Papers

We investigate a hybrid photon blockade (HPB) scheme in a driven two-qubit cavity QED system arising from the combination of eigenenergy-level anharmonicity (ELA) and quantum destructive interference (QDI). By tuning the detuning of a single qubit and pumping field, we identify precise parametric regimes that fully integrate the advantages of high brightness in ELA-based conventional photon blockade and strong antibunching in QDI-based unconventional photon blockade. Interestingly, these regimes are accompanied by hyperradiance, indicating that inter-emitter correlations give rise to enhanced collective emission. The HPB mechanism exhibits parametric generality across varying coupling asymmetries and remains accessible via detuning control, offering a feasible route for generating high-quality single-photon source in diverse quantum platforms.

We develop a numerical approach to optimizing a quantum circuit over a discrete gate set by using gradient descent to tune $R_Z$ angles to a solution where many $R_Z$ gates can be rounded to a Clifford or $T$ gate without introducing further synthesis error. Through benchmarking, we show that our approach is able to match state-of-the-art techniques for multi-qubit Clifford + $T$ circuit synthesis, and is able to find circuits for unitaries that previous approaches fail to find solutions for. Our approach can adapt to any discrete gate set, which we demonstrate using the Clifford + $T$ + $\sqrt T$ gate set.

Beamsplitters represent fundamental components in both classical and quantum optical systems, enabling the distribution of light, as well as the generation of interference, superposition and entanglement. However, optical networks constructed from conventional bulk 2x2-beamsplitters encounter inherent scalability issues, as the number of required beamsplitters scales quadratically with the number of optical modes for a fully connected network. Metasurfaces offer a promising route to overcome these constraints. By manipulating light at the wavelength scale compact optical components with advanced functionalities can be constructed, which address several modes simultaneously. In this work, we design and experimentally utilize a metasurface as a multiport beamsplitter. Furthermore, we realize a multimode interferometer composed of two cascaded metasurfaces. We characterize the individual and cascaded metasurfaces using classical light, showing controllable splitting ratios through tunable phase relations. We then expand the approach to quantum light, employing single photons to demonstrate second- and third-order photon correlations, as well as single photon interference across multiple spatial paths. These results establish metasurface-based multiport beamsplitters as a scalable and reconfigurable platform bridging classical and quantum photonics.

Capturing the dynamics of quantum many-body systems under time-dependent driving protocols is a central challenge for numerical simulations. Existing methods such as tensor networks and time-dependent neural quantum states, however, must be re-run for every protocol. In this work, we introduce the Neural Operator Quantum State (NOQS) as a foundation model for quantum dynamics. Rather than solving the Schrödinger equation for individual trajectories, our approach aims to learn the solution operator that maps entire driving protocols to time-evolved quantum states. Once trained, the NOQS predicts time evolution under unseen protocols in a single forward pass, requiring no additional optimization. We validate NOQS on the two-dimensional Ising model with time-dependent longitudinal and transverse fields, demonstrating accurate prediction not only for unseen in-distribution protocols, but also for qualitatively different, out-of-distribution functional forms of driving. Further, a single NOQS model can be transferred between different temporal resolutions, and can be efficiently fine-tuned with sparse experimental measurements to improve predictions across all observables at negligible cost. Our work introduces a new paradigm for quantum dynamics simulation and provides a practical computational-experimental interface for driven quantum systems.

This review is designed to introduce mathematicians and computational scientists to quantum computing (QC) through the lens of uncertainty quantification (UQ) by presenting a mathematically rigorous and accessible narrative for understanding how noise and intrinsic randomness shape quantum computational outcomes in the language of mathematics. By grounding quantum computation in statistical inference, we highlight how mathematical tools such as probabilistic modeling, stochastic analysis, Bayesian inference, and sensitivity analysis, can directly address error propagation and reliability challenges in today's quantum devices. We also connect these methods to key scientific priorities in the field, including scalable uncertainty-aware algorithms and characterization of correlated errors. The purpose is to narrow the conceptual divide between applied mathematics, scientific computing and quantum information sciences, demonstrating how mathematically rooted UQ methodologies can guide validation, error mitigation, and principled algorithm design for emerging quantum technologies, in order to address challenges and opportunities present in modern-day quantum high performance and fault-tolerant quantum computing paradigms.

Nonstabilizerness, or magic, is a necessary resource for quantum advantage beyond the classically simulatable Clifford framework. Recent works have begun to chart the structure of magic in many-body states, introducing the concepts of long-range magic – nonstabilizerness that cannot be removed by finite-depth local unitary (FDU) circuits – and the magic hierarchy, which classifies quantum circuits by alternating layers of Clifford and FDUs. In this work, we construct explicit states that provably possess two-sided long-range magic, a stronger form of magic meaning that they cannot be prepared by a Clifford circuit and a FDU in either order, thus placing them provably outside the first level of the magic hierarchy. Our examples include the “magical cat" state, $|\psi\rangle \propto |0^n\rangle + |+^n\rangle$, and ground states of certain nonabelian topological orders. These results provide new examples and proof techniques for circuit complexity, and in doing so, reveal the connection between long-range magic, the structure of many-body phases, and the principles of quantum error correction.

Connected and automated vehicles require city-scale coordination under strict latency and reliability constraints. However, many existing approaches optimize communication and mobility separately, which can degrade performance during network outages and under compute contention. This paper presents QIVNOM, a quantum-inspired framework that jointly optimizes vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communication together with urban traffic control on classical edge–cloud hardware, without requiring a quantum processor. QIVNOM encodes candidate routing–signal plans as probabilistic superpositions and updates them using sphere-projected gradients with annealed sampling to minimize a regularized objective. An entanglement-style regularizer couples networking and mobility decisions, while Tchebycheff multi-objective scalarization with feasibility projection enforces constraints on latency and reliability. The proposed framework is evaluated in METR-LA–calibrated SUMO–OMNeT++/Veins simulations over a $5\times5$~km urban map with IEEE 802.11p and 5G NR sidelink. Results show that QIVNOM reduces mean end-to-end latency to 57.3~ms, approximately $20\%$ lower than the best baseline. Under incident conditions, latency decreases from 79~ms to 62~ms ($-21.5\%$), while under roadside unit (RSU) outages, it decreases from 86~ms to 67~ms ($-22.1\%$). Packet delivery reaches $96.7\%$ (an improvement of $+2.3$ percentage points), and reliability remains $96.7\%$ overall, including $96.8\%$ under RSU outages versus $94.1\%$ for the baseline. In corridor-closure scenarios, travel performance also improves, with average travel time reduced to 12.8~min and congestion lowered to $33\%$, compared with 14.5~min and $37\%$ for the baseline.

Fermionic linear optics (FLO) with Gaussian resources is known to be efficiently classically simulable. We show that this changes for fermions with internal degrees of freedom once the circuit is equipped with mid-circuit number monitoring and classical feedforward. In our architecture, the measurement record routes the selected blocks into a fixed-order Bell-fusion pairing geometry. On the level of the classical description, the permutation sum then no longer collapses to a single determinant or Pfaffian. Each accepted branch expands as a signed sum of path-ordered products of typically non-commuting dressed blocks, and branch amplitudes are matrix elements of the resulting non-commutative trace polynomials. Numerically, we observe Porter-Thomas statistics for the conditional branch distribution and rapid growth of the minimal order-respecting matrix product operator bond dimension. Under reasonable complexity assumptions, these results identify mid-circuit measurement-induced non-commutativity as a route to sampling hardness for noninteracting fermions, with the non-Gaussianity confined to a fixed preparation-and-readout interface rather than to the coherent FLO evolution.

Collapse-locality is an untested loophole in the violation of Bell's inequalities. The core of the argument is that the time value of photon detection is delayed by the time Tc required by the collapse of its quantum state. The value of Tc is given by the underlying theory of quantum collapse, and is mostly unknown. Depending on the value of Tc, detections in the performed Bell's experiments may have not been truly space-like separated events. This implies that the inequalities may have been violated as a consequence of (conspiratorial) information propagating at subluminal speed. We report an optical Bell experiment which closes the weaker ('essential') form of this loophole regardless the theory of quantum collapse. This is possible thanks to unique features of the setup. These features are: classical signals sent to the stations to define a time reference, and variable distance between the stations leaving all other parameters constant.

Magic and entanglement are two measures that are widely used to characterize quantum resources. We study the interplay between magic and entanglement in two-qubit systems, focusing on the two extremes: maximal magic and minimal magic for a given level of entanglement. We quantify magic by the Rényi entropy of order 2, $M_2$, and entanglement by the concurrence $\Delta$. We find that the Pareto frontier of maximal magic $M_2^{(max)}(\Delta)$ is composed of three separate segments, while the boundary of minimal magic $M_2^{(min)}(\Delta)$ is a single continuous line. We derive simple analytical formulas for all these four cases, and explicitly parametrize all distinct quantum states of maximal or minimal magic at a given level of entanglement.

Large Language Models (LLMs) are increasingly used for code generation, yet quantum code generation is still evaluated mostly within single frameworks, making it difficult to separate quantum reasoning from framework familiarity. We introduce QuanBench+, a unified benchmark spanning Qiskit, PennyLane, and Cirq, with 42 aligned tasks covering quantum algorithms, gate decomposition, and state preparation. We evaluate models with executable functional tests, report Pass@1 and Pass@5, and use KL-divergence-based acceptance for probabilistic outputs. We additionally study Pass@1 after feedback-based repair, where a model may revise code after a runtime error or wrong answer. Across frameworks, the strongest one-shot scores reach 59.5% in Qiskit, 54.8% in Cirq, and 42.9% in PennyLane; with feedback-based repair, the best scores rise to 83.3%, 76.2%, and 66.7%, respectively. These results show clear progress, but also that reliable multi-framework quantum code generation remains unsolved and still depends strongly on framework-specific knowledge.

Damage in infrastructure is often hidden until it becomes costly or dangerous. Common examples include corrosion under insulation, early fatigue damage in steel, corrosion of embedded reinforcement, and abnormal current flow in batteries and power equipment. Magnetic methods are attractive because they can sense through coatings, insulation, and concrete cover without couplants, but field performance is often limited by lift-off, low-frequency drift, background magnetic noise, and the weak low-frequency response of pickup coils. This review examines two room-temperature quantum receiver platforms: optically pumped atomic magnetometers (OPMs) and nitrogen-vacancy (NV) diamond magnetometers. Rather than treating them as stand-alone sensors, we compare them as parts of a full measurement chain that includes source physics, geometry, readout, calibration, and interpretation. The literature is organized into four magnetic signal classes: driven induction responses, leakage fields in magnetic flux leakage inspection, passive self-fields linked to stress or corrosion, and fields produced by operational currents. OPMs are strongest for low-frequency, phase-referenced induction measurements, while NV sensors are strongest for near-surface field mapping, vector or gradient measurements, and differential current sensing in compact solid-state heads. Across all applications, deployment depends less on best-case sensitivity than on usable bandwidth, dynamic range, background rejection, geometry control, calibration, and validation. The clearest path to field use is therefore robust instrument engineering tied to qualification methods that reflect real inspection conditions.

We develop a family of chiral measures to quantify the chirality of a distribution and assign it a handedness. Our measures are built using the tensorial moments of the distribution, which naturally encode its spatial character, not only via its angular shape consistently with existing multipolar-moment approaches, but also its radial dependence. We combine these tensorial moments into a rotationally-invariant pseudoscalar using a newly-defined cross product and triple product for arbitrary symmetric tensors. We analyze these measures for a variety of toy-model distributions, providing intuition for the geometry and guiding the choice of chiral measure optimal for a given distribution. We also apply our measures to a physically-motivated example coming from photoionization in polychromatic chiral light. Our work provides a robust, flexible, intuitive, highly geometrical, and physically-driven framework for understanding and quantifying the chirality of a wide variety of distributions, together with an open-source software package that makes this toolbox readily applicable for the analysis of numerical or experimental data.

We quantify decoder dependence in surface-code threshold studies under two matched regimes: Pauli noise and native GKP-style Gaussian displacement digitization. Using LiDMaS+ v1.1.0, we benchmark MWPM, Union-Find (UF), Belief Propagation (BP), and neural-guided MWPM with fixed seeds, identical sweep grids, and unified reporting across runs 06–14. At $d=5$ and $\sigma=0.20$, MWPM and UF define the Pareto frontier, with (runtime, LER) = (1.341 s, 0.2273) and (1.332 s, 0.2303); neural-guided MWPM is slower and less accurate (1.396 s, 0.3730), and BP is dominated (7.640 s, 0.6107). Crossing-bootstrap diagnostics are stable only for MWPM, with median $\sigma^\star_{3,5}=0.10$ (1911/2000 valid) and $\sigma^\star_{5,7}=0.1375$ (1941/2000 valid), while other decoders show no valid crossing samples. Dense-window scanning over $\sigma \in [0.08,0.24]$ returns NaN crossings for all decoders, confirming estimator- and window-sensitive threshold localization. Rank-stability and effect-size bootstrap analyses reinforce ordering robustness: BP remains rank 4, neural-guided MWPM rank 3, and MWPM-UF differences are small ($\Delta_{\mathrm{MWPM-UF}}=-0.00383$, 95% interval $[-0.0104,0.00329]$) across $\sigma \in [0.05,0.35]$. Threaded execution preserves statistical fidelity while improving throughput: $1.34\times$ speedup in Pauli mode and $1.94\times$ in native GKP mode, with mean $|\Delta\mathrm{LER}|$ $6.07\times10^{-3}$ and $5.20\times10^{-3}$, respectively. We therefore recommend estimator-conditional threshold reporting coupled to runtime-fidelity checks for reproducible hardware-facing practical future decoder benchmarking workflows.

We introduce a GPU-accelerated multigrid Gaussian-Plane-Wave density fitting (FFTDF) approach for efficient Fock builds and nuclear gradient evaluations within Kohn-Sham density functional theory, as implemented in the GPU4PySCF module of PySCF. Our CUDA kernels employ a grid-based parallelization strategy for contracting Gaussian basis function pairs and achieve up to 80% of the FP64 peak performance on NVIDIA GPUs, with no loss of efficiency for high angular momentum (up to f-shell) functions. Benchmark calculations on molecules and solids with up to 1536 atoms and 20480 basis functions show up to 25x speedup on an H100 GPU relative to the CPU implementation on a 28-core shared memory node. For a 256-water cluster, the ground-state energy and nuclear gradients can be computed in ~30 seconds on a single H100 GPU. This implementation serves as an open-source foundation for many applications, such as ab initio molecular dynamics and high-throughput calculations.

We investigate congestion-aware control of quantum repeater nodes operating under stochastic traffic and finite memory coherence. Entanglement generation is modeled as a probabilistic process producing Werner states subject to depolarizing memory decoherence, while entanglement requests arrive according to Poisson and bursty ON–OFF processes. Using a queueing-theoretic framework, we couple physical-layer memory dynamics with congestion-dependent service behavior to analyze stability, delay, and fidelity trade-offs. Operating regimes are characterized in terms of the load parameter, showing that fixed cutoff policies impose a fundamental fidelity–latency trade-off together with strict stability limits. Queue-aware adaptive control strategies are then introduced that dynamically adjust memory cutoff times and the number of parallel entanglement-generation channels. Cutoff adaptation restores stability near critical load by trading fidelity for service capacity, whereas resource scaling increases capacity without degrading entanglement quality. Under bursty traffic, joint adaptation suppresses delay spikes while activating additional channels only during congestion periods. The framework is further extended to a two-user shared-resource scenario in which independent traffic flows compete for a common resource pool. Stability is determined by aggregate load, while adaptive resource redistribution stabilizes queues that diverge under fixed partitioning. These results provide a queue-aware congestion-control perspective for adaptive resource management in quantum networks.

We introduce Quantum Spectral Authentication (QSA), a symmetric-key entity-authentication and key-derivation protocol in which a remote endpoint proves it still holds a hidden planted state, an eigenstate of the challenge it can prepare, without revealing it. Each round issues a fresh public unitary challenge with its own planted state, and the endpoint returns an eigenphase feature from which both parties derive transcript-bound session material. QSA runs in two provisioning modes with materially different security: a seed mode, storing a classical seed that regenerates the planted state, and a state mode, holding only the physical register carrying it, non-copyable and consumed on use. We give a formal security model in which QSA is an identification scheme, prove mutual authentication under a single label-hiding assumption, and prove unconditionally that the published spectrum is near-uniform at the readout resolution, leaving at least $m-1$ bits of min-entropy per instance; state mode satisfies the assumption by construction. We develop a symmetric verifier-driven compiler compatible with low-depth quantum phase estimation, which also admits a fast path that recovers the label by an inverse-compiler measurement. Simulations show it is more noise-tolerant than an asymmetric alternative, and experiments on IBM ibm_fez provide a hardware sanity check.

An electron in quantum confinement takes on a discrete energy spectrum which is defined based on the solution to the Schrodinger Equation for a given potential. Well defined closed-form energy spectra are known for the particle in a box, circular potential, quarter circle potential, and an equilateral triangle. A closed-form solution for more complex shapes may not be known, but numerical methods can be used to find an approximate solution. In this research, an application of the Finite Element Method (FEM) in Wolfram Mathematica is presented and applied to Quantum Billiards with a variety of geometries. To assess the accuracy of the method, the computed energy states are analyzed in the limit of a polygon with an increasing number of sides, the numerical results are validated against analytical solutions for geometries with known exact forms, and a standard convergence test is conducted. The FEM results closely match analytical solutions for known potentials, demonstrating its high accuracy. For high energy index n, quantum scarring may emerge for certain geometries. The nature of quantum scarring and its presence in the computed models is also investigated qualitatively.

Non-Hermitian skin effect, which is a unique feature of non-Hermitian systems, exhibits the formation of an extensive number of boundary modes under open boundary conditions. However, its manifestation in higher dimensions remains elusive. In our work, we demonstrate a hybrid skin-topological effect arising from the interplay between first-order band topology and non-reciprocal hopping in an engineered two-dimensional brick-wall geometry. The non-Hermitian brick-wall lattice under open boundary conditions in both directions exhibits several unconventional spectral features. Notably, the eigenvalues associated with the corner skin modes do not exhibit non-trivial windings in the complex energy plane; instead, they exhibit dynamically stable exceptional point-like features that do not originate from eigenvector coalescence. In contrast, the remaining modes accumulate at the opposite pair. Of all the corner skin modes, only the two that originate from the topological corner states of the Hermitian brick-wall lattice remain localized at individual corners, while the rest accumulate at the pair of opposite corners. This spatial distribution contrasts sharply with the second-order skin effect, where corner skin modes are more uniformly distributed. Finally, for the non-Hermitian Brick-wall lattice, we design and implement the corresponding topolectrical circuit (circuit for a square lattice is included for comparison) to directly visualize the hybrid skin-topological modes.

We introduce a coefficient-decoupled matrix product operator (MPO) representation for Pauli-sum operators that separates reusable symbolic operator support from a tunable coefficient bridge across a fixed bipartition. This representation provides a direct interface to linear-combination-of-unitaries (LCU) circuits: the symbolic left/right dictionaries define a static Select oracle that is compiled once, while coefficient updates modify only a dynamic Prep oracle. As a proof of concept, we construct compact state-adapted Pauli pools by sampling Pauli strings from a pretrained matrix product state (MPS), pruning them to a fixed symbolic pool, optimizing only their coefficients, and transferring the resulting weights directly to the LCU interface. The resulting workflow provides a reusable classical-to-quantum compilation strategy in which the symbolic operator structure is compiled once, and subsequent updates are confined to a low-dimensional coefficient object.

Quantum optics provides a fundamental framework for understanding the interaction between light and matter at the quantum level. Recently, it has been shown that under incoherent pumping, the resonance fluorescence spectrum dramatically changes. Engineering the resonance fluorescence spectrum paves the way towards solid-state-based single-photon sources. In this paper, we start by reviewing and reproducing some of the results concerning the resonance fluorescence spectrum, single-photon sources, dressed-state lasers, and luminescence spectrum of a quantum dot in a microcavity. Photon correlations in quantum optical systems and spectral properties of radiation emitted by atomic and semiconductor systems interacting with external fields are investigated. The well known Mollow triplet structure of the emission spectrum is discussed, together with the role of dressed states in explaining the origin of the three spectral peaks. Furthermore, the luminescence spectra of quantum emitters coupled to microcavities are reviewed. The numerical results presented here contribute to the theoretical understanding of resonance fluorescence, photon correlations, and engineered emission in quantum optical systems. These studies highlight the rich physical properties arising from light matter interaction at the quantum level and demonstrate their relevance for emerging quantum technologies.

Neutral-atom quantum simulation is susceptible to entanglement between the atom's internal electronic state and its center-of-mass position. In many alkali Rydberg platforms, the 'spin-motion coupling' is exacerbated by the free expansion required to avoid ponderomotive anti-trapping from optical fields. A recent proposal (arXiv:2505.01071) claims sufficiently excited Rydberg states could be trapped in a monochromatic, far-detuned, circularly polarized optical field by harnessing a large vector polarizability. We disprove the proposal through analytic calculation and measurement of the vector polarizability of the $54S$, $54P$, and $53D$ orbitals of Cesium. Regarding the optical angular frequency $\omega$, we analytically derive that the scalar, vector, and tensor polarizabilities scale as $\omega^{-2}$, $\omega^{-3}$, and $\omega^{-4}$, as opposed to the proposed scaling of $\omega^{-2}$, $\omega^{-1}$, and $\omega^{-2}$. We refine the sum-over-states expression for vector and tensor polarizability to be numerically stable and predict negligible vector and tensor polarizabilities far detuned from resonances, in agreement with our measurements. However, we find vector polarizability can enhance a recent proposal for near-detuned attractive trapping. Furthermore, we evaluate the breakdown of the electric-dipole approximation and derive no effect stronger than ponderomotive repulsion. We conclude that an attractive, monochromatic, far-detuned optical trap for alkali Rydberg states is not possible, regardless of the beam geometry.

Quantum mode parameter estimation determines parameters governing the shape of electromagnetic modes occupied by a quantum state of radiation. Canonical examples, time delays and frequency shifts, underpin radar, lidar, and optical clocks. A comprehensive framework recently established that broad families of quantum states can attain the Heisenberg limit, surpassing any classical strategy. This raises a fundamental question: among all quantum-enhanced strategies, which is truly optimal? Answering this requires identifying physically meaningful resources governing each estimation task, so quantum states can be compared on equal footing. We show these resources are connected to the eigenmode basis of the generator of the relevant mode transformation. For time-shift estimation, whose generator is diagonal in the frequency domain, the pertinent resources are the mean frequency and bandwidth; analogous quantities emerge for other transformations. Our framework unifies two historically separate perspectives: the particle-number aspect and the mode-structure of quantum light, providing a coherent picture of quantum-enhanced sensing with multimode radiation. Within this unified framework, we derive a tight upper bound on the quantum Fisher information for multimode Gaussian states, expressed in terms of these natural resources, and analytically identify the optimal Gaussian states saturating it. These optimal states take a particularly transparent form in the generator eigenbasis, a structural simplicity reflecting the deep connection between the geometry of the mode transformation and the architecture of the optimal probe. We further demonstrate that multimode homodyne detection constitutes the optimal measurement, achieving this bound and completing the end-to-end characterization of optimal quantum metrology strategies for mode parameter estimation.

We show that any $n$-qubit Clifford unitary can be implemented using at most $2n$ multi-qubit joint measurements. All the multi-qubit joint measurements used for implementing the Clifford unitary can be chosen to form at most two sets of independent mutually-commuting measurements. Each of these sets is of size at most $n$. This enables very flexible space-time trade-offs when implementing Clifford unitaries. We also discuss a version of the result that relies on multi-target CNOTs and is more relevant for targeting fault-tolerant hardware based on Quantum LDPC codes.

Accurate ground-state energy calculations remain a central challenge in quantum chemistry due to the exponential scaling of the many-body Hilbert space. Variational Monte Carlo and variational quantum eigensolvers offer promising ansatz optimization approaches but face limitations in convergence as well as hardware constraints. We introduce a particular Selected Configuration Interaction (SCI) algorithm that uses auto-regressive neural networks (ARNNs) to guide subspace expansion for ground-state search. Leveraging the unique properties of ARNNs, our algorithm efficiently constructs compact variational subspaces from learned ground-state statistics, which in turn accelerates convergence to the ground-state energy. Benchmarks on molecular systems demonstrate that ARNN-guided subspace expansion combines the strengths of neural-network representations and classical subspace methods, providing a scalable framework for classical and hybrid quantum-classical algorithms.

We generalize the polynomial-time outcome-complete simulation algorithm for stabilizer circuits in arXiv:2309.08676 to track global phases exactly, yielding what we call phased outcome-complete simulation. The original algorithm enabled equivalence checking of stabilizer circuits with intermediate measurements and conditional Pauli corrections for all input states and all measurement outcomes simultaneously, but it tracked quantum states only up to a global phase. Our generalization removes this limitation and enables equivalence checking for an important family of non-stabilizer circuits: stabilizer circuits augmented with single-qubit rotations $\exp(i\alpha Z)$ by symbolic angles. Two such circuits are equivalent if they implement the same quantum channel for all values of the symbolic angles and all measurement outcomes, given a one-to-one correspondence between rotation angles in the two circuits and a mapping between measurement outcomes. This model enables testing of compilation algorithms that transform the Clifford portions of a computation while preserving rotation angles. Examples include Pauli-based computation, edge-disjoint path compilation for surface codes, and custom compilation strategies for reversible circuits such as adders, multipliers, and table lookups. Our efficient classical verification methods extend naturally to circuits with outcome-parity-conditional Pauli gates and intermediate measurements, features that are ubiquitous in fault-tolerant quantum computing but are rarely addressed by existing equivalence-checking approaches.

String breaking is at the core of hadronization models of relevance to particle colliders. Yet, studies of string-breaking dynamics rooted in quantum chromodynamics remain fundamentally challenging. Tensor networks enable sign-problem-free studies of static and dynamical properties of lattice gauge theories. In this work, we develop and apply a tensor-network toolkit based on the loop-string-hadron formulation of an SU(2) lattice gauge theory in 1+1 dimensions with dynamical fermions. We apply this toolkit to study static and dynamical aspects of strings and their breaking in this theory. The simple, gauge-invariant, and local structure of the loop-string-hadron states and constraints removes the need to impose non-Abelian constraints in the algorithm, and allows for a systematic computation of observables at increasingly large bosonic cutoffs, and toward the infinite-volume and continuum limits. Our study of static strings yields a determination of the string tension in the continuum and thermodynamic limits. Our study of dynamical string breaking, performed at a fixed lattice spacing and system size, illuminates underlying processes at play during the quench dynamics of a string. The loop, string, and hadron description offers a systematic and intuitive way to diagnose these processes, including string expansion and contraction, endpoint splitting and particle shower, chain scattering events, and inelastic processes resulting from string dissociation and recombination, and particle production. We relate these processes to several features of the dynamics, such as energy transport, entanglement-entropy production, and correlation spreading. This work opens the way to future tensor-network studies of string breaking and particle production in increasingly complex lattice gauge theories.

Quantum walks constitute a rich area of quantum information science, where multipartite entanglement plays a central role in the dynamics and scalability of quantum advantage over classical simulators. In this work, we study the multipartite entanglement of quantum walks in optical settings. We present methods for computing a geometric measure of entanglement for arbitrary partitions of a single-walker quantum walk and for analyzing the entanglement in multi-walker scenarios. These techniques are used for numerical studies on the entanglement dynamics of quantum walks in large systems and under various initial conditions. For a given bipartition, based on the coin degrees of freedom, we derive exact expressions describing the complete entanglement dynamics for arbitrary localized initial conditions. We use these expressions for analytic statements about the asymptotic behavior of the system. Furthermore, we demonstrate the emergence of entanglement typicality in statistical ensembles of random optical networks.

Under decoherence, an initial Gaussian (free-fermion) state evolves into a non-Gaussian mixed state, so the resulting decohered fermionic state is not exactly solvable in general. We show through an inequality that a class of Rényi-2 correlators of the decohered fermion state are upper-bounded by the Rényi-2 correlator serving as a proximate diagnostic of strong-weak spontaneous symmetry breaking (SW-SSB) of the charge-U(1) symmetry. This inequality holds for arbitrary decoherence strength and suggests that decoherence drives fermionic quantum matter toward U(1) SW-SSB. We also make connections between our inequality and other subjects such as projected quantum spin Hall insulator and Dirac spin liquid states.

Determining whether an observed distribution of events generated in a quantum network is Bell local, i.e., if it admits an alternative realization in terms of independent local variables, is extremely challenging. Building upon arXiv:1907.10552, we develop a software solution that parameterizes local models in networks via neural networks. This allows one to leverage optimization tools available from the machine learning community in the search of network Bell nonlocality. Our solution applies to arbitrary networks, is easy to use, and includes technical improvements that significantly increase performance compared to previous implementations. We apply it to investigate nonlocality in several networks hitherto unexplored, providing insights on the corresponding quantum nonlocal sets and suggesting concrete, promising realizations of quantum nonlocal correlations.