Quantum Approximate Optimization Algorithm

In wireless communication networks, many resource optimization problems are nondeterministic polynomial-time hard (NP-hard) due to their combinatorial nature and high computational complexity. Recently, neutral-atom-based quantum computing has emerged as a promising platform for efficiently solving such problems by leveraging quantum superposition and entanglement. However, its application to wireless communication optimization problems remains largely unexplored. In this paper, we investigate the use of neutral-atom quantum platforms to solve the maximum access problem (MAP), formulated as a mixed-integer programming task that jointly considers admission control, user clustering, channel assignment, and power allocation in a non-orthogonal multiple access (NOMA)-enabled uplink network. To reduce the computational burden, the MAP is equivalently reformulated as a maximum independent set (MIS) problem in graph theory. This reformulation enables the use of the neutral atom platform based on Rydberg atom arrays, where the MIS problem is naturally encoded into the physical geometry and blockade constraints of the quantum system. Numerical results demonstrate the feasibility and potential of this approach for addressing large-scale wireless resource optimization problems.

We study the use of graph neural networks (GNNs) for finding approximate ground states of Ising models. Efficiently finding these ground states is of broad significance because many combinatorial optimization problems can be formulated as an Ising model with the appropriate choice of couplings and fields. Exactly solving these problems is hard but there are many good heuristic methods. A lineage of these heuristics build from mean-field approximations: one approach uses the leading eigenvector of an appropriately defined matrix, another is the min-sum algorithm, also known as the energetic cavity method. Without modification, GNNs perform worse than both of these methods. We consider small modifications to the GNN to incorporate these heuristics and find that this considerably improves performance. While the modified approach is competitive against other deep-learning approaches, we still find that simulated annealing is reliably at least as good as deep learning methods for the same computational cost.

Graph coarsening reduces the large Quadratic Unconstrained Binary Optimization (QUBO) formulations arising when vehicle-routing problems are solved by quantum annealing. Nearby customers with compatible time windows are merged into super-nodes, the reduced problem is solved, and the solution is expanded to the original graph. For the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW), existing coarsening heuristics require family-specific tuning and remain unreliable on random instances. We address these limitations on the Solomon benchmark using simulated annealing and a D-Wave Advantage2 processor. We first introduce adaptive penalty calibration. Uniform penalty scaling has little effect, whereas controlling the internal coefficient range substantially improves raw samples. Removing non-binding constraints, normalising binding ones, and scaling the remaining penalties reduces mean raw constraint violations from 33.0 to 0.06 at the same solver budget (p=3.7e-11, n=56). A variable-count-preserving control attributes this gain to conditioning rather than problem size. Second, we replace the hand-tuned merge score with a graph neural network (GNN) using one configuration across all families. At N=10, it achieves 100% feasibility across all Solomon families, including R-type (100% vs. 80% for the tuned heuristic). Across N=10,...,100, feasibility is 83% vs. 69%, with the GNN better or tied on 85/90 instance-size pairs. At N=80,100, the difference is significant (p=0.002; 25/25 pairs), while the QUBO remains approximately 5-6 times smaller. Finally, hardware experiments reproduce the conditioning effect at fixed logical variable count: feasible samples increase from 0.02% to 39% across 13 instances. Classical repair with local search remains a reference bound for end-to-end solution cost.

Airport landside traffic centers connect terminal arrivals with taxis, ride-hailing vehicles, private cars, buses, metro services, parking facilities, and terminal-area roadways. Peak arrivals can create coupled congestion across passenger queues, vehicle queues, pickup berths, storage areas, and access roads. This study proposes a QUBO-inspired computational framework for bottleneck diagnosis and dynamic dispatch in this setting. Shanghai Pudong International Airport and Hangzhou Xiaoshan International Airport serve as case airports. A five-minute state model links passenger arrivals, vehicle supply, pickup berth service, vehicle storage, and road capacity. Bottleneck diagnosis uses service intensity, road demand saturation, bottleneck frequency, queue severity, shadow-price leverage, and a composite congestion severity index. Two dispatch schemes are tested under consistent demand inputs: finite-action model predictive control and quadratic-unconstrained-binary-optimization-inspired simulated annealing. In the strong-peak baseline scenario, the QUBO-inspired method reduces the final passenger queue from 3445 to 2477 passengers at Shanghai Pudong and from 2053 to 1482 passengers at Hangzhou Xiaoshan. Case results indicate different dominant bottlenecks. Shanghai Pudong is more affected by road saturation, whereas Hangzhou Xiaoshan is more affected by pickup berth service. Robustness tests under demand, supply, service, road-capacity, modal-share, and random-noise perturbations show retained queue-reduction benefits under the tested uncertainty levels.

Exact QAOA simulation spans several computational representations whose useful regions differ sharply across graph structure, circuit depth, precision, and available memory. Choosing only a backend name hides these differences: an executable choice also fixes the representation, adapter, precision mode, and memory policy. We introduce RASP-QAOA, a per-instance selector over ten such actions. It first removes actions that cannot implement the requested QAOA semantics or execution requirements, then orders the remaining actions using instance features; actions outside learned support are handled by analytical work estimates. On a content-disjoint 60-request H200 evaluation, RASP-QAOA succeeds on all 31 requests for which at least one admissible action completes and validates. Within this set it reaches 27/31 top-1 and 31/31 top-2 selection, with 1.051 geometric-mean regret. Its failure-penalized PAR10 score is 0.0396 times that of development-selected CUAOA (95% interval: 0.0085-0.1644). A separate 30-request crossover shows that graph structure changes 16 decisions and improves the paired penalized score, while a depth-1 stump matches gradient boosting. The evidence supports resource-aware representation selection at n <= 35, p <= 5, with gains driven by representation features rather than classifier complexity.

QAOA training repeatedly queries an objective and all shared gradients, making exact evaluation a feasibility bottleneck even when QUBO terms have bounded causal cones. Building on established causal-cone restriction and adjoint differentiation, LC-Implicit-QAOA profiles cone structure and induced-edge counts before local-amplitude and named-workspace allocation, then jointly selects equal-size microbatches and checkpoint schedules under a named active-evaluator workspace budget. "Implicit" means omitting both global state and global cost table, not implicit differentiation; infeasible requests are rejected before those allocations. An independently implemented complex128/float64 dense adjoint agrees with LC over 1,800 graph-angle comparisons, with a worst relative gradient error of 1.56 x 10^-13. LC completes all 104 target requests in a p=2 bounded-cone grid; under a prespecified n <= 24 validation cap, the matched state-plus-cost reference is executed for 28 requests and deliberately not run on 76. Across 80 budgeted requests, measured allocated evaluator memory stays within budget, reaching at most 0.797 of it. On 3-regular n=512, p=2, the adjoint reaches the same finite-budget endpoint in 101 objective-equivalent calls and 189 s, versus 909 calls and 1,565 s for central differences. LC targets fixed-depth one- and two-local diagonal QUBO costs with a transverse-field mixer; it provides neither global states, sampling, nor a hardware-independent fastest-backend rule.

World models learn latent states that summarize interaction histories, evolve over time, and support prediction, simulation, or planning. Most existing world models represent these states using classical vectors, probability distributions, recurrent hidden states, or transformer activations. In this paper, we introduce Quantum-Structured World Models (QSWMs), a quantum-inspired framework for predictive world modeling with structured latent states, latent transition operators, and measurement-inspired decoding maps. We study whether mathematical structures inspired by quantum theory, such as complex-valued representations and density-matrix-like latents, provide useful inductive biases for world modeling. We establish three foundational properties: classical inclusion, predictive sufficiency, and structured compactness. We then instantiate complex-valued and density-matrix-like QSWM variants and evaluate them on elementary cellular automata against strong classical baselines. Results show promising local predictive potential for complex-valued QSWMs, while also revealing limitations in long-horizon rollout, density-matrix variants

The dynamical Lie algebraic (DLA) theory of variational quantum algorithms (VQAs) predicts commonplace exponentially vanishing loss and gradient variances for sufficiently deep parametrized circuits. In this work, we show that these predictions fail dramatically in the shallow-circuit (and particularly constant-depth) regime for the Quantum Approximate Optimization Algorithm (QAOA) applied to the maximum independent set (MIS) problem. In a large-scale numerical study across $\sim$23,000 problem instances, we find that barren plateaus are rare, while landscapes whose variances polynomially increase with system size---which we term "cragged terrains"---are common across graph families. This aggregate polynomial growth persists both for generic, low-symmetry random graphs and for highly symmetric vertex-transitive graphs, indicating that DLA-based variance predictions do not describe landscape scaling in this regime. As a stopgap alternative to the theory, we train empirical hardness models to predict instance-wise hardness metrics for QAOA-MIS. While these models generalize poorly, they nonetheless recover the correct landscape scaling class (barren plateau vs. cragged terrain) with high fidelity. Taken together, our results identify shallow QAOA for MIS as a prototypical setting in which asymptotic, unitary-design-centric predictions may be fundamentally insufficient to describe shallow variational quantum algorithms more broadly, emphasizing the need for more empirically-informed models of VQA loss landscapes.

Molecular optimization is commonly performed under a limited oracle budget, which makes deciding what to evaluate as important as deciding what to generate. We introduce short-term graph memory, a plug-in module that preserves the generator architecture and native update rule while learning from previously evaluated molecules to prioritize subsequent oracle queries. The module maintains an online graph neural surrogate that pre-screens each round's candidate pool, so the fixed oracle budget is spent on molecules with higher predicted utility. Applied to a fragment-based generator on a standard molecular optimization benchmark, it improves the mean top-10 score at no extra oracle cost and never falls behind the base on any oracle; the gain extends to all four generators we tested at a tight budget of one thousand calls. We then analyze how surrogate-guided selection interacts with the exploration and exploitation behavior of different generators. Its benefit at larger budgets is consistent with two properties of the backbone: how broadly it searches, and how effectively its native search already exploits oracle feedback. We provide a simple way to spend a fixed oracle budget more selectively, and evidence on which generators benefit from it.

Quadratic unconstrained binary optimization (QUBO) has emerged as a powerful framework for medical computing problems. Binary decision variables naturally represent clinical choices, making QUBO formulations well-suited for quantum annealing hardware. However, a fundamental scalability challenge limits practical deployment: problem size grows rapidly with input dimensionality, creating computational bottlenecks that restrict applications to simplified scenarios. This paper addresses this challenge through hierarchical problem reduction, as demonstrated in medical image segmentation, where pixel-level QUBO formulations create over 65,000 variables for a 256x256 image, forcing existing approaches to downsample to 42x42 resolution and discard 97% of pixel information. A superpixel-based QUBO framework is proposed using simple linear iterative clustering (SLIC) to group pixels into perceptually meaningful regions, then formulate segmentation as QUBO over a region adjacency graph (RAG) combining min-cut and smoothness objectives. Validation on INbreast mammography breast cancer images demonstrates a 4.2% improvement in segmentation quality (mean IoU 0.76 vs 0.73) with 33 computational speedup (0.67s vs 21.97s) and a 97.3% reduction in problem size (1764 to 48 variables), all achieved while processing full-resolution images rather than downsampled versions. The reduced problem size also fits well within current quantum annealer connectivity limits, removing the embedding overhead that has historically blocked direct deployment of pixel-level QUBO segmentation on quantum hardware.

Short-term disturbances at major passenger railway stations alter train arrival and departure times as well as the release sequence of station resources. Effective recovery therefore requires coordinated adjustment of arrival-departure track allocation, station resource occupation, and train retiming. This study represents the station resources involved in train arrival, track occupancy, and departure operations as zone-level resource-occupation intervals. An arrival-departure track allocation adjustment model is formulated. Resource compatibility is imposed as the feasibility condition, while train delays and resource reassignment costs are jointly considered. A quantum-inspired evolutionary algorithm combined with neighborhood search (QEA-NS) is proposed to solve the model. Perturbation instances are constructed using GTFS timetable data from Frankfurt Hauptbahnhof, Germany. QEA-NS is compared with CP-SAT under the same candidate resource set and feasibility criteria. Both methods generate solutions satisfying the modeled resource compatibility constraints. QEA-NS yields a total delay of 388 min, compared with 519 min for CP-SAT, representing a reduction of 25.2%. The mean delay of delayed trains decreases from 4.99 to 3.73 min, although QEA-NS requires a longer solution time. Across 10 random perturbation instances, QEA-NS achieves lower total delay in every case. Its mean total delay and standard deviation are 390.5 min and 35.945 min, respectively, compared with 673.8 min and 105.739 min for CP-SAT. The results indicate that, under the adopted resource representation and constraints, QEA-NS improves the delay performance of recovery plans. Its computational efficiency, however, requires further improvement.

Photonic-crystal surface-emitting lasers (PCSELs) can combine high-power operation with narrow-divergence surface emission, but optimizing coupled parameters requires costly full-wave simulations. Deep Q-network (DQN) optimization can reuse simulated transitions to guide edits, yet which value-learning mechanisms remain reliable under tight simulation budgets is unknown. We address this gap by comparing baseline DQN and six value-based variants for a seven-variable PCSEL design under a shared objective, simulator, 83-call budget, and four matched initializations. Beyond endpoints, we analyze sample efficiency, policy behavior, and physical response to separate learning gains from favorable starts or exploratory jumps. Dueling DQN is the only variant to improve all four seeds. Relative to the first evaluated designs, its selected structures increase the mean quality factor () from to (), reduce wavelength error by 64%, and increase upward power by 47%; compared with baseline DQN, they achieve a higher mean under the same budget. Other variants yield no consistent improvement; Double DQN reproduces baseline trajectories, while Rainbow-lite shows high upside but strong seed dependence. These results identify Dueling DQN as the most reliable configuration tested for simulation-budget-limited PCSEL inverse design and provide a reproducible framework for attributing algorithmic gains in scientific optimization. The source code is publicly available at https://github.com/Longying-Wen/PCSEL-RL.

Machine-learning surrogates of physical systems face a paradox: explainable models facing the challenge of expressivity to capture complex nonlinear flows, whereas expressive deep surrogates match high-fidelity simulations only through massive parameterisations that turn the learned dynamics into a black box. Here, we introduce quantum-compressed machine learning (QCML), which resolves this tension by compressing the latent propagator of a flow surrogate from $524{,}288$ trainable parameters to no more than $8$. This parameter reduction brings the learned dynamical law to the parameter scale of a physical constitutive relation rather than a black-box neural network, making the surrogate directly interpretable and controllable without sacrificing expressivity. The compression is realised by a structured quantum circuit whose unitary propagator constrains the latent spectrum to the unit circle exactly and by construction, replacing exponential error growth with linear accumulation over autoregressive rollouts. Classical regularisation only approximates this constraint: even a quantum-inspired classical baseline penalised towards unitarity collapses within one Lyapunov time on turbulent channel flow, whereas QCML remains stable over the full rollout. Shared phase and coupling angles parameterising the circuit correspond directly to modal frequencies and inter-mode interactions, giving the learned dynamics a physical interpretation in spectral space. On two patient-specific cardiovascular benchmarks, the structured QCML propagator matches the predictive accuracy of its classical counterpart on surface pressure spectra, pressure drop, and wall shear stress. These results establish QCML as a working component of scientific machine learning and a concrete contribution towards practical quantum advantage in real-world prediction.

While combinatorial optimization problems are central to many scientific and engineering applications, their solution remains challenging due to exponentially large search spaces. Variational quantum algorithms offer a promising route for tackling such problems, yet their practical performance is limited by repeated quantum circuit evaluations and classical parameter updates. In this work, we introduce DQAOA-GPT, a hybrid framework that integrates the distributed quantum approximate optimization algorithm (DQAOA), which decomposes a large optimization problem into smaller sub-problems, with GPT-based quantum circuit generation for solving those sub-problems. Rather than relying on iterative variational optimization, the proposed approach uses a trained generative model to directly generate high-quality quantum circuits for the decomposed sub-problems. As a benchmark, we evaluate DQAOA-GPT against conventional DQAOA on dense HUBO optimization problems with up to 100 decision variables. The results demonstrate that DQAOA-GPT significantly reduces computational cost while maintaining competitive solution quality, with larger acceleration observed for larger sub-problem sizes. Although this work focuses on benchmark-scale validation, the framework provides a promising foundation for larger-scale combinatorial optimization in hybrid HPC-QC environments through increased GPU resources and parallel computing capability.

This paper presents an Optuna-based formulation-level auto-tuning framework for support vector machines (SVMs) implemented on multiple quantum-inspired annealers. In an annealing-based SVM, continuous dual variables are discretized and converted into a quadratic unconstrained binary optimization (QUBO) model. This transformation introduces three coupled classes of parameters: representation parameters-the encoding base B and bit depth K-which determine numerical range, resolution, and QUBO size; the RBF kernel parameter γ, which determines classifier geometry; and the equality-constraint penalty ξ, which controls feasibility and coefficient balance. We formulate their joint selection as a mixed discrete-continuous black-box optimization problem. The framework has two optimization levels: an inner annealer minimizes the generated QUBO, while an outer Optuna loop reconstructs the formulation in every trial and maximizes validation accuracy. The same solver-agnostic procedure is applied to Fixstars Amplify Annealing Engine, Toshiba SQBM+, and Fujitsu Digital Annealer using TPE and Gaussian-process samplers and is compared with conventional grid search. Experiments on linear and nonlinear classification tasks with 0-20% label noise show mean gains over grid search of approximately 0.8 and 2.1 percentage points, respectively. The results demonstrate that formulation quality and backend capability must be evaluated jointly and that task-level feedback can compensate for discretization, penalty imbalance, and backend-dependent approximate optimization.

Pattern recognition problems arise in a variety of physical image processing situations, and convolutional neural networks are a popular scheme for the required feature extraction and classification tasks. The classical networks use diffusion-based smearing and block-wise pooling to downsample the image data and capture important structural features. In this work, we propose and demonstrate a more efficient quantum-inspired strategy involving a mixture of experts. It is a hybrid classical-quantum framework. The quantum part consists of amplitude encoding of the images, convolution using local unitary operations, multiple experts processing the same image with different parameters, and feature extraction using quantum stabiliser codes. The classical part then jointly processes the features extracted by different experts using a standard fully connected neural network for image class prediction. Using MNIST and Fashion-MNIST datasets as benchmarks, we demonstrate that the joint expert analysis outperforms the individual expert one, as well as reduces the failure rate of image class prediction by around a factor of two. The overhead of our quantum-inspired strategy is only moderate on GPU workstations, which makes our proposal a practical alternative to existing classical schemes. We also point out how the quantum part of our framework can be executed on a quantum processor.

This paper presents the design and evaluation of a maintainable hybrid generative architecture for automated music harmony generation from melody. The proposed system combines quantum-inspired candidate exploration over overlapping melodic contexts with explicit rule-based optimization to balance generative flexibility and structural control. The architecture is evaluated using explicit and reproducible metrics covering structural coherence, functional agreement, harmonic similarity, and robustness. The results show that the proposed approach produces harmonizations that preserve tonal structure and cadential behavior while allowing multiple valid harmonic realizations. Furthermore, the optimization layer improves structural coherence, stability, and predictability without requiring a training corpus. The study demonstrates that transparent and controllable hybrid generative systems can be systematically designed and evaluated within the context of Information Systems Development.

This paper introduces a quantum-inspired computational framework for harmonic decision-making in music. The proposed approach formulates harmonization as an optimization problem within a structured combinatorial space, where multiple candidate chord sequences are evaluated under interacting musical constraints. The model combines an interference-based harmonization stage with a classical optimization procedure grounded in tonal harmony. The quantum-inspired component enables the parallel consideration of multiple harmonic alternatives, while the classical stage refines the resulting sequences to ensure structural coherence and stylistic plausibility. The framework is evaluated on selected musical examples, including Autumn Leaves and It's a Long Way to Tipperary. Quantitative analysis shows that the optimization stage significantly reduces chord density, increases harmonic stability, and improves functional organization. At the same time, expert evaluation highlights the importance of stylistic context, demonstrating that increased harmonic complexity is not always perceived as more natural. The results suggest that harmonic generation can be interpreted as a structured decision-making process in a constrained search space. The proposed approach provides a computational model that integrates domain-specific knowledge with an interference-based search mechanism. Although preliminary, this work indicates that quantum-inspired methods may offer a useful framework for modeling complex decision processes in creative domains such as music. The proposed framework contributes to ongoing research on quantum-inspired models of cognition and decision-making in complex biological and creative systems.

Molecular docking predicts how a small molecule binds to a protein and is a key bottleneck in drug discovery. Classical scoring functions sum empirical pairwise contacts, blind to quantum-mechanical effects like orbital charge transfer that govern binding specificity. We introduce Q-Score, encoding GNN-predicted orbital donor-acceptor energies into a weighted graph and scoring binding by solving a maximum-weight vertex clique problem via Digitized-Counterdiabatic QAOA. Each interaction anchor maps to one qubit and compatibility constraints become edges. Across 11 protein targets, DC-QAOA recovers the exact optimum on 8 at 10 qubits. On 1000 AI-generated molecules, Q-Score is orthogonal to classical scoring with Spearman rho of 0.05, driven by orbital quality with rho of 0.90, and free of molecular-weight bias, enriching for strong orbital interactions at twice the random rate. DC-QAOA achieves a mean approximation ratio of 0.94 with 52 percent exact. Execution of 1000 circuits on IBM Eagle confirms 6-qubit solvability on NISQ hardware.

Multiplex CRISPR-Cas9 gene editing requires selecting one guide RNA per target gene subject to cross-gene interactions: a constrained combinatorial problem that can be formulated as a Quadratic Unconstrained Binary Optimization (QUBO) and solved via the Quantum Approximate Optimization Algorithm (QAOA). The one-hot per-gene constraint is conventionally enforced by adding quadratic penalty terms to the cost Hamiltonian, but penalty coefficient selection is heuristic and penalties amplify hardware noise. An alternative is to enforce the constraint structurally via the XY-mixer, which preserves feasibility by construction. We present COMET, a systematic comparison of penalty-based and XY-mixer QAOA on a three-gene, twelve-qubit multiplex editing instance targeting the immune-checkpoint genes PDCD1, LAG3, and HAVCR2. In simulation, the XY-mixer exceeds 95% probability of the optimum by QAOA depth p=3, while three penalty variants spanning an order of magnitude in penalty coefficient remain below 6% at every depth. On IBM's ibm_kingston (Heron r2) processor, the XY-mixer's simulator-hardware energy gap stays within |0.8| across all depths, while the worst-tuned penalty variant's gap reaches +53.9. We provide an honest account of where the structural guarantee partially breaks under gate-level noise. The twelve-qubit instance is classically trivial; our contribution is a methodological comparison of constraint-enforcement strategies in a biologically motivated domain, with real-hardware validation.

Artificial intelligence (AI) and quantum information (QI) are rapidly co-evolving. AI is becoming a practical tool for learning, designing, controlling, and verifying quantum systems, while QI offers new computational models, representational structures, and learning-theoretic questions for AI. This survey reviews the interface from both directions. In the AI for QI direction, we organize recent progress around the central tasks of extracting information from limited measurements, training and discovering quantum algorithms, stabilizing noisy hardware, automating experimental and programming workflows, and extending learning-based methods to sensing and networking. In the QI for AI direction, we examine how quantum computation and quantum-inspired structures affect learning through algorithmic speedups, expressivity, trainability, generalization, neural-network design, and tensor-network representations. We close by identifying cross-cutting challenges in reproducibility, scalability, hardware realism, and co-design, arguing that progress will depend on tighter integration of theory, experiment, and hybrid quantum--classical systems.

We report a machine-verified resolution of a problem open for over a decade in quantum optimization: the Farhi, Goldstone and Gutmann (FGG) conjecture that depth-$p$ Quantum Approximate Optimization Algorithm (QAOA) on the ring of disagrees attains approximation ratio $(2p+1)/(2p+2)$ exactly. We found the proof using a large language model, Claude Fable 5, and verified its correctness end-to-end by the Lean 4 proof assistant. Our methodology includes several ingredients: building on a substantial Lean library of quantum information, we formalized the QAOA components and the known parts of the problem, and reduced the conjecture to a single open mathematical statement. The model was then handed the library and our agentic toolkit, and tasked with closing that gap by constructing a proof in Lean. The resulting process is a feedback loop between the model's natural-language reasoning and Lean's mechanical verification, which converged to a machine-verified proof. Human verification is required only for the structural scaffolding - that the formal statement faithfully encodes the intended claim - while the proof itself is supplied by the model and certified mechanically by Lean. The proof is nevertheless striking - the model uncovered a hidden dynamical symmetry of the problem and exploited it, borrowing tools and machinery from an adjacent field to turn a hard existence problem into an explicit construction. This work paves the way for resolving open conjectures in quantum information science and beyond.

Quadratic unconstrained binary optimization (QUBO)-based quantum computed tomography (CT) casts reconstruction as a binary quadratic problem for quantum annealing and hybrid quantum--classical solvers. For grayscale CT, however, image encoding is constrained by the binary-variable budget: fixed global bit-plane encodings increase QUBO size and coupling complexity as gray-level precision improves, whereas low-bit encodings introduce quantization error. We propose a QUBO-based grayscale CT reconstruction framework that combines dynamic interval encoding with prior-balanced optimization. Each refinement round encodes active pixels only within local gray-level intervals around the current estimate, and a boundary-hit-guided update rule adaptively switches between search expansion and local refinement. To improve optimization stability, the method balances projection-domain data consistency and an edge-preserving quadratic prior before forming the final QUBO. Sparse-view and limited-angle fan-beam CT experiments show that the proposed method recovers structures and gray-level distributions more faithfully than the evaluated analytic, iterative, variational, and representation-based baselines. Expressivity analysis and ablation studies further indicate that the improvement mainly arises from effective gray-level representation through dynamic local encoding and more stable data-fidelity--prior coupling. Experiments on the D-Wave hybrid binary quadratic model (BQM) solver further demonstrate that the formulation is executable on a hardware-backed hybrid quantum--classical backend.

Existing quantum-inspired simulated bifurcation algorithms rely on dynamic scheduling methods but lack the ability to adapt effectively to different problem instances. Additionally, during the evolutionary stage, balancing exploration and exploitation remains challenging. The fundamental issue stems from the widespread use of static preset parameters and globally uniform strategies, which can diminish algorithm effectiveness and lead to result homogenization. This article proposes an Adaptive Enhanced Quantum-inspired Simulated Bifurcation (AE-QSB) framework driven by population states. By leveraging perception indicators of four distinct population states, the QSB algorithm establishes a closed-loop strategy encompassing perception, decision-making, and execution. Within this framework, we introduce three complementary algorithms spanning a spectrum from efficient extremum seeking (ME-BSB), through population-level uniform refinement (SE-DSB), to density-aware adaptive scheduling (SG-DSB). On the medium-sized graph G22, both SE-DSB and SG-DSB achieve a mean gap below 0.05%, while ME-BSB attains the optimal trade-off between runtime and solution quality with a gap of 0.26% and the shortest single-run time. We compared AE-QSB variants with other algorithms across all benchmark graphs from G1 to G81. The results demonstrate that AE-QSB achieved the lowest mean gap on 74.6% of the graphs and the highest average approximation rate on 84.5% of the graphs. Ablation experiments further revealed that subgroup exploration and rescue mechanisms play crucial roles in both multifactor and single-factor components. This study demonstrates that population statistical information during dynamic evolution provides a computable and effective foundation for adaptive control, enabling quantum-inspired optimization methods to transition from fixed scheduling to data-driven closed-loop control.

Black-box optimization (BBO) deals with problems where objective functions lack explicit analytical forms and are expensive to evaluate. Factorization machine with quadratic-optimization annealing (FMQA) constructs a surrogate model using a factorization machine (FM) and optimizes it with an Ising machine. Conventional FMQA applies a single integer-binary encoding throughout the optimization process, although the encoding best suited to surrogate learning may differ from the one best suited to Ising-machine solution search. We propose a stage-dependent FMQA framework and derive conversion formulas between one-hot and domain-wall QUBO matrices that preserve the surrogate objective over feasible integer states up to an additive constant. We evaluate the OhDw variant, which employs one-hot encoding for learning and domain-wall encoding for search, on the Rastrigin function with input dimensions N = 2 and 5 and discretization levels q = 61 and 301. Across all conditions, the dominant factor governing optimization performance is the encoding used in the learning stage, with one-hot encoding consistently yielding lower residual errors than domain-wall or binary encoding. The additional benefit of switching to domain-wall encoding for solution search is condition-dependent. For N = 5 and q = 301, OhDw achieves a lower residual error and solutions closer to the global optimum than one-hot-only FMQA, whereas for N = 5 and q = 61 the latter achieves a lower residual error. These results indicate that one-hot encoding in the learning stage is the primary performance driver and that stage-dependent encoding can provide further improvement under finer discretization.

Hyperdimensional Computing (HDC) is a robust computational framework inspired by human cognition characterized by simple and efficient operations within high-dimensional vector spaces. Quantum-enhanced Hyperdimensional Computing (QeHDC) extends classical HDC by leveraging quantum mechanical properties to enhance computational efficiency. In this paper, we propose a novel Quantum HDC framework featuring a one-pass training method, leveraging sinusoidal and quantum encoding to project classical data into quantum amplitude states efficiently. Our framework introduces an innovative reference-state-based quantum binding operation realized via quantum circuits. Furthermore, we propose a density-matrix-based superclass generation strategy employing eigenvalue decomposition to extract critical quantum state features effectively, enabling a more accurate and robust class representation. Experimental evaluations conducted on standard benchmark datasets demonstrate our approach's superior performance, robustness to noise, and computational feasibility compared to traditional classical and existing quantum-enhanced approaches. The results highlight the practical benefits and potential of Quantum HDC for quantum-enhanced classification tasks and pave the way for future advancements in quantum-inspired computational paradigms.

Quantum chemistry simulations underpin modern materials discovery, yet their impact is limited by steep computational cost and dependence on fixed approximation schemes. Foundation models, such as machine-learned interatomic potentials, have accelerated parts of this workflow, but their reliance on large-scale pretraining restricts adaptability at the frontier of chemical space, where methodological innovation and sparse data are the norm. Agentic AI systems can automate existing simulation pipelines, yet they remain constrained by the predefined tools and algorithms they orchestrate. In response, we introduce LADeQ, an LLM-guided workflow that discovers, implements, and benchmarks candidate approximation algorithms at test-time within existing quantum chemistry codes. Rather than selecting from a predefined repertoire, LADeQ constructs candidate approximation schemes on demand, drawing on techniques from disciplines such as spatial statistics, circuit simulation, and kernel methods that have had little prior presence in electronic-structure theory. Because it builds on an out-of-the-box language model, LADeQ requires no task-specific pretraining or curated data, and the resulting implementations are transparent and inspectable, with explicitly traceable approximation errors that enable principled control of accuracy--efficiency trade-offs. We show that LADeQ accelerates coupled cluster singles and doubles (CCSD) and configuration interaction singles and doubles (CISD) calculations while keeping correlation-energy errors within user-specified tolerances, demonstrating autonomous, objective-driven discovery of approximation algorithms inside existing electronic-structure solvers.

The Quantum Approximate Optimization Algorithm (QAOA) is a leading variational algorithm for combinatorial optimization on near term quantum devices. As circuit depth increases, the number of optimization parameters grows, making the search landscape increasingly nonlinear and difficult to optimize. Previous studies have shown that optimal QAOA parameters often lie on a low dimensional manifold that can be approximated using Principal Component Analysis (PCA) at shallow circuit depths. However, the effectiveness of PCA decreases at higher depths because the underlying parameter manifold becomes increasingly nonlinear. In this work, we investigate Kernel Principal Component Analysis (KPCA) with a radial basis function kernel as a nonlinear dimensionality reduction technique for QAOA parameter optimization. The model is trained using 200 graphs from each of 3 graph families, namely Erdos-Renyi, Barabasi-Albert, and Watts-Strogatz, with graph sizes ranging from 7 to 10 nodes. Performance is evaluated on 30 test graphs containing 12 nodes at circuit depths 1, 2, 4, and 8. Experimental results demonstrate that KPCA consistently outperforms PCA at deeper circuit depths across all graph families. At depth 8, KPCA achieves approximation ratios above 0.86, while PCA declines to approximately 0.81 to 0.83. Both methods reduce the number of quantum circuit evaluations by more than 93 percent relative to unrestricted QAOA optimization. These findings suggest that nonlinear kernel methods more effectively capture the structure of the QAOA parameter manifold and provide a practical approach for scaling variational quantum optimization to deeper circuits.

The growing energy demand for computation is becoming increasingly unsustainable. Thermodynamic computing, which harnesses physical thermal fluctuations as a computational resource rather than suppressing them, offers orders-of-magnitude energy savings for probabilistic and combinatorial tasks. Pharmaceutical R&D, heavily reliant on computational optimization and sampling, is a natural application domain. Here we present what is, to our knowledge, the first concrete pharmaceutical application mapped to thermodynamic hardware with energy estimates grounded in prototype measurements. We reduce mRNA codon optimization, a combinatorial problem routinely solved in drug development, to sampling from an Ising model, making it directly executable on a thermodynamic sampling unit (TSU). Benchmarking three approaches (Potts sampling, Ising sampling, and a genetic algorithm baseline) on the SARS-CoV-2 spike protein, we find that all achieve comparable optimization quality (scores ~234-240), but energy estimates based on validated hardware models indicate that a TSU could solve this problem using approximately 10e6 times less energy than a conventional GPU. All code is released under an open-source license.

As multi-drone fleets scale, zone assignment rapidly evolves into an intractable NP-hard combinatorial problem that overwhelms classical exhaustive search. While quantum optimization promises to shatter these classical bottlenecks, mapping complex spatial tasks from human intent to restricted quantum hardware remains a severe challenge. To bridge this gap, we present an end-to-end framework integrating a fine-tuned Large Language Model (LLM) front-end with a highly scalable, domain-specific quantum-classical backend. The front-end utilizes Supervised Fine-Tuning (SFT) and Direct Preference Optimization (DPO) to translate free-form natural language instructions into structurally robust Quadratic Unconstrained Binary Optimization (QUBO) constraints without false negatives. To overcome the strict qubit limits of near-term quantum devices, our framework features a novel constraint-preserving graph partitioner and a compressed separator-based dynamic programming (DP) merge. By structurally encoding constraints via W-state initialization and XY-mixers in Conditional Value-at-Risk Quantum Approximate Optimization (CVaR-QAOA), the pipeline stays highly compact. Empirical results demonstrate that this architecture circumvents classical scaling walls, recovering the global optimum on 100% of idealized oracle cases and 96.3% under real QAOA sampling, enabling natural-language-guided task allocation at previously intractable scales.

Training parameterised quantum circuits (PQCs) on quantum hardware is bottlenecked by the measurement cost of gradient estimation, which under the parameter-shift rule scales linearly in the number of trainable parameters and dominates the total shot budget of training at scale. In this work, we propose a framework of forward gradient estimators for PQCs, based on the forward mode of automatic differentiation, that yields an unbiased estimator of the gradient by averaging a freely tunable number of random directional derivatives and recovers SPSA, random coordinate descent, and the parameter-shift rule as limiting cases, with no ancilla qubits or controlled-gate overhead. We prove that stochastic quantum forward gradient descent converges under standard assumptions, with an explicit second-moment expansion that interpolates between the single-direction extreme of SPSA and the full-gradient extreme of parameter-shift. Within this framework we derive QUIVER (Quantum Iterative V-adaptive Estimator Rule), an adaptive optimiser for parameterised circuits whose update rule follows from a closed-form minimum measurement-cost allocation. We show numerically that forward gradients train Hamming-weight-preserving orthogonal quantum neural networks with up to 60 qubits and 1770 parameters on the ECG5000 and MNIST datasets orders of magnitude more efficiently than the parameter-shift rule. We also demonstrate that our proposed QUIVER optimiser can outperform iCANS and gCANS measurement-frugal optimisers on optimisation problems using the quantum approximate optimisation algorithm and quantum simulation with the variational quantum eigensolver.

Unmanned aerial vehicle (UAV) object detection requires compact detectors that retain small-object details under onboard computation and memory constraints. Repeated downsampling inlightweight networks weakens shallow spatial information, while manually adding attention orfusion modules may increase cost without stable gains. This study analyzes YOLOX-Nano underedge-deployment constraints by combining a P2 high-resolution detection branch with a quantum-inspired evolutionary algorithm (QIEA) for lightweight structure screening. The search space isdefined by lightweight priority and task specificity, and the evaluation jointly considers accuracy,floating-point operations (FLOPs), latency, memory consumption, and recall. On VisDrone, theP2 branch increases APamall by 31.10% over the YOLOX-Nano baseline. Compared with NanoDet-Plus with similar model size, YOLOX-Nano+-P2 improves APs0.ss by 17.5% and APamal by 44.9%.The QIEA-selected candidate obtains the highest Recallso, but +P2 remains the strongest AP-oriented variant after full training. Full 100-epoch verification of Random-best, GA-best, andSA/QUBO-best candidates further shows that proxy rankings do not necessarily transfer to finalAPse9s. These results support using P2 as the main small-object enhancement path and QIEA as alightweight tool for candidate screening and accuracy-cost analysis. The source code, configurationfiles, diagnostic scripts, and summarized results are available at https://github.com/Ming23233/UAV-QIEA-Edge-Detection

Quantum combinatorial optimization offers theoretical advantages for complex financial modeling, but physical implementation on Noisy Intermediate Scale Quantum (NISQ) devices is severely constrained by hardware topology. This study presents a hardware benchmarking analysis between a Hardware Efficient Variational Quantum Neural Network (HE-VQNN) and the Warm Start Quantum Approximate Optimization Algorithm (WS-QAOA) for a hybrid Mean Variance and Conditional Value at Risk (CVaR) portfolio objective. By implementing a novel classical quantum hybrid proxy matrix to bypass the CVaR auxiliary qubit bottleneck, we map up to 16 assets from the NIFTY 50 index onto an IBM heavy hex processor. We systematically quantify algorithmic resilience to the "SWAP tax" incurred during routing. Empirical results reveal a critical operational trade-off: WS-QAOA provides exact theoretical mapping but suffers catastrophic hardware decoherence due to exponential nonlocal gate overhead. Conversely, HE-VQNN preserves hardware coherence but lacks the mathematical expressibility to capture dense tail risk asset correlations. This study exposes the limitations of dense financial optimization on current architectures forces an nonviable choice between algorithmic inexpressibility and hardware decoherence. This is indicative of a deeper limitation as to what can and cannot be done with NISQ computers lacking in all-to-all connectivity.

This study examines the coordinated optimization of departure sequencing and section-track allocation in railway short-term concentrated departure scenarios. A quadratic unconstrained binary optimization (QUBO) model is formulated to represent departure-position assignment and section-track selection within a unified binary framework. Because the quality of a dispatching scheme depends on time-dependent operational interactions that cannot be fully captured by a static combinatorial model, a simulation-based evaluation layer is introduced to assess section occupation, intermediate-station waiting, platform-capacity pressure, running-time fluctuations, and delay propagation. Within this layered framework, conventional heuristics, quantum-inspired algorithms, and hybrid algorithms are compared on the same decision structure. The results show that the QUBO model can generate feasible candidate schemes after decoding, while the simulation layer clearly differentiates the operational performance of the competing algorithms under both normal and disturbed conditions. In the tested scenarios, QPSO-QAOA performs best under normal conditions, and the quantum-enhanced methods reduce comprehensive cost by 4.28%--26.26% and total delay by 4.37%--24.25% on average under dynamic conditions relative to their conventional counterparts. These findings suggest that the integration of QUBO-based modeling and simulation-based evaluation provides a useful methodological framework for railway short-term concentrated departure scheduling, although validation with real operational data remains necessary.

ASP(Q) extends Answer Set Programming (ASP) with Quantifiers over answer sets. In this paper we focus on the class of ASP(Q) programs with two quantifiers and weak constraints, denoted as 2-ASP(Q)^w. 2-ASP(Q)^w is a practically relevant fragment of ASP(Q) that is expressive enough to capture optimization problems up to the class Delta_3^P. On the theoretical side, we provide a complete complexity characterization of the main computational tasks for 2-ASP(Q)^w programs, including tight completeness results and the analysis of nontrivial cases that have not been addressed in previous works. On the practical side, we introduce novel strategies for computing (optimal) quantified answer sets in the Casper system, that rely on a Counterexample-Guided Abstraction Refinement (CEGAR) technique tailored to ASP(Q). An experimental evaluation on hard benchmarks from different application domains shows that the proposed techniques are effective in practice.

We introduce a physics-inspired continuous relaxation framework that yields substantially improved solutions for NP-hard combinatorial optimization problems, including Quadratic Unconstrained Binary Optimization (QUBO), binary sparse coding, and planted-solution Ising models. By parameterizing discrete binary variables as continuous wave-like states on the complex unit circle, we inherently smooth highly non-convex energy landscapes. We show that representing binary variables as complex phases reveals an implicit regularization mechanism that promotes convergence toward discrete states. Extracting this mechanism yields significant improvements even within standard real-valued optimization frameworks, using this regularizer explicitly. Empirically, this regularization yields vastly higher ground-state convergence rates than standard real-valued alternatives. Our models achieved zero error in large-scale 160x160 QUBO tasks under severe noise (sigma=0.25), and outperformed traditional algorithms (OMP and LASSO) in underdefined sparse coding with perfect recovery at sigma=0.15. The solver's robustness was further validated by recovering exact ground-state configurations in 8 out of 11 rigorously engineered planted-solution benchmarks.

Spatial photonic Ising machines (SPIMs) based on spatial light modulators (SLMs) have emerged as highly effective solvers for many tasks, including combinatorial optimization problems and spin-glass simulations. However, traditional SPIMs relying solely on the simulated annealing algorithm require a large number of measurement-feedback iterations to find a relatively optimal solution in complex energy landscapes, suffering from slow convergence and high time cost. Here, we propose an optical genetic-simulated annealing hybrid algorithm to accelerate the ground-state search of SPIMs. GA conducts a global coarse-grained search in the early iteration stage, while SA performs fine-grained local refinement in the late stage. Numerical simulations show that our method enables a higher solution quality of full-rank Max-Cut problems than pure GA or SA at different scales. We also experimentally demonstrate its superiority over conventional algorithms on a gauge-transformation time-division multiplexing SPIM for high-rank optimization problems under the same iteration budget. Our approach can be further developed with other advanced metaheuristic algorithms toward intelligent optical Ising computing systems.

Negative Selection Algorithms (NSAs), inspired by the self/non-self discrimination mechanism of the human immune system, have been widely employed in anomaly detection. However, their effectiveness is often constrained by the efficiency of detector generation. This paper presents the Quantum Genetic Negative Selection Algorithm (QGNSA), a novel approach that integrates a Quantum Genetic Algorithm (QGA) into the EvoSeedRNSA algorithm, replacing its classical evolutionary optimization process. The proposed method exploits quantum superposition and probabilistic amplitude adjustment to enhance search space exploration and convergence efficiency in the detector generation process. Empirical evaluations using the Metaverse Financial Transactions Dataset demonstrate that QGNSA achieves superior anomaly detection accuracy compared to its classical counterpart while maintaining robustness under varying hyperparameter configurations. The experimental results highlight the potential advantages of quantum computing in artificial immune systems, particularly in high-dimensional anomaly detection tasks. Future research will focus on further optimizing quantum circuit design, deploying the algorithm on real quantum hardware, and exploring hybrid quantum-classical approaches for improved computational efficiency.

The accelerating convergence of smart metering, generative artificial intelligence, and quantum-inspired combinatorial optimisation is reshaping how energy utilities manage physical infrastructure, customer engagement, and environmental accountability

Federated Learning (FL) trains a global model across decentralized clients while preserving data privacy, but at scale it is vulnerable to malicious updates. Byzantine-resilient aggregation methods such as MultiKrum score gradients against their nearest neighbors and can miss malicious updates that preserve the statistical properties of honest ones. We propose a quantum annealing approach that reformulates client selection as a Quadratic Unconstrained Binary Optimization (QUBO) problem, encoding pairwise distances into a cost function solved by quantum annealers (QA). Unlike MultiKrum's greedy per-client scoring, the QUBO formulation jointly optimizes over all subsets to find the mutually closest group of $m$ clients. At small scale (15 clients), QUBO outperforms MultiKrum on the most challenging Byzantine attacks: e.g., Advanced LIE is detected with 95.11% accuracy versus 81.33% on MNIST and 97.78% versus 75.56% on CIFAR-10. QUBO fares poorly on simpler attacks where MultiKrum excels, so the two methods are complementary. QUBO quality also degrades as the number of clients grows. To address this, we introduce a MultiSignal ensemble that uses a dual-feature routing gate based on Euclidean and cosine Krum score gaps to classify attacks into four regimes and routes evasion attacks to a suspicion-penalized QUBO with agreement voting. At 100 clients on MNIST, MultiSignal achieves 95.3% average detection accuracy versus 91.8% for classical MultiKrum, with the largest gains on Sparse Lie (72.0% to 95.2%, +23.2 points) and Advanced Lie (80.4% to 85.2%, +4.8 points). These results show that QUBO-based quantum annealing with MultiSignal is a principled and scalable defense against the most challenging Byzantine strategies in federated learning.

We introduce \textbf{QuantFPFlow}, a reinforcement learning framework that integrates quantum amplitude estimation into the Fokker--Planck~(FP) formulation of stochastic policy optimisation. Classical continuous-space RL agents must estimate the FP partition function $Z = \int e^{-V(\mathbf{x})/D}\,d\mathbf{x}$ at cost $\calO(1/\varepsilon^{2})$; QuantFPFlow replaces this with a Grover-amplified amplitude estimator achieving $\calO(1/\varepsilon)$ -- a provable quadratic speedup. While the full quantum acceleration requires fault-tolerant hardware, the quantum-inspired classical simulation demonstrated here already exhibits the $\calO(1/\varepsilon)$ algorithmic structure. The estimated stationary distribution $\rhostar$ drives a theoretically grounded exploration bonus $\Raug = \Renv + α\log(1/\rhostar(s))$. This bonus steers the agent toward globally optimal regions of multimodal reward landscapes while simultaneously constraining policy variance through FP diffusion matching. On a continuous-control task specifically designed to expose local-optima failure, QuantFPFlow achieves mean reward $1{,}295.7 \pm 423.2$ versus $1{,}284.0 \pm 474.0$ for Soft Actor-Critic~(SAC), while discovering the global optimum \textbf{10.4,% more frequently} (33.9,% vs.\ 30.7,%). Policy entropy remains near $H(π)\approx 6.5$,nats throughout training, whereas SAC collapses to $1.5$,nats, confirming that FP diffusion matching actively prevents premature convergence. Dimensionality experiments further show computational scaling of $\calO(d^{0.35})$ for QuantFPFlow versus $\calO(d^{0.76})$ for classical FP estimation.

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.

The quantum approximate optimization algorithm (QAOA) holds promise for combinatorial optimization but is constrained by limited qubits. While divide-and-conquer frameworks like QAOA$^{2}$ address scalability by partitioning graphs into subgraphs, existing methods suffer from two fundamental limitations: i) misalignment between heuristic partitioning metrics and quantum optimization goals, and ii) topology-blind parameter initialization that leads to optimization cold starts. To bridge these gaps, we propose Neural QAOA$^{2}$, an end-to-end differentiable framework that jointly generates graph partitions and initial parameters. By integrating a generative evaluative network (GEN), our method utilizes a differentiable quantum evaluator as a high-fidelity performance surrogate to provide direct gradient guidance, enabling the joint generator to learn the intrinsic mapping from graph topology to high-quality partition and parameter configurations. Extensive experiments on 183 QUBO, Ising, and MaxCut instances (21 to 1000 variables) demonstrate that our gradient-driven approach broadly outperforms heuristic baselines, ranking first on 101 instances. It exhibits zero-shot generalization across out-of-distribution graph topologies and scales.

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.

Feedback-based adaptive quantum optimization (FALQON) is a promising approach for solving combinatorial problems on noisy intermediate-scale quantum (NISQ) devices, requiring only single circuit evaluations per layer. However, standard FALQON relies on fixed hyperparameters that severely limit convergence speed, requiring hundreds to thousands of layers for acceptable solutions. This paper proposes Optimal FALQON, an optimization-based formulation that treats the per-layer time step ($δ_k$) and scaling factor ($M_k$) as decision variables optimized via classical methods. We present a comprehensive empirical study on all 94 non-isomorphic 3-regular graphs with 12 vertices, comparing Optimal FALQON with standard FALQON and multiple QAOA variants. Results demonstrate statistically significant improvements in success probability, evaluation efficiency, and depth-normalized cost across the evaluated benchmarks. Furthermore, initializing QAOA with parameters from Optimal FALQON yields superior warm-start performance compared to fixed initialization.

The escalating complexity of modern machine learning necessitates solving challenging non-convex optimization problems, particularly in high-dimensional regimes and scenarios contaminated by gross outliers. Traditional approaches, relying on convex relaxations or specialized local search heuristics, frequently succumb to suboptimal local minima and fail to recover the true underlying discrete structures. In this paper, we propose treating these non-convex challenges as a global search problem and introduce a unified framework based on Quantum-Inspired Evolutionary Optimization (QIEO). By leveraging a probabilistic representation inspired by quantum superposition, QIEO maintains a global view of the search space, enabling it to tunnel through local optima that trap conventional gradient-based and greedy solvers. We comprehensively evaluate QIEO across diverse non-convex applications, including sparse signal recovery (gene expression analysis and compressed sensing) and robust linear regression. Extensive benchmarking against state-of-the-art continuous solvers (ADAM, Differential Evolution), classical metaheuristics (Genetic Algorithms), and specialized non-convex algorithms (Iterative Hard Thresholding) demonstrates that QIEO consistently achieves superior structural fidelity, lower mean squared error, and enhanced robustness without support inflation. Our findings suggest that embracing a quantum-inspired global search provides a resilient, unified paradigm for overcoming the inherent intractability of discrete nonconvex machine learning landscapes.

To overcome the limitations of classical partially connected Boltzmann machines and mainstream quantum Boltzmann machines (QBMs), this work extends the conventional circuit of the quantum approximate optimization algorithm (QAOA) to a bilevel optimization architecture and proposes a fully connected QBM. The inner-loop training simulates positive phase energy minimization based on the computational process of the conventional QAOA circuit, whereas the outer-loop training simulates negative phase contrastive divergence learning by optimizing the structural parameters of the target Hamiltonian. It is found that, first, the model exhibits superior performance using only a single layer (p=1) in the QAOA circuit, with an average probability of 0.9559 in measuring the target quantum state under noiseless conditions. Second, the model exhibits notable noise robustness. Under the typical noise level of current mainstream commercial quantum computing devices, the average probability of measuring the target quantum state reaches 0.6047; when the noise rises to a more stringent level with doubled intensity, this probability remains at 0.3859. In both scenarios, the target quantum state maintains the highest measurement probability among all detected states, with a value several times higher than that of the second-ranked state. This indicates that the model retains strong robustness even when noise meets or exceeds the upper limit of current mainstream commercial quantum computing devices. Third, under a block-by-block learning strategy with p=1 and only 10 measurement shots, the model consistently generates the target "qubit" grid image regardless of noise interference, demonstrating strong robustness in image generation.

Factorization machine with quadratic-optimization annealing (FMQA) is a black-box optimization method that combines a factorization machine (FM) surrogate with QUBO-based search by an Ising machine. When FMQA is applied to integer or discretized continuous variables via one-hot encoding, uniform random initial sampling can leave many binary variables never active in the initial training data, and the corresponding FM parameters receive no direct gradient updates from the observed responses. We address this by designing the initial training data to achieve complete marginal bit coverage, namely, ensuring that every binary variable obtained by one-hot encoding takes the value one at least once. We use two space-filling sampling methods, Latin hypercube sampling (LHS) and the Sobol' sequence, yielding LHS-FMQA and Sobol'-FMQA. On the human-powered aircraft wing-shape optimization benchmark with 17 and 32 design variables, both proposed methods achieved numerically higher mean final cruising speeds than the baseline FMQA, with the advantage more pronounced on the 32-variable problem.

Vehicle Routing Problem (VRP) is one of the most complex NP-hard combinatorial optimization problem in transportation and logistics that requires a dynamic solution approach. In this paper we present a new hybrid approach that combines the Quantum Approximate Optimization Algorithm (QAOA) into the QRL policy network, instead of the usual variational layers, QAOA mixing and cost Hamiltonian layers. This enhancement enables the agent to exploit problem specific particular quantum correlations when learning policies, and so richer exploration of the routing solution space. The QAOA-augmented QRL framework shows quicker convergence in training and can tackle larger VRP instances that are beyond the reach of Grover's Adaptive Search (GAS) and Quantum Reinforcement Learning (QRL) approaches. Experiments on standard VRP instances demonstrate better solutions, fewer episodes to converge and good memory usage on near term quantum hardware simulators. These findings demonstrate QAOA- integrated QRL as a viable approach to scalable, high quality quantum-assisted combinatorial optimization.

SAR image classification naturally has to deal with huge noise and a high dynamic range particularly requiring robust classification models. Additionally, the deployment of these models on edge devices, such as drones and military aircraft, requires a careful balance between model size and classification accuracy. This study explores the potential of tensor networks to meet these robustness requirements, specifically evaluating their resilience to data poisoning. Unlike previous works that concentrated on conventional neural networks for SAR object detection, this research focuses on the robustness and model reduction capabilities of tensor networks in object classification. Our findings indicate that tensor networks are adept at addressing both the challenges of robustness and the need for model efficiency, thereby contributing valuable insights to the ongoing discourse in radar applications and deep learning methodologies in general.

In low-depth implementations of the Quantum Approximate Optimization Algorithm (QAOA), the dominant cost is often the number of objective evaluations rather than circuit depth. We introduce a graph-conditioned trust-region method for reducing this query cost. A graph neural network predicts a Gaussian distribution N(mu, Sigma) over QAOA angles. The mean initializes a local optimizer, the covariance defines an ellipsoidal trust region that constrains the search, and the predicted uncertainty determines an instance-dependent evaluation budget. Thus the learned distribution defines a search policy rather than only an initial parameter estimate. Under explicit assumptions on local smoothness, curvature, calibration, and noise, we derive bounds on objective degradation within the trust region, lower bounds on gradient variance, preservation of expected objective ordering under depolarizing noise, and finite-sample coverage guarantees. We evaluate the method for MaxCut at depth p = 2 on Erdos-Renyi, 3-regular, Barabasi-Albert, and Watts-Strogatz graphs with n = 8-16 vertices. Relative to random restarts and the strongest learned point-prediction baseline, the method reduces the mean number of circuit evaluations from 343 and 85 to 45 +/- 7, while maintaining sampled approximation ratios within 3 percentage points of concentration-based heuristics. The method does not improve absolute approximation ratios; its advantage is reduced query cost at comparable solution quality. The predictive uncertainty is calibrated in the experiments, with ECE = 0.052 and Spearman correlation rho = 0.770, and the learned trust regions transfer to graph sizes not used during training. The results identify a low-depth, query-dominated regime in which graph-conditioned trust regions reduce the query cost of QAOA without modifying the ansatz.

We cast the design of parameterized quantum circuits as a four-player potential game whose state is a circuit directed acyclic graph (DAG) and whose players encode trainability, non-stabilizerness, task performance, and hardware cost. Per-player restricted action sets factorize the move space into append, remove, retype, and rewire operations; a block-coordinate $\varepsilon$-Nash residual $δ_\text{Nash}$ certifies that no single player can improve unilaterally. A single weight sweep on MaxCut $K_4$ traces a Pareto frontier from a Clifford endpoint $(M_2/n,\langle H\rangle)=(0,4.00)$ to a non-Clifford endpoint $(0.48,3.30)$. On three four-qubit hardware topologies (heavy-hex, $2\times 2$ grid, Rydberg all-to-all), Nash search achieves the highest mean potential; on the $2\times 2$ grid Nash reaches the theoretical ceiling $Φ_\text{max}=4.10$ on two of five seeds while the simulated-annealing baseline does so on one; paired Wilcoxon tests over five seeds cannot reject the null on any single topology ($p\ge 0.22$). On LiH/STO-3G, seeding Nash from a 58-gate Givens-doubles ansatz produces a 48-operation, depth-25 circuit retaining $97.7\%$ of the correlation energy while simultaneously reducing gate count, increasing non-stabilizerness, and controlling trainability. The framework is complementary to energy-only searches such as ADAPT-VQE and k-UpCCGSD, which reach chemical accuracy with fewer operations but do not optimize the other three axes.

The quadratic assignment problem (QAP) is a fundamental NP-hard task that poses significant challenges for both traditional heuristics and modern learning-based solvers. Existing QAP solvers still struggle to achieve consistently competitive performance across structurally diverse real-world instances. To bridge this performance gap, we propose PLMA, an innovative permutation learning framework. PLMA features an efficient warm-started MCMC finetuning procedure to enhance deployment-time performance, leveraging short Markov chains to anchor the adaptation to the promising regions previously explored. For rapid exploration via MCMC over the permutation space, we design an additive energy-based model (EBM) that enables an $O(1)$-time 2-swap Metropolis-Hastings sampling step. Moreover, the neural network used to parameterize the EBM incorporates a scalable and flexible cross-graph attention mechanism to model interactions between facilities and locations in the QAP. Extensive experiments demonstrate that PLMA consistently outperforms state-of-the-art baselines across various benchmarks. In particular, PLMA achieves a near-zero average optimality gap on QAPLIB, exhibits remarkably superior robustness on the notoriously difficult Taixxeyy instances, and also serves as an effective QAP solver in bandwidth minimization.

This research investigates the performance and efficacy of machine learning models in stock prediction, comparing Artificial Neural Networks (ANNs), Quantum Qubit-based Neural Networks (QQBNs), and Quantum Qutrit-based Neural Networks (QQTNs). By outlining methodologies, architectures, and training procedures, the study highlights significant differences in training times and performance metrics across models. While all models demonstrate robust accuracies above 70%, the Quantum Qutrit-based Neural Network consistently outperforms with advantages in risk-adjusted returns, measured by the Sharpe ratio, greater consistency in prediction quality through the Information Coefficient, and enhanced robustness under varying market conditions. The QQTN not only surpasses its classical and qubit-based counterparts in multiple quantitative and qualitative metrics but also achieves comparable performance with significantly reduced training times. These results showcase the promising prospects of Quantum Qutrit-based Neural Networks in practical financial applications, where real-time processing is critical. By achieving superior accuracy, efficiency, and adaptability, the proposed models underscore the transformative potential of quantum-inspired approaches, paving the way for their integration into computationally intensive fields.

Multi-Agent Route Planning considers selecting vehicles, each associated with a single predefined route, such that route-level coverage utility is maximized while redundant spatial overlaps are limited. This paper gives a formal problem definition, proves NP-hardness by reduction from the Weighted Set Packing problem, and derives a Quadratic Unconstrained Binary Optimization formulation whose coefficients directly encode route utility rewards and pairwise overlap penalties. A single penalty parameter $λ$ controls the coverage--overlap trade-off. We distinguish between a soft regime, which supports multi-objective exploration, and a hard regime, in which the penalty is strong enough to effectively enforce near-disjoint routes. We describe a practical pipeline for generating city instances, constructing candidate routes, building the QUBO matrix, and solving it with a binary quadratic programming baseline (Gurobi), simulated annealing, and D-Wave hybrid quantum annealing. Experiments on Barcelona instances with up to $10{,}000$ vehicles reveal a clear coverage--overlap knee and show that Pareto-optimal solutions are mainly obtained under the hard-penalty regime, while D-Wave hybrid solvers and Gurobi achieve very similar objective values on matching configurations with only minor runtime differences as problem size grows.

A local-valley (LV) centered approach to assessing the quality of sampling from Restricted Boltzmann Machines (RBMs) was applied to the latest generation of the D-Wave quantum annealer. D-Wave and Gibbs samples from a classically trained RBM were obtained at conditions relevant to the contrastive-divergence-based RBM learning. The samples were compared for the number of the LVs to which they belonged and the energy of the corresponding local minima. No significant (desirable) increase in the number of the LVs has been achieved by decreasing the D-Wave annealing time. At any training epoch, the states sampled by the D-Wave belonged to a somewhat higher number of LVs than in the Gibbs sampling. However, many of those LVs found by the two techniques differed. For high-probability sampled states, the two techniques were (unfavorably) less complementary and more overlapping. Nevertheless, many potentially "important" local minima, i.e., those having intermediate, even if not high, probability values, were found by only one of the two sampling techniques while missed by the other. The two techniques overlapped less at later than earlier training epochs, which is precisely the stage of the training when modest improvements to the sampling quality could make meaningful differences for the RBM trainability. The results of this work may explain the failure of previous investigations to achieve substantial (or any) improvement when using D-Wave-based sampling. However, the results reveal some potential for improvement, e.g., using a combined classical-quantum approach.

Quadratic Unconstrained Binary Optimization (QUBO) is a central formulation for combinatorial optimization and has gained increasing attention due to its compatibility with quantum, hybrid quantum-classical, and quantum-inspired solvers. However, translating natural-language problem descriptions into correct QUBO formulations remains difficult, requiring the identification of binary variables, constraints, objective functions, penalty terms, and suitable penalty weights. This process is time-consuming and often demands substantial domain expertise. To address this challenge, we propose an end-to-end multi-agent framework that automatically generates QUBO formulations from natural-language problem descriptions, supported by structured or unstructured test cases. To evaluate its performance, We also introduce QUBOBench, a benchmark containing 100 combinatorial optimization problems across 12 application domains, curated from peer-reviewed literature, competitions, and canonical NP-hard problems. Experimental results show that our framework achieves 68% accuracy on QUBOBench, outperforming a direct single-call baseline by 22%. Further analysis identifies iterative self-repair as the most important component contributing to improved performance. The data and code are open-sourced at https://quitttcat.github.io/QuantumQUBOAgent.