Papers

Quantum Tanner codes are a recently developed family of quantum error-correcting codes characterized by favorable asymptotic performance characteristics. Despite their theoretical potential, practical decoding algorithms that effectively leverage their structural properties remain limited. This work introduces LEAD (Local Ensemble-Assisted Decoder), a structure-aware decoding framework tailored for quantum Tanner codes. The proposed scheme leverages the decomposable structure of Cayley complexes to project the global code onto overlapping local subcodes defined by vertex neighborhoods, where error probabilities are estimated in parallel. To ensure global consistency, LEAD utilizes the inherent topological symmetry of the complex and introduces a soft-information regularization mechanism to mitigate local overconfidence during information aggregation. This framework enables highly parallelized, low-complexity decoding that is intrinsically compatible with various local search heuristics. Simulation results demonstrate that LEAD achieves significantly lower logical error rates than standard decoding framework while substantially reducing the average decoding latency and iteration count.

The extraction of weak signals plays a crucial role in quantum precision measurement, where the estimation results are often limited by low signal-to-noise ratios. Here, we demonstrate a parameter-estimation framework based on the adaptive extended Kalman filter for dynamic magnetic-field estimation in quantum systems using spin-noise measurements – a challenging regime characterized by weak signals. By modeling the magnetic field as an unknown parameter, the proposed approach alleviates model dependence in state estimation. Furthermore, by introducing an adaptive algorithm with real-time noise estimation, our method overcomes the measurement noise intensity constraints of conventional extended Kalman filtering and enhances its practical applicability. Numerical simulations covering three representative magnetic-field dynamics validate the capability of the proposed framework, while experimental results demonstrate successful tracking of a seismo-magnetic-like signal beyond the intrinsic sensitivity of conventional spin-noise spectroscopy.

As quantum computing scales toward practical workloads, future systems are expected to move beyond single monolithic processors toward modular architectures that connect multiple QPUs. Different platforms realize this modularity through different communication models: superconducting systems rely on real-time classical links and dynamic-circuit coordination, trapped-ion systems use photonic interconnects for remote entanglement, and neutral-atom systems provide strong intra-core connectivity with proposed optical links for inter-core communication. This heterogeneity makes communication-aware scheduling essential for shared modular quantum cloud environments. We present InterQ, a communication-aware scheduler for modular QPU architectures with heterogeneous communication models. InterQ jointly considers qubit capacity, placement, parallel execution, and communication-driven dependencies across distributed subcircuits, while enabling adaptive circuit cutting to reduce makespan while balancing fidelity and communication overhead. The framework distinguishes classical-link execution, where measurement and feedforward impose synchronization constraints, from quantum-link execution, where entanglement distribution and state transfer determine coordination cost. Using a unified simulation framework to compare superconducting, trapped-ion, and neutral-atom modular systems, InterQ shows how communication models and scheduler-driven cutting decisions affect throughput, latency, and fidelity. Across evaluated workloads, InterQ exposes an architecture-dependent tradeoff: neutral-atom modular QPUs achieve the highest fidelity, superconducting systems minimize runtime, and trapped-ion systems provide a balanced intermediate profile across fidelity and makespan.

Optical neural networks promise ultrafast, low-energy information processing by performing computation directly with photons. Current implementations, however, are largely restricted to steady-state operation and rely on high-latency electro-optical conversion for nonlinear activation. To address these limitations, we propose an all-optical fully connected neural network architecture in which the basic neuronal functions are realized by coherent transient quantum dynamics. Within this framework, phase-tunable nonlocal interference in a giant cavity implements programmable synaptic weights; an integrator operating in the bad cavity regime performs temporal summation by coherently combining sequential wavepackets; and transient Rabi dynamics of a driven two-level system provide nonlinear activation. Full-physics simulations demonstrate high classification accuracy on MNIST and colored-object recognition tasks. These results eliminate the optoelectronic activation bottleneck, reduce latency, and establish transient light-matter dynamics as a native physical resource for high-dimensional nonlinear information processing, paving the way toward fully optical neuromorphic computing.

The force experienced by a spin in a magnetic field gradient underlies many proposals for hybrid quantum systems. These include schemes for mechanically mediated quantum gates, spin squeezing, searches for exotic forces, and motional superpositions for probing the interface between quantum and gravity. Yet, experimentally observing this spin-force for anything larger than atomic scales has proved challenging. In our work, we demonstrate controllable Center-of-Mass motion of a $128 \rm\: mg$ diamagnetically levitated oscillator due to force from an ensemble of Nitrogen-Vacancy (NV) defects in diamond. We induce coherent motion in the oscillator by periodic optical initialisation of the NV spin states, achieving motional amplitudes exceeding $100 \rm\:nm$. Our results mark a key milestone towards spin-based engineering of motional states deep in the high-mass regime.

Heterogeneous integration of gain and strongly nonlinear materials with ultra-low-loss silicon nitride (SiN) photonics offers a route to scalable quantum circuits, but concurrent wafer-scale manufacturability, low interlayer loss, and high performance have been challenging to realize. Here we demonstrate a wafer-scale III-V-on-SiN quantum photonic platform that directly integrates III-V layers to foundry-fabricated SiN circuits. The SiN layer provides 200-300 nm thick waveguides with $<1$ dB/m loss and a mature passive photonics ecosystem, while III-V materials provide large $\chi^{\left(2\right)}$ and $\chi^{\left(3\right)}$ nonlinearities for parametric gain, frequency conversion and quantum light generation. Adiabatic interlayer couplers yield $<25$ mdB loss to InGaP waveguides and resonators with intrinsic quality factors exceeding $10^6$, enabling $15\times$ brighter entanglement sources and efficient nonlinear conversion on SiN. Integrated components–including low-loss beam splitters, waveguide crossers, and tunable interferometers–are complemented by III-V lasers and InP photodetectors with amplifiers achieving up to $99^{+1}_{-12}\%$ quantum efficiency and $3$ GHz bandwidth. This architecture unites ultra-efficient sources, nonlinear elements and detectors on a wafer-scale, low-loss platform, establishing a path toward large-scale, low-noise quantum photonic systems.

The electronic distribution of a molecular domain is examined in this study. A theoretical formulation of quantum molecular properties is presented using the Quantum Expectation Identity theorem (QEI), with a focus on the three-state model of the density matrix for the quantum state of a molecular domain as an open system. The report examines the relationship between ab initio statistical fluctuation-correlation theorems for quantum observables and their derivatives. We focus on three main quantities of a domain: the electronic population, its chemical potential, and its maximum capacity for accepting or donating charge with the neighbors. The analytical expressions for the quantities are presented and discussed in detail. At the end, we explore the concept of quantum purity and its proper application in the molecular domain.

We introduce a quantum Viterbi decoding algorithm for hidden quantum Markov models (HQMMs) motivated by quantum information processing and quantum algorithms. Given a finite sequence of measurement outcomes, the algorithm identifies hidden quantum trajectories that maximize a joint decoding functional, serving as a genuine quantum analogue of the classical Viterbi score. Unlike classical hidden Markov models, where decoding optimizes over a finite discrete state space, our method performs optimization over a continuous manifold of pure quantum effects, thereby exploiting coherent superpositions in the hidden memory. We prove a strict quantum advantage: coherent hidden trajectories can achieve decoding scores that strictly exceed any classical strategy constrained to diagonal (commuting) effects, even when both models share the same observed statistics. These results position quantum Viterbi decoding as a concrete quantum algorithmic primitive for sequential decision-making, with direct applications to quantum memories, quantum communication with memory, and near-term quantum machine learning on NISQ devices.

Teleportation through a non-maximally entangled pair, e.g., $\ket{\psi(\theta)}_{AB}=\cos\theta\ket{00}+\sin\theta\ket{11}$, induces a noisy channel and cannot achieve deterministic unit-fidelity transmission unless $\theta=\pi/4$. We introduce a framework of assisted quantum teleportation in which a third party (the “Bank”) supplies auxiliary multipartite entanglement to restore a perfect Bell pair on the original $AB$ registers. We analyze two operational roles for the Bank: a Bank-measures model (measurement and broadcast) and a transfer model (the Bank transfers its subsystem and then leaves). For GHZ-class and W-class assistance we derive explicit feasibility regions for deterministic restoration and show an operational inequivalence for W resources. We further characterize finite-shot optimal success probabilities for probabilistic restoration and formulate Bank-measures feasibility for general pure Bank resources as a minimax optimization.

Quantum batteries utilize nonclassical resources to achieve charging speed and energy storage performances that surpass classical thermodynamic limits. However, the practical realization of quantum batteries is often constrained by the inevitable environment-induced dissipation of both stored ergotropy and coherence. To actively counteract these losses, we propose a dual-channel coherence framework that exploits dark-state protection to stabilize ergotropy. We conduct, for the first time, an investigation of the synergistic interplay between internal charger coherence and reservoir squeezing, the latter acting as a source of external coherence. In the resource-efficient regime where charger and battery sizes are comparable, our study shows that internal charger coherence and reservoir squeezing jointly enhance the transient charging power. Crucially, initial charger coherence is the fundamental resource for maximizing and stabilizing steady-state ergotropy through dark-state protection. Our analysis reveals that these advantages are driven by the buildup of local battery coherence, which emerges from the integration of both internal and external coherence sources. These results offer a robust pathway for high-power, stabilized energy storage in quantum architectures.

Cardinality-constrained portfolio selection is routinely cast as a quadratic unconstrained binary optimization (QUBO) and submitted to a quantum processing unit (QPU) for direct annealing. We show that this standard penalty encoding is the binding constraint for direct-QPU execution on current D-Wave Pegasus and Zephyr hardware. Expanding the exact cardinality penalty contributes a dense rank-one term that makes the logical interaction graph complete regardless of the covariance, producing chain-break fractions from 83% at small universes up to 92% at the full forty-nine-industry Fama–French universe, and zero feasible raw samples at every tested scale. Topology-aware sparsification reduces chain breaks to near zero, but any sparsifier that removes off-diagonal entries also dilutes the cardinality constraint; an ablation reveals that this sparsify-and-project pipeline is dominated by the classical projector, not the QPU. We propose removing the penalty entirely: sample an objective-only QUBO built from expected returns and the risk-scaled covariance on hardware, and enforce cardinality classically through a deterministic feasibility projector. Across 4,468 saved embedding records on live Pegasus and Zephyr hardware, spanning equities up to forty-nine assets and football-betting instances up to forty-eight, this penalty-free pipeline reduces mean chain-break fractions from 71%–92% down to at most 0.04%, and post-processed regret is at most 0.03% relative to greedy classical references at every tested scale. We do not claim quantum advantage; the penalty encoding, not the sparse hardware topology, is the limiting factor for direct-QPU portfolio optimization at currently accessible scales.

Hybrid quantum-classical solvers conceal how reported performance divides between quantum-processing-unit (QPU) access and other service time. We audit D-Wave's Leap service on cardinality-constrained mean-variance portfolio instances from N=10 to 640, comparing constraint-native CQMs, penalty-encoded BQMs, Gurobi MIQP, simulated annealing, and a matched-budget Tabu baseline, and we propose a four-metric operational audit of the exposed timing fields. LeapHybridCQM matches Gurobi's proven optimum on all 54 head-to-head instances at N<=120, yet its mean QPU access is 0.034 s: 0.68% of the nominal five-second budget; telemetry does not resolve the residual into classical computation, orchestration, or budget granularity. Across 108 fixed-seed five-second CPU runs on 36 instances, TabuSampler reaches CQM-level objectives with mean absolute delta 0.00078 (maximum 0.00798); at N in {400,640} the mean is 3.04e-5. This establishes classical objective achievability, not an internal QPU ablation. We prove that quadratic encoding of exact cardinality adds a dense rank-one term and, apart from isolated exact coefficient cancellations, yields a complete logical graph independent of covariance support, with a bounded-degree embedding lower bound; the resulting density collapse is consistent with hybrid-BQM degradation. A descriptive five-window Fama-French overlay of post-projection direct-QPU portfolios yields mean Sharpe 1.94 versus 2.22 for 1/N. These results do not establish a quantum-sampling advantage; they motivate reporting QPU wall-clock fraction, optimality gap, density amplification, service-output variance, and matched-budget classical controls, keeping operational accounting separate from causal attribution.

Reverse annealing initializes a programmable quantum annealer in a chosen classical state, reintroduces quantum fluctuations down to a pause point, and returns to readout; repeated cycles form a configurable dissipative dynamics whose schedule knobs are routinely treated as a temperature. On mixed-frustration 12-qubit Ising instances on two D-Wave generations (Advantage2 and Advantage_system6.4), we measure schedule-driven redistribution of the subsystem readout and calibrate each schedule's effective scales, using exhaustive enumeration of the $2^{12}$ configurations, a locked analysis plan with a prior-knowledge disclosure, and regenerated classical reference families. First, schedule shape redistributes basin occupation: 11 of 20 random instances respond to a single-pause-to-two-pause change (15 of 20 for long-hold; block permutation, FDR-controlled), with shifts up to 38 percentage points and changes of dominant-configuration identity. Second, the single-qubit probe temperature does not transfer to the many-body problem: moment-matched inverse temperatures span 0.63-9.1 against a probe value of 7.22, and pause depth and duration each shift the scale on most instances (19/20 and 15/20). Third, no observation requires more than the tested classical families: with update budgets extended below one sweep per cycle, all 33 (device, instance, schedule) cells are reproduced within the tested family (minimum intersection-union $p=0.76$), and schedule-aware spin-vector Monte Carlo brings the late-window statistics within semiclassical reach. A pre-registered linear predictor fails on held-out instances, and an earlier pilot's two-pause enhancement claim is contradicted (Fisher $p=0.0013$). Reverse-anneal schedules are instance-specific basin-occupation controls whose effective scales must be calibrated per instance and schedule; nothing here licenses a quantum-mechanistic reading.

This note contains a simple construction of complete sets of MUBs, using bent functions to write the new basis vectors as explicit linear combinations of the standard basis.

Ordered realizations of discrete POVMs are studied through a residual transform generated by sequential tests. One application of the transform replaces each coordinate by the effect obtained after all earlier tests have failed, and appends the remaining mass as a terminal outcome. Under natural hypotheses, iterating the transform produces a collapsed POVM whose non-escape coordinates are the parts of the original effects that survive all earlier tests. The resulting collapse map gives an equivalence relation on ordered POVM realizations. Its range and fibers are characterized. The range consists of collapsed POVMs, whose non-escape coordinates are mutually orthogonal and whose support projections strongly sum to the identity. The fiber over a collapsed POVM consists of all ordered realizations with the same residually visible compressions. In particular, different ordered realizations, including ones with different off-diagonal coupling data, can have the same collapsed image. After collapse, the non-escape coordinates are fixed under further residual iteration. The remaining dynamics takes place in the escape effect, which is fragmented by a universal scalar functional calculus.

Quantum kernel methods have emerged as a promising approach for leveraging high-dimensional feature spaces in machine learning, particularly in domains where classical kernel methods face scalability limitations. In this work, we present the first large-scale study of fidelity-quantum-kernel support vector machines for hyperspectral data classification without requiring heavy prior feature selection or dimensionality reduction. By simulating quantum kernels using tensor network contraction techniques and GPU acceleration, we overcome the computational bottlenecks traditionally associated with quantum models, achieving quadratic scaling O(n^2) in the number of qubits. Our approach enables the evaluation of quantum kernels on hyperspectral data with hundreds of spectral bands, aligning quantum feature spaces with real-world remote sensing applications. We provide an in-depth analysis of kernel bandwidth optimization, demonstrating its crucial role in mitigating exponential concentration effects and ensuring the model's ability to generalize. Experimental results on binary classification (Indian Pines and Methane Detection) and multiclass classification (Indian Pines) demonstrate that quantum kernels achieve competitive performance compared to a broad range of state-of-the-art classical baselines. As illustrative cases, on four 50-band splits selected from Indian Pines, the quantum model achieved a 78.0 pm6.2% accuracy for a binary classification task compared to 72.0 pm5.0% for the standard radial basis function (RBF) kernel. For a four-class classification task, the quantum kernel reached 83.3 pm3.1% accuracy, outperforming several state-of-the-art baselines. On five 75-band splits selected from the Methane Detection dataset, the quantum approach yielded 58.5\pm5.0% accuracy versus 55.1\pm2.5% for the classical counterpart...

In a recent paper it was shown that all the Hilbert space formulas for quantum probabilities can be realized as functions of geometric properties of the associated projective space, but those functions were expressed using the structures of the associated Hilbert space. In this paper a direct description of all these probabilities is given as formulas involving only the geometric properties of the projective space itself without referring to the associated Hilbert space theory. In large part this depends on a projection theorem for complex projective space which is analogous to the projection theorem for Hilbert spaces. The importance of this is that this exhibits quantum probability in terms of the geometry of a Riemannian metric in a non-linear Kähler manifold without any reference to a linear Hilbert space. As such this is a part of a larger program of the geometrization of physics. This opens the possibility of generalizations of quantum theory in other similar geometric settings. The theory presented includes projective spaces of both finite and infinite dimension. Some comments explain how quantum theory based on a von Neumann algebra is compatible with this approach.

This thesis studies two distinct frontiers of quantum information processing: the fundamental physical limits of dynamical evolution and the practical realization of secure quantum communication networks.

This Letter shows that a supersymmetric structure is inherent to the time space inverted (TSI) quantum mechanics (QM) framework, where the spatial evolution of states is generated by the operator $\hat{\mathcal{P}}^{\pm}(\hat{\mathcal{H}},\hat t;q)=\pm\sqrt{2m[\hat{\mathcal{H}}-\mathcal{\hat V}(q)]}$ [\href{https://doi.org/10.1103/PhysRevA.95.032133}{Phys. Rev. A. 95, 032133 (2017)}], named here Momentunian, whose square-root structure that can be factorized. Such factorization leads directly to a supersymmetric algebra with supercharges and partner Hamiltonians. For the relativistic Momentunian the zero mode states are shown to be evanescent states, independent of the physical potential. Furthermore, the existence of non-relativistic and relativistic Momentunian partners is demonstrated, whose zero-mode states are no longer necessarily zero energies, but vanishing momenta states. The natural emergence of the $1/2$-fractional time derivatives in the TSI QM, leads to supercharges which incorporate memory effects into the supersymmetric wave functions. Results indicate that supersymmetry emerges as a structural property of the TSI QM rather than being imposed phenomenologically.

Searches for axion and axionlike dark matter based on solid-state spin qubits are fundamentally limited by strong longitudinal dephasing, which rapidly suppresses the sensitivity gains offered by entanglement. Here we show that quantum error correction (QEC) can substantially enhance axion search sensitivity in realistic semiconductor spin qubit platforms by mitigating this dominant noise source. By integrating an optimally chosen repetition code QEC with logical GHZ block entanglement, we derive closed-form expressions for the quantum Fisher information that explicitly incorporate the finite coherence time of the axion field. Our analysis demonstrates that modest QEC cycle frequencies are sufficient to significantly reduce the effective dephasing rate, thereby restoring a broad parameter regime in which entanglement-enhanced sensing surpasses the standard quantum limit. Projecting these results onto CMOS-compatible device parameters, we find that QEC-protected entangled sensing can revive otherwise inaccessible quantum advantages, yielding up to order-of-magnitude improvements in sensitivity to the axion-electron coupling $g_{ae}$. These results establish a practical and theoretically controlled pathway for using QEC to improve qubit array searches for physics beyond the Standard Model.

The nonadditivity of channel capacity is a defining feature that distinguishes quantum communication from classical communication. In the quantum realm, the channel capacity is determined by coherent information, which is defined through the von Neumann entropies of the output and its environment. Despite its fundamental importance, experimental evidence of such nonadditive quantum communication has been elusive because of the complexity of the required quantum channel. Here, we experimentally observe entropic-singularity-induced coherent-information nonadditivity using the qutrit platypus channel implemented on a photonic platform. By preparing six-dimensional photonic entanglement, we directly measure the coherent information of a platypus channel, a qubit amplitude damping channel, and their joint uses, revealing a clear violation of additivity. Quantum process tomography further reveals the entropic singularity responsible for this effect, demonstrating how singular entropy landscapes in low-dimensional channels can enhance quantum communication beyond additive limits.

We present a quantum attack on ML-KEM and related 2-power cyclotomic lattice schemes. Combining with Parts I-III, we provide an algorithm and verify the resulting approximation factor satisfies $\gamma\le 21 < q/2=1664.5$ for ML-KEM-1024, with a success probability $\ge 0.99$. We apply a tower decomposition of the Principal Ideal Problem (PIP) through the chain $\Q\subset \Q(\zeta_8)\subset\cdots\subset \Q(\zeta_{2^k})$ which yields a polynomial-time quantum algorithm costing $O(n^3 \log^2 n)$ gates, $O(n^2 \log n)$ qubits, and poly$(n)$ classical bit operations. We extend the analysis to Falcon, Hawk, and NTRU over 2-power cyclotomic rings with polynomial-time quantum algorithms.

We prove that the $L^2$ CVP distance from a random short ring element to the log-unit lattice of $\Q(\zeta_{2^k})$ converges to $\frac{\pi}{2\sqrt{6}}\sqrt{n}$ as $n=2^{k-1}\to\infty$. We then show that this target lies inside the Voronoi cell of the origin for $k\ge 4$. For the $L^\infty$ norm, the maximum over $n$ sub-Gaussian coordinates yields $O(\sqrt{\log n})$ which translates into a sub-polynomial approximation factor for the Short Generator Problem. We show a Coarse Lattice Theorem that Babai's algorithm returns zero for all structured targets, yet exactly recovers unit perturbations of arbitrary size. For module determinant ideals, we further prove the Trigamma Theorem that proves an intrinsic imbalance $\sigma_{g_0}=O(1)$ independent of the modulus $q$. Finally, combined with Parts I and II, we reduce the CDPR factor for ML-KEM from $\exp(\tO(\sqrt{n}))$ to a sub-polynomial value.

Non-classical photon sources made of semiconductor quantum dots (QDs) emitting in the telecommunication C-band are crucial components for low-loss, long-distance photonic quantum communication networks. Here we designed and fabricated strain–free In$_{0.7}$Ga$_{0.3}$As/In$_{0.7}$Al$_{0.3}$As QDs grown on GaAs(111)A substrates working as single-photon emitters in the 1550 nm window. The QDs were grown via local droplet etching method in a molecular beam epitaxy environment, employing a thin In$_{0.7}$Al$_{0.3}$As metamorphic buffer layer with the same lattice constant of the QD material, thus allowing for a completely strain–free self-assembly of the QDs. The QDs exhibit a C$_{3v}$ symmetry with a ground state emission in the 1400–1600 nm range. The exciton lifetimes of $\approx$ 1.3–1.9 ns and linewidths as low as $\approx$ 300 $\mu$eV show the good quality of the fabricated QDs. Second-order autocorrelation measurements under pulsed excitation confirmed the single-photon purity of the emitters, yielding a $g^{(2)}(0)$ value of $0.141 \pm 0.027$

Quantum error correction (QEC) is indispensable for realizing fault-tolerant quantum computation, yet its effectiveness hinges critically on the classical decoding algorithm that interprets noisy syndrome measurements. Among all possible decoding strategies, maximum likelihood decoding (MLD) is provably optimal, since it identifies the logical group with largest likelihood by summing over all possible errors within logical class consistent with the observed syndrome. Despite its optimality, MLD is computationally intractable in general (#P-hard), motivating a rich landscape of exact and approximate algorithms. In this topical review, we provide a unified perspective on MLD by surveying recent advances through three complementary lenses: statistical mechanics, tensor networks, and artificial intelligence. From the statistical mechanics viewpoint, the MLD problem maps onto evaluating partition functions of disordered spin models, enabling exact solutions for certain codes and noise models as well as threshold estimation via phase-transition analysis. From the tensor network perspective, approximate contraction of tensor networks on the code's factor graph yields decoders that closely approach MLD accuracy with polynomial computational cost. From the artificial intelligence perspective, neural-network-based decoders, including autoregressive generative models and recurrent transformers, learn to approximate the MLD distribution from data, achieving high accuracy with the parallelism afforded by modern hardware accelerators. We discuss the connections among these three approaches, review their application to both simulated and experimental quantum hardware, and outline open challenges including real-time decoding, scalability to large code distances, and generalization to high-rate quantum low-density parity-check codes.

Marine oil spills require rapid detection to mitigate severe ecological and economic damage. While satellite-based Synthetic Aperture Radar (SAR) provides essential all-weather monitoring, analyzing this data remains challenging. Deep learning models often require massive datasets and incur high latency. To address this, a pixel-wise quantum-assisted Support Vector Machine (QSVM) bagging ensemble is developed. Quantum annealing is leveraged to optimize the support vectors of individual weak SVMs on small data subsets, which are then classically aggregated. The approach is evaluated on Sentinel-1 imagery using both quantum simulation and physical quantum annealing hardware. The quantum-assisted pipeline achieved performance comparable to a rigorous classical baseline, yielding an Intersection-over-Union (IoU) of 0.60 and a balanced accuracy of 0.89. Complementary experiments with gate-based quantum computing demonstrated similar segmentation accuracy, although the annealing approach offered superior inference efficiency. Generalization was further assessed on independent oil spill imagery from the Strait of Hormuz, demonstrating the potential transferability of the trained pipeline to geographically distinct spill events. These results establish the feasibility of quantum-assisted, segmentation pipelines for near-real-time environmental monitoring.

We use nearly parallel pure states to characterize positive linear functionals $\phi$ on $\mathbb{M}_n$ as positive multiples of the trace if and only if $\phi(A \natural B) \leq \sqrt{\phi(A) \phi(B)}$ for all positive definite matrices $A$ and $B$. Here $A \natural B = (A^{-1} \# B)^{1/2} A (A^{-1} \# B)^{1/2}$ represents the spectral geometric mean. For further clarification, we establish novel characterizations through the inequality $\phi(A \natural B) \leq \phi((A+B)/2)$ for all positive definite matrices $A$ and $B$. We also present a trace inequality related to quantum fidelity that applies to all positive definite matrices, and demonstrate that it does not characterize the trace.

We develop a mathematically rigorous framework for simulating multiscale physical systems using quantum computational resources, by translating the language of asymptotic-preserving (AP) schemes into the formalism of quantum channels and Lindbladian dynamics. For stiff open quantum systems governed by singularly perturbed generators $\cL_\eps = \eps^{-1}\cL_{\mathrm{fast}} + \cL_{\mathrm{slow}}$ with $\eps \to 0$, we prove that layered quantum protocols, which implement fast-scale relaxation via native analog evolution or analytic manifold projection, converge uniformly in the diamond norm to consistent discretizations of the limiting slow dynamics, with explicit error bound $\mathcal{O}(\eps\Delta t + \Delta t^2)$ independent of stiffness. We establish precise resource-complexity bounds showing that superlinear gate-count savings $\Omega(\kappa\cdot(d_{\mathrm{tot}}/d_{\mathrm{slow}})^c)$ arise if and only if fast dynamics are resolved via (i) hardware-native analog evolution, or (ii) analytic adiabatic elimination reducing effective Hilbert space dimension. The framework is illustrated through cavity QED in the bad-cavity limit and a quantum-inspired AP discretization of kinetic equations converging to fluid limits, with quantified error propagation in trace and diamond norms. This work provides a principled mathematical bridge between classical multiscale numerical analysis and quantum simulation algorithms.

This work provides an overview of key historical developments in the formulation of the Second Law of Thermodynamics, focusing on the notorious challenge of “Maxwell's Demon”, a hypothetical creature who could presumably violate that law. It begins by recalling Maxwell's challenge and discussing the apparent loophole in the Second Law that appears to make such a violation possible. An alternative formulation of the Demon challenge by Szilard is considered, along with his attempted defeat of the Demon through reference to measurement. A similar effort by Brillouin is also analyzed. The proposal of Bennett to defeat the Demon through the requirement of memory erasure is critically discussed. Finally, it is proposed that the Second Law gains a firm foundation through neglected features of quantum theory. In particular, an application of the Heisenberg Uncertainty Principle is shown to decisively defeat the Demon, as well as to serve as justification for Landauer's Principle, albeit in terms distinct from the usual computational formulation.

Quantum error correction (QEC) is essential for building fault-tolerant quantum computers, requiring decoders that are simultaneously accurate, fast, and scalable. Most state-of-the-art neural decoders achieve high accuracy but process the full dense syndrome array of size $O(d^2 R) $regardless of the actual error rate, where d is the code distance and R is the number of measurement rounds. At physically relevant error rates (p ~ 0.1%), fewer than 5% of syndrome entries contain active detection events – yet existing decoders process the entire syndrome volume. We introduce the Sparse Mamba Decoder (SMD), a defect-centric neural decoder that processes only the k active detection events using a 13-dimensional feature representation per defect and a Mamba state-space backbone, achieving $O(k)$ complexity. Across depolarizing, uniform circuit-level, SI1000, and Google Sycamore experimental benchmarks, SMD reduces the MWPM logical error rate by up to 49% at $d \le 5$ under SI1000 noise, runs 95-467x faster than the Tesseract near-MLD decoder and 232-463x faster than Belief Matching, and maintains nearly constant latency (24-57 us) across d = 3-9 under uniform circuit-level noise. On the Sycamore experimental dataset, the SMD ensemble matches or slightly surpasses the dense Mamba decoder of Varbanov et al. All results are obtained on commodity NVIDIA GPUs with 7.5-16M parameters, without specialized accelerators.