Papers

Scalable quantum Fisher information (QFI) estimation becomes actionable when the numerical estimate is paired with a trustworthy stopping decision. Krylov-shadow QFI estimation has two resource directions: the Krylov order sets the population resolution, whereas the sample count controls statistical uncertainty at that resolution. We show that treating these directions as one can produce false stops, where a width-based rule reports a narrow interval around a biased low-order estimate. We turn adaptive stopping into a two-component reliability problem, separating Krylov truncation from finite-sample uncertainty, and introduce AKS-QFI, a component-aware stopping interface for Krylov-shadow estimators. On a noisy mixed-state benchmark at $n=4$ qubits, width-only stopping has false-stop rates from $0.16$ to $0.68$. Under the same resource limit, AKS-QFI returns no false success declarations; after recalibrating Krylov resolution and sample counts, it returns accurate success declarations at true 5% relative tolerance. These results make adaptive stopping a reliability layer for shadow-based QFI estimation.

As quantum computers become available through multi-tenant cloud platforms, ensuring privacy against adversaries sharing the same quantum processing unit becomes critical. We introduce and explore covert quantum computing, a new concept that ensures an adversary with access to all other quantum computational units (QCUs) of a quantum computer cannot detect computation on the subset that they cannot access. Analogous to covert communication, we employ information theory. However, since here the adversary controls the systems used for detection, we require a richer framework for covertness analysis that accounts for the use of quantum memories and adaptive operations. Thus, we adopt the quantum-strategy framework used in quantum game theory and memory channel discrimination. Current quantum computers use planar graph circuit layouts and typically assume nearest-neighbor crosstalk. We derive discrete isoperimetric inequalities to show that, for an $n$-qubit circuit under this model, only $\mathcal{O}(\sqrt{n})$ border qubits provide detection information to the adversary. We then explore this scaling law on IQM's 54-qubit Emerald processor and IBM's 156-qubit ibm\_fez machine employing the Heron 2 architecture. We implement Ramsey experiments on qubits not used in computation, and detect nearest-neighbor crosstalk, as expected. However, we also observe long-range coupling effects beyond the border qubits, revealing a side channel that the adversary can exploit. We hypothesize that this long-range crosstalk is induced by leakage from the drive and control lines. Beyond weakening covertness, it exposes co-tenants to both adversarial and unintended crosstalk and degrades circuits that span spatially distributed qubits, motivating further work on spatial isolation and crosstalk characterization.

Superconducting nanowire single-photon detectors (SNSPDs) have demonstrated timing jitter in the few-picosecond regime, yet their timing resolution deteriorates substantially under high-count-rate operation. Existing interpretations mainly attribute this degradation to deterministic waveform distortions, such as multiphoton responses and pulse pile-up, yet the experimentally observed jitter broadening at high count rates cannot be fully accounted for within this picture. Here, we show that stochastic baseline fluctuations arising from finite-memory readout dynamics constitute an intrinsic source of the count-rate-dependent timing jitter in SNSPD systems. For stochastically arriving photons, overlapping recovery responses accumulate in the readout chain and generate statistically fluctuating baselines, which are converted into timing uncertainty through threshold-based timing extraction. We develop a stochastic-process framework that quantitatively connects photon statistics, readout dynamics, and timing jitter. The framework predicts characteristic scaling behaviors, including a nonmonotonic dependence of baseline fluctuations under pulsed excitation with a maximum near half of the repetition frequency. These predictions are quantitatively verified through systematic variations of count rate, circuit time constant, and detector dynamical properties. Our results identify stochastic baseline dynamics as a fundamental mechanism limiting timing resolution in high-count-rate SNSPD operation and provide a general framework for optimizing finite-memory high-speed photon-counting systems.

Frequency modes of light are one of the most promising platforms that provide access to high-dimensional quantum states amongst different photonic degrees of freedom capable of high-dimensionality, enabling robust, error-tolerant, and scalable quantum optical information systems. We demonstrate engineering of precisely controlled two-photon high-dimensional states entangled in frequency through time-domain Fourier optical synthesis. We generate and convert a continuous broadband frequency-entangled state into a large range of discrete frequency bins suitable for ITU standards, with spacings ranging from 12.5 GHz to 750 GHz, and observe spectral anticorrelations over 38 frequency bins, including intra-bin pure states at a 100 GHz bin spacing. We characterize the full quantum state dimensionality via Schmidt decomposition and observe lower bounds on the frequency-binned Hilbert-space dimensionalities of at least 289, formed by two entangled qudits with dimension 17. Furthermore, we demonstrate quantum nonlocality via frequency correlations in a transmission experiment over a campus-scale two-node fiber network. This work represents a crucial step towards building a versatile and relatively simple way of generating precisely controlled high-dimensional spectral qudits, with the potential of harnessing in wavelength-multiplexed quantum networks, high-dimensional information processing, and communication of quantum states specifically, and fiber-optic quantum remote sensing.

Complex numbers play an indispensable role in quantum mechanics and quantum information, as validated by both theoretical analysis and experimental verification. Since quantum information processing inherently relies on quantum channels, the resource theory for quantum channels is equally fundamental to that for quantum states. In this paper, we propose two frameworks for quantifying the imaginarity of Gaussian channels. The first framework regards all real superchannels as free superchannels. Within this setting, we introduce two concrete imaginarity measures for Gaussian channels: I_s^GC based on existing imaginarity measures of Gaussian states, and I_d^GC derived directly from the intrinsic parameters of Gaussian channels, which enjoys high computational simplicity. The second framework adopts only a proper subset of real superchannels as free superchannels. Under this framework, we put forward another imaginarity measure I_c^GC , which is fully determined by the inherent parameters of Gaussian channels and features continuity as well as tractable computation. As a practical application, we employ I_c^GC to investigate the dynamical behavior of Quantum Brownian Motion Gaussian channels throughout the entire evolutionary process.

Periodically driven quantum many-body systems can spontaneously break discrete time-translation symmetry, realizing discrete time crystals. To date, both experimental and theoretical efforts have largely focused on the simplest case of spontaneous period-doubling in $\mathbb{Z}_2$ discrete time crystals realized with qubits. This owes, in part, to the challenge of stabilizing eigenstate order in higher discrete symmetry ($\mathbb{Z}_n$) time crystals, due to the presence of richer domain wall physics. Here, we demonstrate the realization of a $\mathbb{Z}_3$ discrete time crystal by implementing a Floquet chiral clock model in a chain of 15 superconducting qutrits. Unlike the conventional Ising setting, our system features a tunable chiral angle that governs domain-wall dynamics, spectral degeneracies, and crucially, the stability of time-crystalline order. Using disordered nearest-neighbor chiral interactions, we observe robust subharmonic period tripling that persists across a wide range of drive strengths and is independent of initial state. Finally, we highlight the special role that chirality plays in our $\mathbb{Z}_3$ discrete time crystal – in its absence, the system's Floquet dynamics exhibit a marked initial state dependence governed by domain wall degeneracies. Our results establish native qudit hardware as a powerful platform to access a broader landscape of non-equilibrium phases.

We develop an open quantum theory for shot-noise dynamics in dissipative chiral transport. By mapping a system under consideration onto a quantum circuit, we show that current noise is governed by two competing factors: the average occupancy distribution and particle-number fluctuations. With energy fully relaxed, shot noise is strongly suppressed, reflecting the stacking of electrons into lower energy states due to dissipation. This process quenches the partition noise from partially occupied levels, and finally isolates the residual noise protected by strong $U(1)$ symmetry. Moreover, selectively heating the source against the bath uncovers the underlying competition between the noise contributions from the occupancy distribution and those from the particle-number fluctuations. It triggers a sign reversal in inter-channel correlation noise, a signature masked by seemingly identical single-channel thermal noises. We propose an inversion scheme to experimentally reconstruct the hidden occupancy distribution directly from measurable noise cumulants.

We study distributed inner product estimation for $n$-qubit states using local randomized measurements, for which rigorous worst-case guarantees are less understood. We first reduce the minimax kernel optimization to Hamming-distance kernels. Within this class, unbiasedness fixes a unique kernel. For this kernel under local Clifford sampling, we prove a sharp fourth-moment bound using the single-qubit Clifford commutant. This yields worst-case sample complexity $\mathcal{O}(\sqrt{4.5^n})$, attained by identical pure product stabilizer states. For the same kernel under local Haar sampling, we prove a local twirling identity that compares its fourth moment with the Clifford fourth moment. This gives the same rigorous upper bound as in the Clifford case, but the comparison is lossy. This motivates the conjectured sharper Haar scaling $\mathcal{O}(\sqrt{3.6^n})$ attained by product states, and verify it for several important classes of states. We also show that independent single-qubit Pauli shadows have worst-case scaling $\mathcal{O}(\sqrt{7.5^n})$ for large $n$.

Nitrogen-vacancy (NV) centres in diamond can be used to detect radiofrequency (RF) signals through coupling of the RF magnetic field with the NV spins, combined with optical readout of the spin state. The sensitivity of such RF detectors has so far been mainly studied in terms of magnetic field sensitivity, which is relevant when the RF signal is generated by a near-field source. However, for applications where the RF input is delivered externally, a more relevant quantity is the sensitivity in terms of the input RF power. Here we theoretically analyse the power sensitivity of NV-based RF detectors as a function of the RF-spin interface geometry. We derive scaling laws of the power sensitivity for both slope-detection and variance-detection RF sensing protocols, and for various noise regimes. We find that, in most scenarios, the power sensitivity scales inversely with the characteristic physical dimension of the RF-spin interface, for instance the width of a coplanar waveguide or the diameter of a loop antenna. In other words, the smaller the structure and the probed NV volume, the better the power sensitivity, which is contrary to the case of magnetic field sensitivity. Lastly, we numerically estimate that photon shot noise limited sensitivities of 10^{-20} W Hz^{-1} (slope) and 10^{-12} W Hz^{-1/2} (variance) are achievable. This work lays the groundwork for further optimisation of NV-based RF detectors.

We present an empirical evaluation of quantum entanglement in agent coordination within quantum multi agent reinforcement learning (QMARL). While QMARL has attracted growing interest recently, most prior work evaluates quantum policies without provable baselines, making it impossible to rigorously distinguish quantum advantage from algorithmic coincidence. We address this directly by evaluating a decentralized QMARL framework with variational quantum circuit (VQC) actors with shared entangled states. In the CHSH game, which has a mathematically proven classical performance ceiling of 0.75 win rate, we show that entangled QMARL agents approach the Tsirelson limit of 0.854, providing clear evidence of their quantum advantage. We show that unentangled quantum circuits match the classical baseline, confirming that entanglement and not the quantum circuit itself is the active coordination mechanism. We also explore the effect of specific entanglement structures, as some Bell states enable coordination gains while others actively harm performance. On cooperative navigation (CoopNav), QMARL without entanglement achieves $\sim2\times$ improvement in success rate over classical MAA2C ($\sim$0.85 versus $\sim$0.40), with the hybrid configuration, quantum actor paired with a classical centralised critic, outperforming both fully classical and fully quantum solutions. We present our experimental analysis and discuss future work.

Hybrid quantum-classical (HQC) algorithms, such as the Variational Quantum Eigensolver (VQE) and the Quantum Approximate Optimization Algorithm (QAOA), are central to near-term quantum computing but remain challenging to test. Sampling-based fuzzing can expose faulty or non-convergent configurations, but under realistic execution budgets, it may miss failure-prone regions in the joint space of classical optimizer settings and quantum circuit parameters. This paper studies failure-guided fuzzing for HQC programs. It models a hybrid input as a pair of classical optimizer hyperparameters and quantum circuit parameters, and evaluates a two-phase strategy that first searches for non-convergent seeds and then locally fuzzes circuit parameters around those seeds. To understand where the gains come from, five budgeted strategies are compared: random hybrid testing, classical enumeration without fuzzing, random-seed local fuzzing, enumeration-seed local fuzzing, and concolic-seed local fuzzing. The study is implemented on a VQE instance and a QAOA MaxCut instance in Qiskit. The results show that failure-guided local fuzzing is the main driver of improvement over random testing, while concolic seed discovery provides additional benefits on VQE but is less stable on QAOA. These findings suggest that reusing failure information is a promising direction for HQC testing, but that the value of concolic seed discovery is workload-dependent.

Device-aware quantum simulation increasingly requires HPC-scale accelerators, yet secure supercomputers expose batch-scheduled execution environments rather than the interactive, backend-oriented interfaces expected by quantum software. The key obstacle is not only remote job submission: an HPC-hosted virtual QPU must preserve topology, native-gate, and calibration semantics across queue delay, scheduler allocation, compute-node isolation, and partial execution-side failures, without opening inbound paths into the cluster. We present HPC-vQPU, a service-export architecture for virtual QPUs on batch-scheduled HPC systems. HPC-vQPU separates a cloud-facing control plane, which owns device identity, task lifecycle, snapshot binding, and event projection, from an HPC-resident execution plane, which claims work and realises it through scheduler-backed GPU jobs. Coordination is exclusively outbound and agent initiated. The central abstraction is a topology- and calibration-aware device snapshot bound atomically at claim time and carried into execution as an immutable contract, making each scheduled job hermetic while preserving fresh device semantics. We implement HPC-vQPU at the Pawsey Supercomputing Research Centre using Setonix GPUs, Qiskit-Aer/cuQuantum, and IBM Fez calibration data. Production experiments show that service overhead is bounded and additive, while workload scaling remains confined to the simulator; calibration-bearing snapshots produce measurable output shifts; claim-time binding prevents stale execution after pre-claim device mutation; concurrent agents complete 50/50 tasks exactly once; and explicit recovery restores stale running tasks after agent failure. These results show that secure, scheduler-mediated HPC infrastructure can export device-faithful quantum simulation as an interactive virtual-QPU service.

We present an adoption-ready instructional module for introducing quantum superposition in a two-state system. The package combines a five-activity classroom sequence with grading-ready assessment materials organized around six conceptual barriers documented in the physics education research literature: interpreting superposition as physical splitting, confusing coherent superposition with classical mixture, making basis-change errors, misreading finite-sample fluctuations as changes in the underlying state, using inconsistent notation, and, in an optional extension, reasoning about ordered operations. The main claim is that the bottleneck for introductory quantum instruction is rarely the absence of a usable simulator, but rather the absence of a coherent activity sequence, barrier-targeted prompts, and aligned assessment tools that an instructor can deploy without additional development work. We make the instructional rationale explicit through backward mapping from documented barriers to activity prompts and rubric-based evidence. The resulting module is designed for a single 50-minute class meeting and can be implemented with the included notebook or adapted to comparable two-state quantum simulators.

Contextual combinatorial optimization (CCO) plays a critical role in decision-making under uncertainty, yet remains a significant challenge. We present Quantum End-to-End Learning (QEL), the first quantum computing-based end-to-end learning framework for CCO that leverages Quantum Approximate Optimization Algorithms. Inspired by the integration of state preparation and evolution in data re-uploading, we propose a context re-uploading phase-separator that jointly captures the complex relations among contexts, uncertain coefficients, and optimal solutions. This allows a contextual encoder to be seamlessly integrated within a quantum surrogate policy, enabling joint end-to-end training with a stationarity guarantee. Exploiting an optimization-aware structure grounded in physical principles that classical methods cannot readily leverage, our approach demonstrates practicality by directly training on task loss despite the discreteness and nonconvexity, while avoiding calls to NP-hard optimization solvers. QEL empirically achieves competitive performance while requiring substantially fewer parameters than classical benchmarks, highlighting its industrial-level potential for the future quantum era.

Public access to pulse-level and control-electronics interfaces in commercial quantum computing has bifurcated. This paper proposes a six-axis rubric for measuring control-plane openness, the layer between gate-level circuit specification and physical control electronics, defined operationally so that the same evidence produces the same grade across vendors. The rubric is validated three ways: a blinded re-grading pass that tests whether the cited evidence and the level definitions alone reproduce the recorded grades, a boundary-case methodology that fixes where each level begins and ends, and a published grading protocol that lets others reproduce and contest any cell. A time-point comparison anchored on the February 2025 removal of pulse-level access from IBM hardware establishes that the rubric measures change rather than describing a snapshot. The rubric is applied to thirteen commercial vendors across superconducting, trapped-ion, neutral-atom, and photonic modalities as of May 1, 2026, and one of the three harms it detects is demonstrated through a reproduction-access audit of five pre-2025 IBM Qiskit Pulse experiments, carried through to a structural port to Rigetti Quil-T. The catalog ships as a machine-readable artifact under CC-BY-4.0 with per-cell source URLs (https://doi.org/10.5281/zenodo.20163276). The readings will go stale; the rubric is the contribution that survives them.

What does a book look like to a quantum computer? This paper takes eight classical works of the Renaissance and its late-antique inheritance – from Augustine to Galileo – and runs each through a neutral-atom quantum processor. The bridge is graphs: each textual unit becomes an atom, and graph edges are physical blockade constraints for engineered exact unit-disk designs, or a 2D approximation to the semantic graph for natural texts. Three contributions follow. First, we introduce rigidity rho, a metric for how unique a book's structural backbone is – distinguishing Marguerite de Navarre's Heptameron (rigid, twelve-nouvelle hard core) from Boethius (fully fungible, every chapter substitutable). Second, we invert the pipeline: rather than extracting a graph from existing prose, we pick a target graph the hardware encodes natively, and write a book whose structure matches it. The twenty-nine texts written this way, collected under the name QOuLiPo, extend the OuLiPo tradition to graph-topological constraints and, together with the eight natural texts, form a benchmark distribution against which neutral-atom hardware can be tracked as it scales. Third, we run both natural and engineered texts on Pasqal's FRESNEL processor up to one hundred atoms; engineered texts reach high approximation ratios, the cleanest instances returning the exact backbone. A cloud-accessible quantum machine plus an agentic coding environment now lets a single investigator run this pipeline end-to-end. What is reported is an application layer, not a speedup – humanistic instances ready to load onto neutral-atom processors as they scale, already complementing classical text analysis. The Digital Humanities community has a stake in building familiarity with this hardware now: the engineered-corpus design choices made today fix the benchmark distribution future hardware will be measured against.

We investigate the suppression of matter-wave Talbot interference under environmentally induced decoherence. The system is modeled as an atomic beam diffracted by a periodic grating whose transverse dynamics is described within the paraxial approximation. Environmental coupling is introduced through an effective open-system model that exponentially damps spatial coherences between diffracted components, allowing a continuous interpolation between the coherent Talbot regime and the incoherent far-field diffraction limit. In addition to the usual intensity and transverse-momentum distributions, we analyze the local probability flow associated with the diffracted matter wave. The corresponding Bohmian, or hydrodynamic, representation is used here as a diagnostic tool fully equivalent to the standard quantum description, with no additional assumptions beyond the probability current of the paraxial wave field. In the present Talbot geometry, this analysis shows how decoherence progressively suppresses the carpet structure and smooths the transverse-momentum distribution, while the flow may remain organized into channels determined by the grating periodicity. The results illustrate, in a periodic matter-wave Talbot geometry, that the loss of visible interference and the degradation of the grating-defined flow-domain organization need not occur simultaneously. In particular, flux-channel structures can persist in parameter regimes where multislit interference features have already been strongly reduced. This distinction provides a local characterization of decoherence in matter-wave Talbot interferometry and complements previous trajectory-based analyses of coherence loss in simpler interference and confined geometries.

We investigate the spectral consequences of the uniquely determined Hermitian ordering of the Dirac Hamiltonian with spatially varying mass. In contrast to the nonrelativistic case, where continuous families of admissible prescriptions exist, the relativistic Dirac operator admits a single consistent ordering compatible with probability-current conservation. This requirement generates an additional logarithmic-gradient term proportional to the spatial variation of the mass profile. We show that this contribution modifies the effective kinetic operator and induces a universal deformation of the spectral quantization condition. In compact geometry, an explicit analytic computation reveals a mode-dependent second-order spectral shift that becomes strongly enhanced near the mass-inversion threshold. These results demonstrate that the consistent relativistic ordering of the Dirac operator leads to observable modifications of discrete spectra in spatially inhomogeneous scalar backgrounds.

We propose an adiabatic-elimination formalism in the dispersive regime based on a transition-centric perturbation theory. The perturbative expansion is recast into a diagrammatic framework, while adiabatic elimination is implemented through controlled projections onto transition subspaces. Our approach applies systematically at arbitrary perturbation order, and is suited to multilevel systems and multiple qubits in both cavity and waveguide quantum electrodynamics. It ultimately enables the explicit construction of effective higher-order Hamiltonians while bypassing important limitations of existing techniques, thereby providing a practical toolbox for multiphoton processes in the dispersive regime.

We introduce a framework where light-matter transitions, rather than states, are the primary dynamical objects. Successive compositions of elementary transitions yield multiphoton processes with compact diagrammatic bookkeeping of resonant and off-resonant pathways. This approach enables transparent derivations of effective high-order Hamiltonians in the dispersive regime, foundational to quantum-information applications. Applied to the paradigmatic Jaynes-Cummings model, our framework reveals a photon-number-independent intrinsic Rabi frequency and persistent polaritonic hybridization in the dispersive regime, unifying resonant and dispersive limits.

We propose a superconducting circuit based on the Bloch transistor, a quantum device consisting of two small-capacitance Josephson junctions, connected in series and having a small superconducting island in between. This device is driven by two dc electrical sources controlling Josephson oscillations of frequency $f_J = 2e\overline{V_J}/h$, related to the average transistor voltage $\overline{V_J}$, and Bloch oscillations of frequency $f_B = \overline{I_B}/2e$, related to the average current $\overline{I_B}$ injected into the transistor island. We show that due to the Bloch transistor properties, these two types of oscillations are coupled and can mutually phase-lock, i.e., $f_J = f_B$. This leads to the formation of a current step on the current-voltage curve at $\overline{I_B} = 2ef_J$, which is similar to the dual Shapiro step, appearing under microwave irradiation of frequency $f$ on the current-voltage curve of a small Josephson Junction at current $I=2ef$. Moreover, the Bloch transistor transconductance $\overline{I_B}/\overline{V_J}$ takes the fundamental value of $1/R_Q$, where $R_Q = h/4e^2$ is the resistance quantum. The obtained results pave the way to an alternative quantum standard of resistance, based on the superconducting circuit and operating without applying a strong magnetic field.

Achieving practical quantum advantage on fault-tolerant quantum computers (FTQC) is fundamentally constrained by the substantial spatial and temporal overheads required to map logical operations onto physical hardware. Existing compilation approaches typically adopt coarse-grained, slice-based abstractions that overlook fine-grained microarchitectural effects, such as routing contention, leading to inefficient resource utilization and limited alignment between algorithm structure and hardware capabilities. We introduce Qomet, a microarchitecture-aware compiler that tightly couples algorithmic properties with lattice surgery (LS) execution. By exploiting C-Phase gate commutativity, Qomet translates sequential operations into simultaneous multi-target interactions, natively leveraging LS to eliminate false dependencies and expose instruction-level parallelism. To support this, Qomet employs an adaptive, event-driven scheduler that captures precise spatial and routing constraints to overlap instructions temporally. By minimizing grid idling and routing contention, Qomet achieves a geometric-mean execution speedup of 4.29$\times$ and a maximum speedup of 59.7$\times$ across realistic workloads.

Quantum computing has demonstrated its potential to solve various optimization problems, including drone scheduling, which is important not only for drone delivery but also for logistics in general. However, one of the main obstacles is that practical drone scheduling settings typically require quantum resources that current hardware cannot provide. Therefore, in this work, we introduce a new Quantum Optimization via Coordinate Descent (QUACOD) approach to address this problem under the constraint of a limited number of available qubits. By leveraging coordinate descent, QUACOD decomposes the original high-complexity problem into multiple subproblems, which are then solved using quantum optimization. In our experiments, QUACOD outperforms the state-of-the-art (SOTA) quantum-based drone scheduling method not only in optimized drone completion times but also in scalability, handling up to 5 times more drones and 35 times more routes. In addition, QUACOD demonstrates that hardware-efficient circuits are effective for optimization problems. Together, these contributions advance quantum computing toward practical applications in the noisy intermediate-scale quantum (NISQ) era.

We introduce Graphical Algebraic Geometry (GAG), a family of diagrammatic languages extending the Graphical Linear Algebra programme. We construct several languages within this family and prove that they are universal and complete for the corresponding (co)span semantics of commutative algebras and affine varieties. This framework provides clear graphical representations of algebraic structures – such as polynomials, ideals, and varieties – enabling intuitive yet rigorous diagrammatic reasoning. We showcase two practical viewpoints on GAG. First, we show that instances of counting constraint satisfaction problem (#CSP) are recast as rewrite problems of closed diagrams in GAG. This means that deciding rewritability in GAG is #P-hard, and GAG can be viewed as a complete and compositional rewrite system for networks of polynomial constraints. Second, we characterize the qudit ZH calculus, a diagrammatic language for quantum computation, as an extension of Graphical Algebraic Geometry. This establishes the correspondence that Graphical Algebraic Geometry is to the ZH calculus what Graphical Linear Algebra is to the ZX calculus. Using this construction, we show that computing amplitudes in qudit ZH requires only a constant number of queries to a GAG oracle.

Inverse problems in scientific sensing are often solved with either hand-designed regularizers or supervised networks trained on simulated labels, yet both can fail when the forward model is nonlinear, spectrally coupled, and physically delicate. We study this issue for noise sensing based on nitrogen-vacancy (NV) centers in diamond, where a quantum sensor measures magnetic-noise spectra generated by sparse spin sources. We show that replacing a common scalar/coherent forward approximation with a tensor power-summed dipolar operator changes the inverse landscape and exposes a center-collapse failure mode in free-density optimization. We propose NeTMY, an amortization-free coordinate neural field coupled to the differentiable NV forward model, with annealed positional encoding, multiscale optimization, sparsity/gating, and spectrum-fidelity losses. Across sparse synthetic reconstructions generated by the corrected operator, NeTMY achieves the best localization and distributional metrics in the tested benchmark. Mechanism experiments show that NeTMY does not directly execute the raw density-space gradient; its parameterization smooths and redistributes updates, mitigating the center-collapse pathology. These results position NV quantum sensing as a useful testbed for physics-faithful neural inverse problems.

Solving non-linear Diophantine systems lies at the mathematical core of integer optimization and cryptography. While the general unbounded problem is undecidable, even over bounded integer domains it remains classically intractable in the worst case. In this work, we introduce a fully reversible quantum algorithmic framework tailored to solve arbitrary polynomial Diophantine equations over bounded integer domains. The core of our approach is the explicit, gate-level synthesis of an evaluation oracle for amplitude amplification. By coherently evaluating polynomial constraints via in-place two's complement arithmetic and routing operations into a single recycled accumulator, this garbage-free strategy achieves a compact and scalable synthesis of the underlying non-linear arithmetic. Through analytical derivations and empirical circuit simulations, we prove that the overall spatial complexity is bounded by $q = \mathcal{O}((n + d^2)\log_2 N)$ logical qubits for $n$ variables, maximum degree $d$, and interval length $N$. The non-Clifford Toffoli depth is upper-bounded by $\mathcal{O}(q^2)$. This structural scaling exponent remains invariant to the variable count, modulated linearly only by the coefficients' Hamming weights. By moving beyond abstract black-box assumptions, this explicit architectural synthesis guarantees that the necessary quantum arithmetic acts as a bounded polynomial overhead. This ensures a quadratic speedup over classical exhaustive search, whether retrieving a unique assignment or dynamically enumerating an unknown number of solutions.

Quantum machine learning (QML) aims to accelerate machine learning tasks by exploiting quantum computation. Previous work studied a QML algorithm for selecting sparse subnetworks from large shallow neural networks. Instead of directly solving an optimization problem over a large-scale network, this algorithm constructs a sparse subnetwork by sampling hidden nodes from an optimized probability distribution defined using the ridgelet transform. The quantum algorithm performs this sampling in time $O(D)$ in the data dimension $D$, whereas a naive classical implementation relies on handling exponentially many candidate nodes and hence takes $\exp[O(D)]$ time. In this work, we construct and analyze a quantum-inspired fully classical algorithm for the same sampling task. We show that our algorithm runs in time $O(\operatorname{poly}(D))$, thereby removing the exponential dependence on $D$ from the previous classical approach. Numerical simulations show that the proposed sampler achieves empirical risk comparable to exact sampling from the optimized distribution and substantially lower than sampling from the non-optimized uniform distribution, while also exhibiting exponentially improved runtime scaling compared with the conventional classical implementation. These successful dequantization results show that sparse subnetwork selection via optimized sampling can be achieved classically with polynomial data-dimension scaling on conventional computers without quantum hardware, providing an alternative to the existing quantum algorithm.

Semiconductor hole-spin qubits offer a promising route to quantum computation due to their weak hyperfine interaction, and strong intrinsic spin-orbit coupling enabling electric control of qubits. Scalable architectures, however, require coherent long-distance quantum state transfer, which is hindered in these systems by spin-orbit induced anisotropic exchange. Here we show that this limitation can be overcome by using an all-electric control protocol. By tuning the electric field strength, we identify discrete spin-orbit phase-matching conditions that restore near-perfect state transfer, independent of the rotation axis. Complementarily, controlling the electric field direction aligns the spin-orbit axis, suppressing excitation non-conserving processes and enabling robust transfer without fine tuning. Our results establish that electrical control of spin-orbit phases through either magnitude tuning or axis alignment as a practical route for robust quantum information transport in hole-spin quantum dot arrays.

Recent work has identified a dynamical squeezing phase transition in power-law interacting bilayer XXZ spin models, separating a fully collective phase with Heisenberg-limited squeezing from a partially-collective phase with universal critical scaling. Here we test and establish the universality of this transition along two qualitatively different microscopic axes: lattice geometry, by studying square, triangular, and honeycomb $2\mathrm{D}$ bilayers as well as $1\mathrm{D}$ ladders, and a symmetry-preserving rescaling $\lambda$ of the interlayer couplings relative to the intralayer ones. Combining a Bogoliubov instability analysis with discrete truncated Wigner simulations, we find that the transition persists across all four lattice geometries and over a wide range of $\lambda$ with critical exponents consistent within error, providing strong evidence for a genuine non-equilibrium universality class. The Bogoliubov theory recovers the previously identified scaling $a_Z^* \propto L$ in the long-range interacting regime $\alpha < d+2$, and yields an analytical scaling $a_Z^* \propto L^{2/(\alpha-d)}$ for the critical aspect ratio with system size for $\alpha>d+2$, with $\alpha$ the power-law exponent in dimension $d$. This uncovers a previously unrecognized sub-linear regime for short-range interactions. By tuning $\lambda$ we vary the interlayer coupling strength at fixed layer spacing, demonstrating that the dynamical transition can be driven purely through interaction engineering without modifying the underlying geometry. These findings provide a versatile route toward controlling entanglement generation in Rydberg-array, polar molecule, and trapped-ion platforms with applications in quantum sensing and simulation.

We construct families of deformations of the double-scaled SYK (DSSYK) model and investigate their bulk interpretation. We introduce microscopic deformations of the SYK model which, after ensemble averaging and in the double-scaling limit, are described by a transfer matrix encoding the recurrence relations of basic orthogonal polynomials in the q-Askey scheme. For certain families of deformations in the semiclassical limit at finite temperature, the chord number (encoding Krylov complexity) corresponds to the length of an Einstein-Rosen bridge connecting an End-Of-The-World brane to an anti-de Sitter asymptotic boundary. By increasing one of the deformation parameters, the models eventually exhibit discrete energy levels, signaling a new geometric transition in sine dilaton gravity. Via the SYK-Schur duality, Krylov complexity also admits a representation-theoretic interpretation as the spread of the SU(2) spin in the index of an $\mathcal{N}=2$ SU(2) gauge theory. We study the operator algebras of the deformed theories. The algebras can be type II$_1$ or type I$_\infty$ factors, depending on the operators that are included. The entanglement entropy between the type II$_1$ algebras for a pure state manifests as an extremal surface through the Ryu-Takayanagi formula. We discuss connections between our results and the emergence of baby universes in the bulk.