poorly understood. In the van der Waals antiferromagnet FePS3, strong magnon-phonon coupling is established at low temperatures. At the same time, recent terahertz experiments revealed the counterintuitive stabilization of a long-lived metastable magnetic state with an exceedingly long lifetime of 5 msec at the antiferromagnetic transition, not at the base temperature. This was attributed to a strongly coupled spin-lattice scenario, challenging the conventional wisdom that increased magnetic and thermal fluctuations near TN should be detrimental to the coherent control of a metastable phase. Thus it requires an independent examination for correct understanding. Using high-field Raman spectroscopy, we systematically investigate the temperature evolution of magnon-phonon coupling in FePS3. We observe a pronounced avoided crossing between magnon and phonon modes across a wide range of temperatures and find that the coupling strength remains remarkably robust with increasing temperatures. The zero-field magnon-phonon detuning decreases progressively with warming, driving the system toward resonance and thereby enhancing their hybridization near the transition temperature. This anomalous thermal evolution provides the crucial key to understanding the unusual terahertz-driven states recently reported in FePS3. More broadly, our results highlight van der Waals magnets as a promising platform for strong coupling among collective excitations and for controlling magnetic states through light-matter interactions.
The standard definition of entanglement entropy in quantum field theory requires regularizing the entangling surface and factorizing the Hilbert space, which in turn involves a choice of boundary conditions at the regularized surface. This raises two natural questions which are open at present. The first is under what conditions there is a choice of boundary conditions that leads to a unitary map between the original Hilbert space and the factorized one, which is a necessary condition for a well-defined entanglement entropy. The second concerns the situation where there are multiple such choices, in which case the question is whether they all yield the same entropy, or at least the same terms usually referred to as universal. Focusing on topological theories and using three-dimensional Chern-Simons theory as a concrete illustration, we show under specified assumptions that different such choices affect only the non-universal terms in the entropy, such that the remaining terms are universal in this sense as well, while we explicitly demonstrate that boundary conditions corresponding to non-unitary maps can change these terms. We then explain how a similar argument applies to two-dimensional conformal field theories and discuss a condition for universality in general theories.
Atomic arrays provide a cooperative platform for light-mediated interactions in nonlocal metasurfaces which can operate in the quantum regime without nanofabricated optical elements or intrinsic material absorption. We present a minimal atomic implementation to harness wavefront engineering and create a near-ideal intrinsic atomic Huygens' surface. A simple bilayer square lattice with a two-atom unit cell, not limited to small lattice spacings, provides near-unity reflectionless transmission and a full $2\pi$ phase control of transmitted light without the localized site-dependent level shifts of previous proposals. This simplification is achieved through nonlocal radiative excitations that provide the familiar electric-dipole response with even radiation parity as well as an odd-parity radiation channel whose leading multipolar interpretation combines magnetic-dipole and electric-quadrupole contributions in atoms exhibiting only electric dipole transitions. This eliminates the need to simultaneously excite pure electric-dipole and magnetic-dipole responses with exactly matched radiation. We derive a two-mode model for this response and show that it accurately captures full coupled-dipole simulations near the optimal lattice spacings. Because of the wide applicability of coupled-dipole models, the relevance of our microscopic analysis extends beyond atomic physics to nanostructured metasurfaces. Moreover, the same platform also connects directly to established subradiance-protected single-photon storage protocols, suggesting a route toward combining wavefront engineering, storage, and retrieval in a simple atomic bilayer.
We revisit the classical spectral problem for the Laplace-Beltrami and Laplace-Bochner operators on complex Grassmannians. After reviewing the standard approach based on non-commutative harmonic analysis, we develop two complementary methods originating from the quantization of the corresponding one-dimensional sigma model, both with and without a magnetic monopole field. The first is based on $\mathbf{SU}(n)$-equivariant first-order GLSM formulation and gives explicit eigenfunctions in terms of projectors and Pl\"ucker coordinates. The second uses a spin-chain realization of free particles on manifolds and describes the space of square-integrable functions, or sections in the magnetic case, through limiting tensor products of long rectangular $\mathbf{SU}(n)$ representations. Together, these approaches provide a more explicit picture of the spectral geometry of Grassmannians and clarify the relation between harmonics, Young diagrams, magnetic bundles, and Laplacian spectra.
Strongly correlated matter without quasiparticles is central to many-body physics, quantum chaos, and quantum gravity, motivating a considerable effort toward its realization in tabletop experiments. Two challenges remain: laboratory platforms are open systems, so conformal behavior must survive dissipation, and it must be identified through measurable quantities. We address both challenges in the Yukawa-Sachdev-Ye-Kitaev (YSYK) model, in which bosons and fermions interact as in, e.g., light-matter systems, but through random all-to-all couplings that drive the boson to criticality without fine tuning. Solving the model in real time using the Schwinger-Keldysh formalism, we treat closed and open systems within a unified framework and, in both cases, consider a thermal steady state to map their phase diagrams. In addition to the known conformal and impurity (or SYK$_2$) regimes, we identify novel high-temperature regimes in which the fermions are driven by an essentially bare boson and show that their dynamics is captured by a quadratic model with time-dependent random hopping. Across all regimes, the fermionic softening of the boson is bounded by a ``criticality budget'' determined only by the Yukawa coupling and the temperature. Coupling the boson with a thermal environment induces a mass shift that deforms the boundaries between different regimes and exhausts the criticality budget, thus imposing a bound on temperature and dissipation rate compatible with self-tuned criticality. We further introduce a set of markers built from the two-point functions that separate all identified regimes, are accessible in linear response, and require no fit of the conformal exponents. We complement them with the quantum Fisher information, deriving upper bounds with and without dissipation. These results may help characterize holographic quantum matter beyond the closed setting.
Magnetic field detection is of great significance in modern fields such as medical diagnostics, geological exploration, inertial navigation, and space physics. We have previously investigated the expansion dynamics of a spin-orbit-coupled Bose-Einstein condensate. Building on these results, here we propose a scheme for magnetic-field-gradient detection by establishing a quantitative relationship between the condensate's rotational deflection angle and the magnetic-field gradient. In this work, we present the parameter dependence of this scheme and perform a systematic optimization. We introduce a Bayesian optimization algorithm to automatically and efficiently search for the optimal combination of key parameters, thereby significantly enhancing the sensitivity of the magnetic field gradient measurement. The results show that the optimized gradiometer improves the sensitivity by a factor of five. This work not only provides a new approach for magnetic field gradient measurement but also serves as a reference for machine learning-empowered quantum precision measurement.
Topological insulators can host chiral, disorder-robust edge states that dissipate energy when coupled to an external bath. We show that nonlinear interactions enable all-optical control over edge-state dissipation in a laser-written Floquet topological insulator periodically coupled to a photonic bath. Although moderate nonlinearity enhances dissipation due to mode mixing, increasing the nonlinear strength to an optimal value dramatically suppresses dissipation by forming highly localized traveling edge solitons. These results establish engineered system-bath coupling and nonlinear interactions as a route to suppress dissipation of chiral topological edge transport.
This work investigates the application of Quantum Recurrent Neural Networks to the binary classification of sleep-disordered breathing events in time-series data, aiming to distinguish between apneic and normal breathing episodes. A variational classical--quantum architecture is proposed and evaluated against classical Recurrent Neural Network models. Experiments were conducted on multiple real-world datasets with varying levels of complexity to assess the strengths and limitations of the quantum approach. In the comparative analysis, both classical and quantum models showed comparable performance. The quantum model achieved superior performance on the smallest dataset, while yielding slightly weaker results in the most complex setting. However, the quantum approach exhibited notable strengths, such as competitive performance despite a drastically reduced parameter count and low-qubit regime, as well as good generalization capabilities. These results suggest that, despite current hardware and algorithmic limitations, variational quantum recurrent models represent a promising alternative for time-series classification as Quantum Computing technologies continue to mature.
In two dimensions, the kinetic and contact energies scale identically under dilation, a trap $V=r^s/s$ as $\lambda^{-s}$. We follow this balance through the power-law family $-2\le s\le4$, $s\neq0$, for both signs of the coupling $g$, with rotation, using scaling bounds, radial solutions, Bogoliubov spectra, and two-dimensional imaginary-time states. Attraction collapses the cloud at the Townes coupling $g_{*}$ in every trap, with width $\ell\propto\delta^{1/(s+2)}$, $\delta=1-|g|/g_{*}$; repulsion spreads it to a Thomas--Fermi (TF) radius $\propto g^{1/(s+2)}$. A rotating collapse leaves the axis once the rotation frequency $\Omega$ exceeds its dipole frequency, which softens only for $s>2$; in a quartic trap this happens at $\delta\simeq0.32\,\Omega^6$, within $3\%$ of the Bogoliubov threshold; it then collapses on the minimum ring of the rotating-frame potential, which also empties a repulsive TF cloud at $\Omega=(3g/\pi)^{1/6}$. For repulsive vortex states the TF energy error splits exactly into a density-gradient and a flow part of comparable or larger size. At $s=-2$ only the cutoff sets a length: the energy is exactly covariant with it, the condensate falls to the center for both signs, and repulsion leaves a halo of density $\propto1/(gr^2)$ whose extent grows exponentially with $g$. Near collapse, split-step imaginary time has a first-order stationary bias invisible to residual tests.
Nanostructured semiconductors provide an actively tunable platform for light-matter interactions across a broad spectral range. As feature sizes shrink to the deep nanoscale (~10 nm scale), nonclassical carrier dynamics and surface plasmonic responses become prominent, creating substantial challenges for a rigorous and efficient theoretical treatment. Here we develop a generalized Lorentz framework for quantum surface plasmonics in nanostructured semiconductors with arbitrary energymomentum dispersion relations. The framework enables efficient quantitative treatment of carrier nonlocality, carrier surface accumulation and depletion, and nonlocal damping in three-dimensional semiconductor nanostructures, under electrical tuning and across a wide range of doping densities. Building on this framework, we further establish a rigorous quasinormal-mode analysis that provides transparent physical insight into complex surface plasmonic responses of multiscale semiconductor structures. We demonstrate electrically controlled deep-nanoscale carrier accumulation and depletion in a semiconductor nanoantenna, leading to pronounced plasmonic-response modulation that can be interpreted in terms of eigenmode shifts, creation, and annihilation. By quantifying and linking complex nonclassical carrier dynamics with plasmonic eigenmodes, our work establishes a comprehensive quantitative framework for active semiconductor quantum surface plasmonics and will foster the convergence of electronics and photonics at the deep nanoscale.
Simulating quantum many-body systems classically encounters exponential bottlenecks, which quantum devices circumvent by natively encoding wavefunctions. In the Noisy Intermediate-Scale Quantum (NISQ) era, however, hardware noise constrains simulation accuracy. As a stepping stone toward strongly correlated materials, we compute the band structure of 2D monolayer graphene and 1D nanoribbons (zigzag and armchair) using a single variational workflow in the $p_z$ tight-binding approximation. Non-interacting ground states also provide essential initial reference states for subspace and warm-started variational methods to solve interacting spectra. By mapping the Bloch Hamiltonian to Pauli operators, we extract the ground band via the Variational Quantum Eigensolver (VQE) and excited subbands via Variational Quantum Deflation (VQD), validating our approach from ideal simulations to execution on physical IBM Quantum processors. In ideal simulations, the workflow reproduces exact diagonalization results with high precision, whereas hardware noise introduces energy deviations of a few hundredths of the hopping parameter. While qubit counts scale logarithmically with ribbon width, fixed-depth ansatz accuracy degrades with Hilbert space dimension. Crucially, deepening the ansatz improves ideal simulation accuracy by over three orders of magnitude but worsens energy estimates under noise, proving that practical circuit depth is bounded by hardware noise rather than expressivity. Finally, we complement energy evaluations with a wavefunction-level diagnostic measuring subspace containment. This diagnostic captures degenerate manifolds and exposes optimization failure modes disguised by energy agreement alone. Operating directly on NISQ hardware, this validated workflow establishes a controlled baseline for studying topological and strongly correlated phases in realistic materials.
Ultracold polar molecules present a rich platform for experimental quantum science leveraging their unique properties. Of particular relevance is the intrinsic electric dipole moment of the molecule, which results in strong coupling to microwave fields and can be used to engineer long-range, anisotropic, and tunable dipole-dipole interactions. Such interactions can generate entanglement between molecules and enable the study of novel quantum many-body phenomena in parameter regimes inaccessible in other systems. Modern experiments in optical tweezers and optical lattices have demonstrated controlled interactions between molecules in coherent quantum states, and recently bulk gases of molecules have been cooled to quantum degeneracy. Motivated by these landmark advances, we present this article to explain many of the key concepts relevant to current research in the field.
Quantum impurity calculations become challenging when multiple correlated orbitals are treated explicitly, particularly in nonequilibrium steady states. We introduce Coupled-Cluster Coupled Lindblad (C$^3$L), a deterministic approach that combines the recently developed coupled-Lindblad compact bath representation with coupled-cluster theory to compute steady states and Green's functions directly in imaginary and real frequency. C$^3$L has favorable polynomial computational complexity and avoids the sign problem of quantum Monte Carlo (QMC). In a real-time multiorbital benchmark, it agrees closely with state-of-the-art QMC while reducing computational cost by four to five orders of magnitude, with a further 10--100-fold speedup on a GPU. Beyond the practical reach of established real-time QMC solvers, four-orbital nonequilibrium impurities with general interactions and biased reservoirs become accessible with C$^3$L. We obtain resonance-resolved transport signatures relevant to scanning tunneling microscopy experiments on molecular junctions.
We investigate quantum error correction protocols for topological codes deformed away from their stabilizer limits, particularly as they are pushed towards quantum phase transitions into trivial phases. Our focus is primarily on quantum information stored within the ground-state manifold of the transverse-field toric code (TFTC), subjected to independent bit-flip and phase-flip decoherence. Although the transverse field induces strong quantum fluctuations of $m$ anyons in the ground states, we show that projective measurements of the "bare" toric code stabilizers can nevertheless be used to construct an efficient decoding algorithm which exhibits a finite threshold to both types of decoherence, even when the transverse field is tuned infinitesimally close to the quantum critical point. Our construction of the optimal postmeasurement decoders---that is, the optimal decoders assuming that the stabilizers are first measured---crucially relies on the stoquastic nature of the TFTC Hamiltonian, which affords a description of its ground states in terms of a classical lattice gauge theory. Using stoquasticity, we first prove that stabilizer measurements act unitarily on the undecohered TFTC ground states to excellent approximation, and that the optimal postmeasurement decoder can be efficiently implemented via Monte Carlo simulation of a constrained lattice gauge theory. We then construct the optimal postmeasurement decoder for the TFTC states under bit-flip and phase-flip decoherence, where we numerically demonstrate a finite threshold close to the quantum critical point. We provide theoretical evidence (without a rigorous proof) that stabilizer measurements constitute an optimal decoding strategy in this setting. For phase-flip decoherence, we further prove that the optimal postmeasurement decoding threshold is independent of the transverse field strength throughout the topological phase.