Papers

A third order expansion for Wigner-Kirkwood commutation function, a complex function in classical phase space that accounts for the Heisenberg uncertainty relation, is approximated and integrated over momentum to give a real function in position configuration space. Metropolis Monte Carlo computer simulation results are given for liquid Lennard-Jones $^4$He below 10\,K.

Although the $k$-mode marginal distributions of Canonical Boson Sampling (CBS) are known to be computable in polynomial time, the physical mechanism driving this computational efficiency remains mathematically opaque. In this work, we provide a direct, bottom-up physical derivation of the exact 1-mode marginal distribution in CBS, computable in $\mathcal{O}(R^2)$ time, where $R$ is the total number of photons. We explicitly bridge this physical derivation with the mathematical theory of rank-1 matrix permanents, proving that multiphoton interference natively reduces to a symmetric polynomial scaled by a factorial bosonic bunching factor. Crucially, we demonstrate that our recursive combinatorial formulation circumvents the algorithmic overhead of characteristic function methods, entirely bypassing the need for polynomial interpolation or Fourier transforms. Finally, we apply this formula to identify macroscopic signatures of bunching, providing a rigorous, highly scalable metric for distinguishing genuine quantum interference from classical distinguishable-particle models using standard threshold detectors.

High-dimensional quantum systems offer a new playground for quantum information applications due to their remarkable advantages such as higher capacity and noise resistance. We propose potentially practical schemes for remotely preparing four- and eight-level equatorial states in complex Hilbert spaces exactly by identifying a set of orthogonal measurement bases. In these minimal-resource-consuming schemes, both pre-shared maximally and non-maximally entangled states are taken into account. The three-, five-, six-, and seven-level equatorial states in complex Hilbert spaces can also be obtained by adjusting the parameters of the desired states. The evaluations indicate that our high-dimensional RSP schemes might be possible with current technology. The collection operations, necessary for our high-dimensional RSP schemes via partially entangled channels, can be avoided by encoding the computational basis in the spatial modes of single-photon systems.

Preparation of nonclassical light with special quantum properties is essential for quantum technologies. High-harmonic generation (HHG) is a process which not only enables the creation of attosecond pulses but also has the potential to generate light with intricate quantum properties. In a recent experiment [PRX Quantum 5. 040319], nonclassical inter-harmonic correlations have been measured from a HHG source between low-order harmonics. In this work, we theoretically investigate entanglement between different harmonics within an effective, phenomenological quantum optical model. This model implements a significant degree of simplification regarding the processes within the target material, treating the material through susceptibilities, as it is usual in quantum optics. Such an approach yields a general description of HHG in the few-harmonic generation regime, permitting the implications that can be derived within it to hold broadly within the domain of validity. We find that entanglement is produced as a result of the often neglected back-action. We can qualitatively reproduce experimentally measured nonclassicalities, which suggests that intermodal entanglement can, to an extent, be considered a universal phenomenon associated with HHG, rather than a result of using specific material targets.

We study the prepare-and-measure scenario in which Alice transmits a quantum system to Bob, who then performs a quantum measurement. The quantum state of the system is unknown to Bob, and the measurement is unknown to Alice. It has recently been shown that shared randomness and two bits of classical communication are necessary and sufficient to simulate the transmission of a qubit. We show that the communication cost can be reduced to an average of $1.89$ bits. We then study restricted sets of state preparations: First, for a restriction to real-valued qubit states, if the communication of a classical trit is sufficient, we show that the corresponding protocol must have a convoluted form. We then reduce the smallest qubit scenario requiring two bits of classical communication to only $6$ state preparations and $5$ measurements. For a qutrit, it is not known whether the communication cost is finite; we identify a scenario that requires at least $5$ classical messages, already for the simulation of the real qutrit. Finally, we develop a method for restricted sets of states, that allows us to lower bound the classical communication cost based solely on the set of quantum states.

We show that a simple qubit-regularized $\mathrm{SU}(3)$ lattice gauge theory on a plaquette chain admits a continuum limit with massive gauge-invariant excitations, providing a minimal toy model of strong interactions without quarks. By mapping the plaquette-chain Hamiltonian to the three-state quantum clock model in a magnetic field, we demonstrate that the theory can be tuned to a continuum limit governed at short distances by the $\mathbb{Z}_3$ parafermion conformal field theory, which serves as the ultraviolet fixed point. A small relevant magnetic perturbation then drives the system to a massive continuum quantum field theory in the infrared, featuring relativistic particles. In this continuum theory we compute two universal ratios: the mass ratio of the lightest massive particles with opposite charge conjugation, $m^{-}/m^{+} = 1.459(2)$, and $\sqrt{\sigma}/m^{+} = 0.2648(2)$, where $\sigma$ denotes the string tension between a static quark and antiquark.

Quantum networks are envisioned to enable reliable distribution and manipulation of quantum information across distances, forming the foundation of a future quantum internet. The fair and efficient allocation of communication resources in such networks has been addressed through the quantum network utility maximization (QNUM) framework, which optimizes network utility under the assumption of predetermined routes for competing user demands. In this work, we relax this assumption and aim to identify optimal routes that correspond to the maximum achievable network utility. Specifically, we formulate the single-path utility-based entanglement routing problem as a Mixed-Integer Convex Program (MICP). The formulation is exact when negativity is chosen as the entanglement measure for utility quantification or the network supports sufficiently high entanglement generation rates across demands. For other entanglement measures considered, the formulation approximates the problem with over 99.99% accuracy on evaluated real-world examples. To improve computational tractability, we propose a randomized rounding-based heuristic and an upper bound via the relaxation of the MICP. Furthermore, based on min-congestion routing, we introduce an alternative randomized heuristic and upper bound. This heuristic is computationally faster, while both the heuristic and the upper bound often outperform their counterparts on considered real-world networks. Our work provides the framework for extending classical flow-based and quality of service-aware routing concepts to quantum networks.

Single photons are the flying qubits of choice for distributing entanglement in a quantum internet. Quantum memories embedded in quantum repeaters are crucial to overcome transmission loss and enhance the rate of quantum communication. A multimode memory can further boost the channel capacity. However, benchmarking and building a practical quantum memory that simultaneously optimizes multiple performance metrics poses two key challenges. Here, we introduce quantum interconnect rate to comprehensively quantify quantum memories, and further demonstrate a high-performance quantum memory that simultaneously integrates three essential criteria at once: large multimode capacity, high efficiency, and high fidelity. Operating on 11-dimensional spatial modes, our memory achieves a uniform efficiency exceeding 80% and qubit storage fidelities above 99%, enabling the efficient storage of high-dimensional qudits. Based on these capabilities, we estimate a distribution of 3.56 bits of quantum information over a 1000-km repeater link in one minute, highlighting a practical pathway toward scalable quantum interconnects and quantum networks.

We analyze the geometric phase and dynamic phase acquired by a qubit coupled to an environment through pure dephasing, establishing a direct connection between phase accumulation and ergotropy. We show that the dynamic phase depends solely on the incoherent ergotropy, reflecting its purely energetic origin. In contrast, the geometric phase exhibits a nontrivial dependence on both the coherent and incoherent contributions to the total ergotropy, encoding the interplay between coherence, dissipation, and energy extraction. By performing a perturbative expansion in the qubit-environment coupling strength, we demonstrate that, in the weak-coupling and long-time regime, the geometric phase becomes determined exclusively by the incoherent ergotropy, which coincides with the asymptotic value of the total ergotropy reached under decoherence. These results provide a clear physical distinction between dynamic and geometric phases in open quantum systems and establish geometric phases as sensitive probes of energetic resources. Furthermore,~in superconducting circuit implementations, our findings suggest that the ergotropy of a two-level system could be inferred indirectly from geometric-phase measurements using standard techniques such as quantum state tomography.

This paper studies multipartite observables formed from sums of local self-adjoint contractions on tensor product Hilbert spaces. The square of such a sum has a parity structure: after decomposing each local product into commutator and anticommutator parts, the odd parity terms cancel and only even parity contributions remain. This yields a norm bound in terms of a family of pairwise defect weights built from local commutator and anticommutator norms. These defect weights also control an information theoretic estimate. The excess of the observable expectation above the product state threshold is shown to necessarily carry a definite amount of total correlation. Under a natural $\ell^{2}$-type bound on each local family, this product state threshold becomes explicit, which leads to a fully explicit lower bound on total correlation. A simple depolarizing example illustrates the resulting decay mechanism under local noise.

The current state, emerging trends, and practical challenges of optical fiber-based power network SCADA quantum communication must be addressed to fully utilize the technological platform's potential in real-world power system SCADA communications involving massive volumes of real-time data, as well as in managing, encoding, and applications such as quantum cryptography. Quantum key distribution (QKD) is an essential part of the cybersecurity paradigm for quantum communication. Even though quantum computing with individual circuits yields probabilistic outcomes for the problem at hand, real-world datasets are complex and challenging to handle, even with telemetry. When using the cybersecurity triad of availability, confidentiality, and integrity (CIA) in reverse order (AIC), availability is given priority in electric power networks. This research assesses the use of the BB84, E91, B92, and SARG04 cryptographic protocols by applying them to large, multivariate power-system SCADA datasets and comparing the outcomes. By leveraging the variety of QKD protocols available with quantum electronics hardware, this simulation work provides a promising avenue for developing implementable frameworks and deploying SCADA/PMU networks in actual power systems.

Scientific inquiry seeks causal explanations of observed phenomena. The Bell experiment provides a paradigmatic case, revealing correlations between spatially separated systems that no local model can reproduce. Such correlations, known as Bell non-locality, are typically analyzed under the non-signaling assumption, which requires that local statistics be independent of distant measurement choices. Yet real experiments, as well as applications beyond physics, often involve signaling, raising the question of how non-locality should be characterized without this constraint. We introduce a general method for quantifying Bell non-locality in the presence of signaling, designed to relax locality as little as necessary. Our approach is guided by the question: how often can locality be preserved across repeated trials in explaining the observed correlations? The task reduces to finding the optimal convex decomposition of the observed correlations into local and genuinely non-local components. We solve this problem within the linear-programming framework, obtaining a closed-form solution valid for arbitrary correlations. We further evaluate a corresponding measure of signaling, demonstrating the generality of the method and the non-trivial character of the results. By extending the notion of non-locality beyond the non-signaling regime, our framework reshapes the basis for experimental analysis in physics and offers tools applicable outside physics.

Given the goal of maximizing CHSH violation, we compare the optimal strategies of entanglement and nonlocality distillation. In the limit of the number of copies of the shared state, entanglement distillation is guaranteed to work by generating a Bell state. For a small number of copies of the state, we show that nonlocality distillation can achieve a higher CHSH value, even though optimal entanglement distillation requires communication. Nonlocality distillation not only outperforms entanglement distillation but also demonstrates superior resource efficiency across multiple metrics for quantum resource estimation.

Multipartite device-independent quantum key distribution (DI-QKD), also known as device-independent conference key agreement, enables more than two remote parties to share a common key with information-theoretic security even without trusting the devices. So far, several multipartite DI-QKD protocols have been proposed where Greenberger-Horne-Zeilinger (GHZ) states are used as multipartite entanglement. A natural question is then whether one can construct multipartite DI-QKD with the other type of multipartite entanglement. W state is of particular interest since it is intrinsically different from GHZ state and in some cases, easier to optically implement. In this paper, we show that multipartite DI-QKD is possible with W states. To this end, we construct Bell inequalities largely violated by W states, which can be used for the multipartite DI-QKD. Furthermore, we consider several different implementation scenarios. First, we analyze the minimum required detection efficiencies to extract finite amount of keys. Then we propose a long-distance multipartite DI-QKD protocol with single-photon interference and make detailed analyses with several physical implementation scenarios. We show that the protocol enables secret key distribution over longer distances than the existing multipartite DI-QKD protocols based on GHZ states. This study provides new insight about the relationship between multipartite entanglement and device-independent quantum information processing as well as opens an alternative path toward long-distance multipartite DI-QKD.

We present a deterministic framework for preparing an arbitrary three-qubit pure state. To leverage entanglement structure in the state-preparation task, we classify three-qubit pure states into five types with respect to a $1|2$ bipartition. Given a target state specified by its amplitudes, we provide concrete criteria and concurrence-based tests that determine its type. For each type, we derive an explicit circuit template composed of elementary single-qubit rotations and CNOT gates, with gate parameters determined systematically from the Schmidt decomposition. The full construction is described step by step from the target amplitudes, with no procedural ambiguity. As an application, we further group frequently encountered three-qubit pure states in quantum information into four classes and provide an explicit circuit for each class. Compared with prior approaches, our circuits are designed for practical use: they admit a direct algorithmic instantiation, use only CNOT gates between adjacent qubits, and for certain classes achieve smaller gate counts and circuit depth.

DeepONet enables retraining-free inference across varying initial conditions or source terms at the cost of high computational requirements. This paper proposes a hybrid quantum operator network (Quantum AS-DeepOnet) suitable for solving 2D evolution equations. By combining Parameterized Quantum Circuits and cross-subnet attention methods, we can solve 2D evolution equations using only 60% of the trainable parameters while maintaining accuracy and convergence comparable to the classical DeepONet method.

Quantum error correction (QEC) promises to exponentially suppress qubit noise, but typically assumes spatially-uniform and temporally-constant noise rates. However, real quantum hardware exhibits variation in noise levels over time, which will be amplified by QEC if not addressed. To mitigate this drift in error rates, we leverage transient information readily available in surface code quantum error correction to predict logical error rates (LER) in real time. We infer a prediction model by sampling physical error rates from real hardware, and mapping detector fire rate (DFR), or parity of stabilizer measurements across QEC rounds, to LER. This allows for on-the-fly LER predictions without the typical characterization overhead required to determine LER. This method can easily be extended to other stabilizer codes. Importantly, we observe that this prediction should be accurate yet conservative (i.e. give an upper estimate) to enable appropriately fast responses to real-time physical error changes. That is, responses should be executed marginally ahead of time to allow for their execution to complete, and minimize time spent (ideally none) above intolerable error rates. More importantly, we pair this predictor with a scheme which remaps drifted logical qubits to fresh tiles in a patch-based architecture while their original tiles are recalibrated. Our results demonstrate DFR-based prediction to be an effective LER predictor, and remapping as a spatially efficient and timely mitigation response for small code distances, both of which are significant steps in furthering practical QEC.

We construct stationary coherent states concentrated on Lissajous figures of the isotropic and anisotropic harmonic oscillators, the latter having coprime frequencies, by projecting products of ordinary coherent states (one coherent state for each degree of freedom) onto sets of degenerate states. By performing these projections, we are deriving our states from sets of coherent states that are known to follow the classical motion of a two-dimensional harmonic oscillator for arbitrary frequencies. We clarify the nature of any singularities present in the phase of the wavefunction for each of the states we derive, and we establish a rigorous connection between the laminar flow of probability current and the emergence of quantum interference. Through this analysis, we are able to provide a clear and quantifiable definition for a vortex state of the two-dimensional harmonic oscillator (2DHO). In an appendix, we show that our stationary states are true coherent states as they can be used to resolve the relevant identity operators (the above mentioned projection operators) on their respective degenerate subspaces. In the special case of the isotropic oscillator, the states obtained are the SU(2) coherent states, and we derive from our formalism the familiar resolution of unity for these states.

Autonomous navigation under uncertainty requires solving partially observable Markov decision processes (POMDPs) for planning and assigning sensor measurements to tracked targets–a task known as multi-target data association (MTDA). Both problems become computationally demanding at scale: belief conditioning costs $\mathcal{O}(P(e)^{-1})$ per node under rare evidence, while MTDA is NP-hard. Quantum amplitude amplification can quadratically reduce the belief-update query cost to $\mathcal{O}(P(e)^{-1/2})$, while QUBO reformulations expose MTDA to quantum and quantum-inspired optimisation heuristics. We present QANTIS, a modular platform that integrates quantum belief update (Grover amplitude amplification and BIQAE), QUBO-based data association via FPC-QAOA, and composable error mitigation, and we report a 45-experiment hardware study on three IBM Heron backends. On hardware, a single Grover iterate applied to a Tiger belief oracle amplifies a rare observation probability from $0.179$ to $0.907$ ($5.1\times$; ISA 18) while preserving the Bayesian posterior (Hellinger $0.0015$), increasing usable-shot yield from 1,463 to 7,429. We interpret this as a hardware validation of the quadratic query-complexity mechanism at $k=1$ with posterior preservation, rather than a wall-clock advantage claim. We further demonstrate, to our knowledge, the first closed-loop hybrid quantum-classical Tiger POMDP on superconducting hardware ($T=8$, max Hellinger below $0.015$), and empirically characterise NISQ feasibility boundaries: ZNE-based error mitigation is beneficial below ISA $\approx 100$ and harmful above ISA $\gtrsim 1{,}000$; FPC-QAOA is meaningful at $\leq 15$ QUBO variables (ISA $\lesssim 450$). These results characterise practical operating regimes on current superconducting hardware rather than wall-clock quantum advantage at today's problem scales.

Collective radiance effects in quantum degenerate systems, such as superradiance and subradiance of a partially inverted ensemble, are shaped by the interplay of spatial confinement and exchange statistics. We investigate this interplay using a purely dissipative field theoretic quartic Lindblad master equation, which captures the nonlinear dynamics of the combined motional and electronic manifolds. This approach captures the interplay between the permutational symmetry of the Lindbladian and the exchange symmetry of the particles, quantifying how bosonic enhancement and Pauli blocking dictate superradiant and subradiant scaling. We identify two distinct routes to distinguishable dynamics: thermal dilution of the initial state at high temperatures and the dynamical breakdown of collective order via recoil induced transport in soft traps. This analysis provides a benchmark for collective emission in quantum-degenerate atomic systems with coupled motional and internal dynamics, such as optical lattice clocks and spinor gases, when dissipation is engineered to control recoil and motional heating.

We present COMPOSER, a compile-once modular parametric oracle for similarity-encoded effective reduction of electronic-structure operators (e.g., Schrieffer-Wolff-type constructions). Low-rank factorizations compress Hamiltonians and anti-Hermitian generators into rank-one bilinear and projected-quadratic ladders with near-linear scaling at fixed thresholds; each ladder admits deterministic, number-conserving preparation and a block encoding using constant number of signal ancillas. A fixed PREP-SELECT-PREP template multiplexes these ladders, and one QSP polynomial performs the spectral transformation with degree set by operator norms. For a fixed orbital pool and qubit register, the two-qubit fabric is compiled once; geometry, active-space (mask) updates, and truncations are absorbed by re-dialed single-qubit rotations. We introduce a mask-aware similarity-sandwich effective-Hamiltonian construction and benchmark stability under low-rank and second-order-perturation-guided screening. COMPOSER is an execution architecture: algorithmic errors (block-encoding and QSP approximation) are tunable for any supplied parameters, while physical accuracy depends on how those parameters are obtained if not refined.

Data flow scheduling for high-throughput multibeam satellites is a challenging NP-hard combinatorial optimization problem. As the problem scales, traditional methods, such as Mixed-Integer Linear Programming and heuristic schedulers, often face a trade-off between solution quality and real-time feasibility. In this paper, we present a hybrid quantum-classical framework that improves scheduling efficiency by casting Multi-Beam Time-Frequency Slot Assignment (MB-TFSA) as a Quadratic Unconstrained Binary Optimization (QUBO) problem. We incorporate the throughput-maximization objective and operational constraints into a compact QUBO via parameter rescaling to keep the formulation tractable. To address optimization challenges in variational quantum algorithms, such as barren plateaus and rugged loss landscapes, we introduce a layer-wise training strategy that gradually increases circuit depth while iteratively refining the solution. We evaluate solution quality, runtime, and robustness on quantum hardware, and benchmark against classical and hybrid baselines using realistic, simulated satellite traffic workloads.

A higher-order relativistic k.p model is developed to describe plasmon excitations in two-dimensional (2D) electronic systems with spin-orbit coupling (SOC) and magnetic-exchange interactions. Derived entirely from ab initio band structure, the model allows for a non-Rashba spin-momentum locking and enables a direct coupling of the exchange field to the real spin of electrons. Using the BiTeI trilayer (hexagonal C3v symmetry) and the Si-terminated surface state of TbRh2Si2 (cubic C4v symmetry) as prototypes, we show that the exchange field induces strong, symmetry-dependent modifications of the band structure and plasmon dispersion. In BiTeI, it breaks the sixfold symmetry and leads to anisotropic, nonreciprocal plasmon modes, while in TbRh2Si2 it suppresses the characteristic triple spin winding and alters the plasmon damping. The results reveal that the interplay between SOC and exchange magnetism enables magnetic control of collective charge excitations in 2D spin-orbit systems beyond the Rashba paradigm.

DFT+X methods, such as DFT+U and DFT+DMFT, are important supplements to standard density functional theory when strong on-site Coulomb interactions are present. However, the involvement of external parameters in the underlying model Hamiltonian introduces intrinsic ambiguity when comparing the total energies obtained with different model parameters. This renders DFT+X approaches semi-empirical and severely hinders their capability to describe phase ordering and phase stability, especially when reliable experimental benchmarks are unavailable, such as under high pressure. In this work, we resolve this longstanding problem by proposing a general linear correction method that eliminates the ambiguous energy contributions introduced by the model Hamiltonian in DFT+X approaches, thereby enabling direct comparison of their energies calculated with different interaction parameters. The method is demonstrated and validated within the framework of DFT+U, an important member of the DFT+X family. It is then applied to important nuclear materials of uranium-based binaries U-M (M=Al, Ga, In) alloys. With this approach, we resolve the long-standing discrepancy between theoretical predictions and experimental observations of phase stability with unprecedented accuracy, and predict several previously unknown stable intermetallic compounds under high pressure. The broad applicability of the method is further confirmed by accurate predictions of formation enthalpies for diverse systems, including Np-Al, U-Si, and Cu-O binaries, the ternary MnSnAu compound, and oxygen adsorption on the Cu(111) surface. This work establishes linear-corrected DFT+U as a fully first-principles approach and validates the linear correction method as a robust and general scheme that can be readily extended to other DFT+X methods.

We present an exact semi-classical analysis of a coupled multi-degree-of-freedom quantum system governed by a symmetric quartic potential with four degenerate minima. Starting from the Euclidean path integral, we identify distinct paths that are longitudinal, transverse, and diagonal, each corresponding to distinct instanton configurations that mediate tunneling between vacua. The continuous translational zero mode for each coupled trajectory is extracted rigorously by transforming the fluctuation operator into a comoving rotating frame, explicitly incorporating curvature-induced fictitious forces. By evaluating the exact functional determinants via the Gelfand-Yaglom method and mapping the multi-flavor dilute instanton gas onto a weighted $K_4$ adjacency matrix, we analytically derive the transition amplitudes and ground-state energy splittings. Crucially, our exact continuum treatment reveals that for strong coupling, the usual exponential can be overpowered in certain parameter ranges by the "pre-factor". This quantity, which arises from quadratic level fluctuations in the direction transverse to the free direction, turns out to have an essential singularity that would be hard to spot in standard discretized instanton approximations.

Hybrid quantum-classical neural networks (HQNNs) integrate quantum circuits with classical layers, each operating under fundamentally different computational paradigms, which makes hardware resource estimation challenging. The training of quantum circuits on real devices requires thousands of circuit executions, which is impractical on current NISQ devices. Therefore, most HQNNs are evaluated on classical simulators, with hardware cost approximated using floating-point operations (FLOPs). However, FLOPs and existing quantum resource estimation methods (e.g., gate counts) overlook key quantum hardware-specific factors such as gate durations, limited qubit connectivity, and noise, all of which ultimately determine the true cost and scalability of quantum circuits. In this paper, we propose an analytical quantum cost model that estimates quantum hardware resources using real backend calibration data, incorporating gate durations, routing overheads, and noise-induced sampling inefficiencies. To complement this, we develop a classical cost model that converts FLOPs into device-specific throughput, enabling a unified time-based representation of hardware resource cost for both subsystems of HQNNs. Building on these analytical models, we present Hyb-HANAS, a hardware-aware hybrid neural architecture search framework, which jointly optimizes accuracy, hardware cost, and parameter count using NSGA-II. Hyb-HANAS identifies Pareto-optimal trade-offs and cross-domain co-adaptation between classical and quantum components of HQNNs. Beyond NAS, the proposed analytical quantum cost model is broadly applicable to quantum hardware benchmarking, compiler evaluation, and training-time estimation of quantum circuits on NISQ devices.

Quantum computing shows substantial potential in accelerating simulations and alleviating memory bottlenecks in computational fluid dynamics (CFD), owing to its inherent properties of superposition and entanglement. The lattice Boltzmann method (LBM), being largely algebraic in nature, has inspired the development of various quantum LBMs. However, most existing approaches fix the relaxation time at $\tau$ = 1, thereby confining a given mesh resolution to simulations at a single Reynolds number. Although our earlier quantum lattice kinetic scheme (LKS) lifted this restriction, it suffers from instability at high Reynolds numbers. To address this challenge, we propose a quantum fractional-step LBM (FS-LBM). In this framework, the predictor step is implemented on a quantum circuit using the standard LBM formulation, while the corrector step is performed classically. The relaxation time is retained at $\tau$ = 1 to ensure seamless compatibility with existing quantum LBMs. Benchmark simulations of representative two- and three-dimensional incompressible isothermal and thermal flows demonstrate that the quantum FS-LBM achieves accuracy and convergence orders consistent with its classical counterpart, while significantly outperforming the quantum LKS in both precision and stability. Notably, this work presents the first quantum LBM simulation of three-dimensional incompressible thermal flows.

One-time programs (OTPs) aim to let a user evaluate a program on a single input while revealing nothing else. Classical OTPs require hardware. Quantum measurement suggests a physical basis for one-time use, yet deterministic functionalities remain impossible due to gentle-measurement attacks (Broadbent, Gutoski and Stebila, 2013). Recent constructions cover randomized functionalities with high-entropy outputs (Gunn, Movassagh 2025; Gupte et al., 2025), but the strongest achievable security remains unclear. Inspired by classical obfuscation, we ask for a "best-possible" one-time compiler that, for any functionality, leaks the least information compared with any other one-time implementation. We prove that such a generic compiler cannot exist even for classical randomized functionalities assuming $\mathsf{SZK} \not\subseteq \mathsf{BQP}$. We then identify a natural subclass: testable OTP compilers, which output quantum states augmented with reflection programs for themselves. We formulate a simplified, generalized Single-Effective-Query (SEQ) simulation security notion for quantum channels, using self-adjoint implementations whose behavior under arbitrary quantum interactions depends only on the channel. SEQ security implies best-possible testable one-time security. We construct SEQ-secure OTPs for all quantum functionalities in the classical oracle model, giving the first positive results for arbitrary quantum channels beyond classical randomized functionalities. SEQ security could thus serve as a testable one-time analogue of virtual black-box (VBB) security. Finally, we propose stateful quantum indistinguishability obfuscation (stateful quantum iO): quantum state obfuscation for stateful quantum programs. It implies best-possible testable OTPs and is achievable in the classical oracle model, offering an approach towards best-possible testable OTPs in the plain model.

We study Bopp shifts in two-dimensional noncommutative quantum mechanics (NCQM) through a functorial lens. A nondegenerate NCQM sector with central character $(\hbar,\vartheta,B_{\rm in})$ determines a self-adjoint infinitesimal representation of the NCQM Lie algebra $\mathfrak{g}_{\rm NC}$. A Darboux normalization of its represented phase-space operators produces a self-adjoint infinitesimal representation of the Weyl-Heisenberg Lie algebra $\mathfrak{g}_{\rm WH}$ with central parameter $\hbar$, and hence defines a Bopp-shift functor collapsing $(\hbar,\vartheta,B_{\rm in}) \mapsto \hbar$. In particular, a generic NCQM sector is not equivalent, as a $\mathfrak{g}_{\rm NC}$-sector, to the ordinary QM sector $(\hbar,0,0)$, even though their Bopp-shift images have the same Weyl-Heisenberg parameter. To measure what this collapse forgets, we construct a toroidal shadow functor assigning to each periodic datum $L=(a_x,a_y)$ and each NCQM sector $\chi$ a phase-space noncommutative four-torus $A^4_{\Theta_{\chi,L}}$. Its $K_0$-trace pairing yields sector-sensitive gap labels whose top-degree coefficient is $(\vartheta B_{\rm in}-\hbar)/((2\pi)^2\hbar)$. This coefficient is independent of the spatial cell area $a_xa_y$ and equals the Pfaffian ${\rm Pf}(\Theta_{\chi,L})$, the top-degree generator of the $K_0$-trace range. Since strong Morita equivalence preserves this trace range up to positive scaling, non-proportionality of the trace ranges obstructs Morita equivalence of the shadows, separating equal-$\hbar$ sectors that the Bopp-shift functor identifies. In the arithmetic subfamily where $\vartheta/A$ and $B_{\rm in}A/\hbar$ are algebraic, the trace-range scale is forced to be trivial and $|{\rm Pf}|$ becomes a computable separation criterion: $|\vartheta B_{\rm in}-\hbar| \neq |\vartheta' B'_{\rm in}-\hbar|$ already implies inequivalence.

In this work, we explore physical systems which support not only multipartite interparticle entanglement, but also intraparticle entanglement between different degrees of freedom of the constituent particles and entanglement between different degrees of freedom of different particles, i.e., algebraic entanglement. We derive a simple method for calculating the algebraic entanglement entropy between two of the particles' degrees of freedom from collective states of the whole ensemble. Our procedure makes use of underlying symmetries in these systems, in particular permutation symmetry of the particle indices, and shows a connection between the algebraic entanglement entropy in these systems and the irreducible representations of Lie groups which describe the particles' degrees of freedom. Namely, we use the direct sum over irreducible representations to diagonalize the reduced density matrices in a block-by-block manner, then utilize the multiplicity of these irreducible representations to reproduce the results from an exponentially-scaled Hilbert space in only polynomial complexity. We use this to explore a variety of systems where the constituent particles support two degrees of freedom each with two levels, such as atoms with two electronic states and two momentum states. Notably, these systems may be exactly simulated in a polynomial-scaled Hilbert space, yet they support an algebraic entanglement entropy that grows linearly with the particle number which typically requires an exponentially-scaled Hilbert space.