Quantum Machine Learning

The real-time orchestration of microgrids that combine fluctuating renewable sources, dispatchable units, storage and curtailable consumers requires the repeated solution of combinatorial dispatch and coalition formation problems under hard control deadlines. In this paper, a quantum-assisted agentic distributed artificial intelligence (DAI) framework is proposed in which the dispatch problem of each control slot is formulated as a quadratic unconstrained binary optimization (QUBO) problem by Belief-Desire-Intention extended (BDIx) agents and is solved by a portfolio of quantum, quantum-inspired and classical solvers. Solver selection is elevated to a first-class agentic deliberation action of the coordinator agent. Learned beliefs about solver latencies are maintained and the solver intention that is expected to satisfy the prevailing deliberation deadline is committed in each slot. In addition, a belief-shaped storage valuation mechanism is introduced through which the storage agent prices its energy at a discounted future-peak value, injecting intertemporal information into the otherwise myopic per-slot optimization. The framework is evaluated on a 24-hour simulation of a grid-connected microgrid with photovoltaic, wind, battery, genset and demand-response assets, with the Quantum Approximate Optimization Algorithm (QAOA) executed by statevector simulation and benchmarked per slot against tabu search, simulated annealing, binary particle swarm optimization, greedy descent and exhaustive enumeration. Zero deliberation deadlines are missed, the committed dispatch attains the exact optimum on every slot and the realized daily cost of 146.24 EUR equals the exact lower bound, with 97.83 percent renewable utilization and zero unserved energy. When the storage valuation mechanism is deactivated, the daily cost is increased to 152.75 EUR, a 4.5 percent increase.

Neural topic models enable scalable semantic discovery, but their integration with quantum hardware remains largely unexplored. We present a proof-of-concept hybrid classical-quantum variational autoencoder (VAE) for topic modeling, embedding parameterized quantum circuits within the VAE inference network while retaining a classical topic-word decoder. To address the resource constraints of quantum hardware, we propose a modified Gaussian Softmax posterior that decouples latent space dimensionality from the number of topics to be extracted, enabling the model to operate with a low-resource 10-qubit quantum device. On the AgNews dataset, the hybrid VAE outperforms state-of-the-art neural topic models (NTMs), reaching a $C_v$ coherence score of 0.71 and an NPMI score of 0.20 while preserving high topic diversity. For comparison, we also construct a fully classical variant, which also outperforms state-of-the-art models on AgNews and exhibits clear class separation in the latent space. These results demonstrate that hybrid VAEs are computationally viable even on NISQ-era devices and represent a promising direction for quantum-enhanced topic modeling.

Can Large Language Models (LLMs) understand and reason about quantum operators? Despite their remarkable capabilities in mathematics and symbolic reasoning, LLMs remain inherently blind to quantum representations such as unitary matrices. In this work, we take a step toward bridging this gap by introducing an approach that maps unitary operators into the latent space of an LLM, enabling unified modeling over quantum and linguistic inputs. We instantiate this idea on Clifford+T circuit synthesis over a Pauli rotation gate set, where our model achieves results competitive with state-of-the-art methods and scales consistently with training data, with no signs of saturation. Our approach further enables language-conditioned synthesis, allowing gate constraints unseen during training to be specified directly in natural language. This work suggests a path toward quantum--aware foundation models that can natively interpret and reason about quantum operations, which could have broader implications reaching across quantum compilation and algorithm discovery.

We develop theoretical foundations for a practical quantum-advantage mechanism in quantum-informed machine learning for chaotic dynamical systems. A family of $k$-indexed higher-order quantum statistical priors (Q-Priors) hosts the $k$-point marginal of the invariant measure on $n_q = kq$ qubits, extending the single-site construction of prior work. We prove a two-stage advantage. In the representation stage, superposition and entanglement compactly store non-factorisable spatial correlations of the invariant measure on $n_q$ qubits. In the extraction stage, joint Bell measurements on two copies estimate any \emph{post hoc} Pauli functional with a copy-pair count independent of $n_q$, whereas any adaptive single-copy protocol for the corresponding full-Pauli read-out requires $Ω(2^{n_q})$ copies; this is a provable quantum-classical separation in copy-measurement complexity. The two-copy read-out is realised in simulation and on IQM superconducting processors. Two case studies instantiate the mechanism in workflows of independent scientific value. In a turbulent channel-flow study, the two-copy read-out yields the velocity-direction coherence as a named non-diagonal correlator of the invariant measure, and the multi-site $k = 2$ Q-Prior recovers DNS-level invariant-measure statistics that the unregularised baseline loses. In a medium-range weather forecasting workflow on the European Centre for Medium-Range Weather Forecasts ERA5 reanalysis, the diagonal $k \leq 2$ Q-Prior steers a Koopman rollout, improves anomaly correlation skill by 10% to 39% across 48 to 240h lead times, and stabilises long-horizon rollouts against collapse onto a static mean field. Together, the mechanism and these two case studies satisfy our practical-advantage definition, identifying a candidate route to practical quantum advantage before fault-tolerant hardware.

The design of high performing quantum circuits remains largely dependent on human expertise. We introduce an autonomous agentic framework that employs large language models (LLMs) to conduct iterative quantum circuit designs under explicit design constraints. Our system integrates seven components: Exploration, Generation, Discussion, Validation, Storage, Evaluation, and Review. These components form a closed-loop workflow that combines web-based knowledge acquisition, literature-grounded critique, executable code generation, and experimental feedback. We evaluate the framework on two tasks: quantum feature map construction for quantum machine learning and ansatz generation for variational quantum eigensolver applications in quantum chemistry. In image classification benchmarks, the best generated feature map outperforms representative quantum feature maps and, when scaled to larger qubit counts, surpasses the classical radial basis function kernel. In molecular ground state estimation across seven molecules, the generated ansatz attains competitive accuracy with widely used chemically inspired and hardware-efficient constructions while satisfying the imposed scaling constraints. These results establish LLM driven agentic system as a viable paradigm for automated quantum circuit design and illustrate how AI systems can participate in iterative scientific optimization workflows across scientific domains.

Quantum circuit routing is a key step in compiling programs for noisy intermediate-scale quantum processors. Routes that appear efficient by standard overhead metrics can still lose fidelity when they pass through poorly calibrated couplers. We study a calibration-aware graph reinforcement-learning router that uses same-day IBM Heron r2 calibration data to choose hardware-edge SWAPs. We train the policy with proximal policy optimization and evaluate it with exact simulated fidelity across nine Munich Quantum Toolkit (MQT) Bench circuits and three calibration snapshots. Across these evaluations, pooled mean exact fidelity is $0.727$, compared with $0.440$ for SABRE-best20 and $0.481$ for target-aware SABRE. We observed that fidelity gains came with higher routed two-qubit counts and were concentrated in 5 qubit and 8 qubit circuit families; under the fixed tree action graph, all 10 qubit families favored SABRE-best20. Overall, our results show that calibration-aware learned routing can improve fidelity beyond gate-count-driven compilation.

Proton dissociation constants (pKa) are critical for functional molecule discovery and molecular modeling. Building on iBonD, the largest experimental pKa database established, we and other researchers have developed several methods including machine-learning-based empirical prediction and high-accuracy energy calculations. Despite this foundation, the rapid augmentation of high-quality pKa data remains fundamentally constrained. As part of this work, we performed large-scale regression-based pKa prediction on unlabeled molecular datasets using a collection of extensively optimized machine-learning models. The results indicate that, since the feature distributions of unlabeled molecular datasets, the pKa data distribution approximates normality, with extreme scarcity of tail-region samples. Although such augmentation is highly valuable for improving overall data availability and predictive modeling, it remains insufficient for efficiently discovering molecules with broad-spectrum pKa properties. To address this, we explore the targeted generation of molecules with sparse pKa properties from the vast chemical space. Given that traditional continuous latent space VAE-RNN methods for molecular generation suffer from insufficient stability and fail to demonstrate clear advantages in complementing sparse data, we design and implement a quantum-assisted sparse-pKa molecular generation. Feasibility is validated on a simulated quantum annealer, and superior extreme-value sampling is further achieved on physical coherent Ising machines (CIMs). (to be continued)

A central principle in quantum machine learning is that an ansatz should be expressive enough to represent the quantum data of interest. Yet, the expressibility is statistically meaningful only insofar as it can be learned from finitely many copies of an unknown quantum state. In this work, we develop an information-theoretic Occam theory for quantum data generated by finite-size quantum circuits. For the class $S_{n,G}$ of $n$-qubit pure states preparable with at most $G$ two-qubit gates, a metric-entropy argument gives the realizable sample law $\widetildeΘ(G/ε^2)$ in the circuit-limited regime. For an arbitrary source $\hatρ$, we introduce the best $G$-gate approximation error $d_G(\hatρ)$ and the approximate circuit complexity $C_η(\hatρ)$. We prove an agnostic quantum Occam theorem: with $M$ copies, one can learn up to the best $G$-gate approximation error plus a statistical penalty $\widetilde{O}(\sqrt{G/M})$. We then remove the need to know $G$ in advance through an adaptive model-selection theorem whose oracle inequality selects the circuit complexity justified by the data. Matching lower bounds yield a sample-supported expressibility law: at trace-distance accuracy $ε$, $M$ samples can support only $G_{\rm supported} \simeq Mε^2$ gates, up to logarithmic factors and tomography saturation at $2^n$. Thus, the circuit complexity becomes an adaptive statistical resource rather than a static promise. Our framework turns bounded circuit complexity into a model-selection principle for quantum machine learning.

Machine-learning approaches to quantum state tomography can achieve high reconstruction fidelity, but the physical structure used by the trained model often remains implicit. Here we ask whether a sparsified Kolmogorov-Arnold Network (KAN) can be used not only as a regressor, but also as an inspectable reconstruction rule whose internal organization can be checked against known Pauli structure. We study a controlled three-qubit GHZ-family benchmark in which all 63 non-identity Pauli expectation values are used to reconstruct three GHZ-subspace variables: the population imbalance $z$, the real off-diagonal component $c$, and the imaginary off-diagonal component $s$. Under finite-shot sampling and depolarizing noise, external ablation identifies the extended 12-channel GHZ-relevant Pauli set from the 63 measurements, with exact top-12 recovery across the tested shot counts and depolarizing-noise strengths. These support patterns remain stable across multi-seed random-initialization and noise-level analyses, and collapse under random-label controls. The dominant pruned input-hidden-output pathways organize Z-type population observables and X/Y off-diagonal observables in a pattern consistent with the analytic GHZ Pauli grouping, and sparse formula recovery recovers the canonical signed Pauli relations. The contribution of the KAN is therefore pathway-level structural interpretability within a neural reconstruction model, rather than superior sparse regression. Together with negative controls, these probes provide a consistency chain for auditing learned reconstruction rules against known physical structure.

Standard dot-product self-attention computes, in a single layer, only pairwise (order-2) interactions between tokens; representing a generic order-$k$ interaction is known to require either super-quadratic resources in one layer or composition across depth. We introduce \textbf{Quantum Higher-Order Attention (QHA)}, a shallow, hardware-realizable quantum attention head that, via data re-uploading and an all-to-all non-Clifford entangler, synthesizes order-$k$ token interactions inside the circuit and exposes them through a local single-qubit read-out. We prove (i) an expressivity separation: any single standard self-attention layer with embedding dimension $m$, $H$ heads and $p$-bit precision satisfying $mHp=o(N/\log\log N)$ cannot represent the order-$k$ correlation family that one QHA head represents with circuit depth $O(\log k)$ ($O(k)$ two-qubit gates); and (ii) a trainability guarantee for its local-design instantiation: with a local read-out and $O(\log n)$ depth the gradient variance is $Ω(1/\mathrm{poly}(n))$ (no barren plateau), which we confirm empirically -- while being explicit that the more expressive all-to-all instantiation we benchmark is trained empirically and shows exponentially decaying gradients. Empirically, at a $6.5\times$ smaller parameter budget, QHA generalizes hidden-subset parity of every order $k\le6$ from disjoint inputs, whereas the larger classical attention head collapses past order~2; consistent with theory, the size of the advantage tracks the target's Fourier degree - largest for parity and shrinking when low-order structure is present. As an application, QHA serves as a compact high-order interaction detector across three domains - genetic epistasis, learning-parity-with-noise, and graph triangle detection - reaching the noise ceiling at the smallest parameter budget where field-standard linear methods fail.

Approximate tensor-network simulators enable classical simulation of quantum circuits beyond the reach of exact methods, but selecting optimal approximation parameters -- such as bond dimension thresholds -- remains a costly trial-and-error process. We present a family-aware neural architecture that predicts both the minimum approximation threshold required to achieve target fidelity and the expected wall-clock runtime for quantum circuit simulation, given only the circuit's OpenQASM description and execution context. Our key insight is that quantum circuits from different algorithmic families (e.g., QFT, Grover, VQE) exhibit fundamentally distinct simulation cost profiles due to their differing entanglement structures. We employ family-conditioned residual corrections -- additive, family-specific adjustments atop a shared backbone, drawing on established conditional computation techniques -- enabling the model to capture both universal circuit properties and algorithmic nuances. The architecture incorporates a pretrained family classifier (97.5% accuracy) and domain-informed algorithm fingerprint features derived from gate-composition heuristics. Evaluated on circuits spanning 7--130 qubits across 10 algorithm families, our system achieves 79.5% exact threshold accuracy (91.2% within one rung) and $R^2 = 0.82$ runtime correlation, with inference completing in approximately 50 ms -- replacing trial-and-error simulation runs that may take minutes to hours. Ablation studies confirm that family-aware modeling provides the single largest performance improvement (+3.2 percentage points), validating the hypothesis that algorithm family is a first-class feature for simulation cost prediction.

Asynchronous, event-based graph neural networks (AEGNNs) have recently emerged as an efficient paradigm for processing the sparse and high-temporal-resolution data from event cameras. In this paper, we propose quantum analog AEGNNs (QA-AEGNNs), a novel framework to implement an AEGNN on a neutral-atom quantum computer. Neutral-atom quantum processors offer a programmable analog quantum computing platform based on controllable Rydberg-atom interactions. To this end, we map the streaming event data to an array of trapped neutral atoms, where each atom represents a graph node (event) and is positioned such that geometric proximity reflects the spatio-temporal neighborhood of events. The native Rydberg Hamiltonian of the quantum processor is programmed to mirror the message-passing computations of the AEGNN, with atomic qubit states serving as node feature embeddings and inter-atom interactions realizing graph edges. Furthermore, we propose a hybrid quantum-classical training scheme in which the analog Hamiltonian parameters (e.g., laser pulse amplitudes and detunings) are optimized using classical feedback to learn the quantum AEGNN model from data. Our approach leverages the continuous Hamiltonian dynamics and massive parallelism of neutral-atom quantum systems to natively execute event-based graph computations with potential accuracy improvements

Recent advances in error-corrected qubits have accelerated the timeline for practical quantum computing. It poses a threat to cryptographic primitives used to secure financial systems, government infrastructure, communication networks, and DeFi (Decentralized Finance) ecosystems. This paper introduces a post-quantum secure federated DeFi framework that enables inter-bank collaboration to improve the inclusivity of individuals underserved by local lenders due to limited financial histories. Multiple banks contribute encrypted information batches to a virtual server, where lattice-based Fully Homomorphic Encryption (FHE) enables end-to-end homomorphic computation. The server fuses local data-driven probabilistic assessments, expert beliefs, and verifiable evidence generated by the NASA-IBM Prithvi Geospatial Foundation Model (GFM), in encrypted format. Decentralized technologies are employed to ensure tamper-proof evidence and auditable accountability for all encrypted data exchanges between institutions and the server. The framework is tested on agricultural lending decisions for rural borrowers in Virginia.

Quantum Circuit Born Machines (QCBMs) offer a natural approach to generative machine learning by leveraging the Born rule. Recent work has provided a method to classically train QCBMs with Instantaneous Quantum Polynomial (IQP) circuits via the Maximum Mean Discrepancy (MMD) loss. Despite the assumed intractability of sampling from IQP circuits classically, their expectation values can be computed classically, enabling training of these IQP QCBMs. However, quantum machine learning (QML) models have various other challenges, including trainability issues caused by exponential concentration or barren plateaus. While these issues have been explored for parameters sampled from a uniform distribution, little work has been done to rigorously treat the use of arbitrary Gaussian initialization schemes. This work leverages Stein's lemma and Lipschitz concentration bounds for Gaussian random variables to provide an analytical lower bound of the variance of the gradient and a probabilistic concentration bound of the deviation of the gradient from its mean. It discusses strategies to either avoid or encourage exponential concentration, as well as the conditions under which barren plateaus are more likely to occur.

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.

The NISQ era places stringent constraints on quantum computation, where noise and decoherence fundamentally limit performance. In classical deep learning, model robustness and resilience to perturbations are well studied: deep neural networks (DNNs) maintain high performance despite pruning, noise injection, and structural perturbations due to inherent redundancy in their representations. A central challenge in quantum machine learning is to transfer this notion of robustness to quantum neural networks (QNNs) under realistic NISQ noise. While classical deep learning exhibits robustness through structural redundancy, analogous principles for QNNs remain underdeveloped. We propose JGRA: a framework for assessing robustness in noise-aware QNNs via Jacobian geometry, capturing model sensitivity to parameter perturbations induced by noise. Our method includes entropy-matched noise calibration, noise-aware training, and noise-conditioned Jacobian extraction, yielding geometric descriptors that link clean-regime structure to noisy inference behaviour. We also empirically demonstrate that these descriptors encode predictive information about robustness under unseen noise.

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

Generative models are increasingly used to capture correlations in many-body systems, but the representations they learn remain largely opaque to physical interpretation. Here, we establish an intuitive criterion that quantifies the capacity of a variational autoencoder (VAE) to faithfully reconstruct the joint probability distribution of a many body system. In a nutshell, a bound on the VAE capacity is obtained by comparing the rate of the latent channel to the bipartite mutual information of the data. Using this bound, we show that the conditionally independent decoder of any successful VAE is structurally identical to a finite-size mean-field factorization. Hence, a successful reconstruction is direct evidence for a latent mean-field theory and the microscopic parameters of that theory can be read off the trained decoder. We validate these conclusions on a hierarchy of solvable models with scalar (Curie-Weiss), vector (Hopfield) and tensor (Maier-Saupe) order parameters, recovering the full Hopfield pattern matrix from equilibrium samples alone. We find that, when applied to Salamander retinal recordings, a two-latent VAE reproduces the population statistics with only two effective collective variables allowing us to recover the `stored patterns' of the neural population and write a generalized Hopfield model which correctly models the experimental data.

Efficient quantum error correction is essential for the advancement of quantum computing. We propose a quantum neural network with a global structure that reduces the number of unitary matrices required in quantum circuits. This approach resulted in a 97% reduction in training time and up to a 25% improvement in the training completion rate, ultimately achieving a 100% success rate in training while surpassing the error correction performance reported in previous studies. In addition, we demonstrated the enhanced robustness of quantum error correction against internal network noise. Moreover, the fidelity of quantum error correction under internal network noise increased by up to 15% due to the reduced computational load.

Hard-constraint decision systems usually veto infeasible candidates. This is too rigid when the system can act: if a known affordable repair would make an infeasible candidate feasible and valuable, rejection is a false veto rather than a ranking error. We introduce Q-RACL (Quantum Repair-Augmented Constraint Learning), a repair-before-veto framework that first defines RACL decision semantics and then identifies the single inference link where quantum feature access can be load-bearing. RACL accepts a candidate when a sequential repair plan restores feasibility and preference; otherwise it returns structured rejection credit. The hard link is repair-feasibility inference: which repair class restores feasibility from an observed candidate and context. We construct a discrete-logarithm-hidden RACL family where the repair class is a shifted interval rule in the latent exponent a = log_g(x), while the learner observes only x = g^a mod p. Under standard DLP-based learning separation, this coordinate is inaccessible to efficient raw-input classical policies but accessible to a quantum agent through Shor/Fourier structure. Across six primes and ten seeds, bounded raw-input classical policies and a wrong raw-Fourier encoding remain near chance, whereas the Q-DLP policy keeps false-veto rate below 1.1%, wins all paired seeds, and yields QNI_cond = 0.9777 to 0.9972. A classical DLog oracle matches it, isolating feature access rather than classifier capacity. Thus quantum AI is not added as a generic model upgrade; for this DLP-hidden repair family, it supplies the missing feature that closes the repair-before-veto loop.

We present a quantum--classical hybrid pipeline for polarimetric material classification that casts this as a point-matching problem. Voxel cubes, containing polarized light reflections, are used to train an encoder to produce 32-dimensional embeddings for the voxels of the cubes. At inference, the encoder head is discarded and the embeddings are encoded as probability amplitudes of quantum states. Next, a SWAP-test circuit estimates the fidelity between each of the 32D embeddings from the query cube and a dataset of anchor cubes. The aggregated fidelity serves as materials similarity scores, and the class of the anchor with highest aggregated fidelity is deemed as the class of the queried material. We evaluate our approach on a dataset of 23 materials ($\approx$800 samples each) derived from their Mueller matrices. The point-matching approaches from the proposed quantum SWAP-test and a classical classifier using Optimal Transport are compared. Our results demonstrate the competitive classification accuracy alongside open-set discrimination potential, establishing it as a viable path toward NISQ-based material recognition.

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.

The deployment of embodied artificial intelligence via world-model-based robotics presents a transformative opportunity for blockchain infrastructure, establishing urgent demand for trustworthy data provenance, cross-organizational governance, and incentive-compatible sharing across decentralized ecosystems. Simultaneously, quantum computing advances recognized by the 2025 Nobel Prize in Physics and the Turing Award threaten the cryptographic primitives securing these data economies, creating an interdependent imperative: long-lived verification for embodied AI depends on crypto-agile architectures capable of withstanding quantum adversaries. This tutorial examines blockchain as the coordination layer bridging this dual transition, from financial substrate to foundational Cyber-Physical-Social Systems infrastructure that simultaneously secures against quantum cryptanalysis and enables scalable, trustworthy data economies. The session opens with an immersive AWS Braket demonstration engaging participants with superconducting, trapped-ion, and neutral-atom hardware to assess cryptographic threat timelines and witness ECDSA-to-post-quantum signature transitions. Five integrated modules progress from embodied AI and world-model requirements through quantum hardware reality and evidence-based security migration, to scalable cross-shard architectures via BrokerChain protocols, trustworthy data economies implementing Croissant metadata standards and robotic learning provenance, and industry ecosystem integration for multi-modal cloud deployment. By bridging quantum hardware realities with embodied AI data requirements, this tutorial charts blockchain as unified infrastructure for next-generation decentralized intelligent environments, providing open-source frameworks and roadmaps for architecting quantum-resistant, interoperable, and data-trustworthy systems.

Financial crashes, cascading failures in infrastructure, and critical errors in AI systems are frequently triggered by events that occur with extremely small probability. Efficiently discovering and sampling events with probability below a threshold is therefore of critical interest. Yet this task is highly non-trivial using existing classical or quantum methods. Being rare, such events require an immense sampling overhead to collect sufficient data samples. Moreover, because the rare events are not known in advance, they cannot be flagged for amplification using standard techniques. Here, we introduce a quantum algorithm for rare-event discovery and sampling without first learning which events are rare. The algorithm achieves the optimal quantum scaling with the rarity threshold. We further demonstrate that this can achieve a quadratic speedup for heavy-tailed systems whose tail has nonvanishing total mass, and translates into a robust polynomial speedup for stationary stochastic processes, with the exponent determined by its entropy-rate structure.

Quantum key distribution (QKD) is increasingly considered for deployment in realistic communication networks, where long distances, heterogeneous fiber infrastructure, and coexistence with classical traffic present substantial challenges. Here, we demonstrate trusted-node QKD between Linköping University and the Stockholm hub of the Swedish national quantum communication infrastructure over 270 km of deployed single-mode fiber, extended by a 33 km multi-core fiber (MCF) segment emulating a metropolitan access link, for a total distance of 303 km. The two sub-links use commercial QKD systems whose receivers are interfaced with external superconducting nanowire single-photon detectors, enabling operation at losses beyond those supported by standard internal gated-mode detectors. We operate the link while actively switching the QKD channel between two MCF cores, with co-propagating Ethernet traffic and injected broadband optical noise in the other cores. The results demonstrate the integration of commercial QKD into demanding, dynamically reconfigurable fiber infrastructure relevant to future hybrid quantum-classical networks. Finally, using the generated secret keys, we illustrate how limited and time-varying QKD throughput affects one-time-pad-protected image transmission: image fidelity depends strongly on the available QKD-generated key budget and the choice of compression algorithm, highlighting application-level challenges for QKD-based encryption in realistic scenarios.

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.

Noisy intermediate-scale quantum (NISQ) processors are entering an early fault-tolerance regime where full quantum error correction carries prohibitive resource costs, yet lightweight error detection can meaningfully improve algorithmic success rates. Existing compilation and error-detection toolchains treat these concerns in isolation, with no principled way to balance detection overhead against success probability under latency constraints. We present an integrated hardware-aware compilation and data-driven quantum error-detection (QED) framework that jointly optimises qubit mapping, SWAP insertion, and syndrome-schedule placement via a noise-weighted cost function and a learned multi-objective scheduler. Simulation experiments on an HPC cluster using GPU-accelerated density-matrix simulation (NVIDIA cuQuantum SDK) across VQE, phase-estimation, and Grover benchmarks, three noise profiles, and circuit sizes of 6-20 qubits (depths 10-160), show that joint co-design raises algorithmic success probability by up to 68 percent (95 percent CI: 60 percent to 76 percent) over SABRE on an 8-qubit VQE instance with post-selection.

Traffic sign recognition is crucial for intelligent transportation and autonomous driving, as it can improve driving efficiency and ensure road safety. However, traditional recognition methods are based on large datasets and intensive computation, which limits their real-time applicability. Spiking Neural Networks (SNNs) offer a biologically inspired, energy-efficient alternative due to their spatiotemporal processing capabilities, but suffer from information loss and vanishing gradients during training. To overcome these limitations, this study proposes a Quantum Deep-supervised Spiking Neural Network (QDS-SNN) that integrates Quantum Neural Networks (QNNs) for efficient, low-power deep supervision. Using quantum superposition and entanglement, QNNs enable expressive representations and parallel computation, thereby enhancing performance without compromising energy efficiency. The proposed QDS-SNN incorporates a temporally and spatially adaptive LIF (TSA-LIF) neuron and a quantum-assisted classifier module (QACM) to mitigate gradient issues and improve training effectiveness. This study conducts experiments on the PennyLane quantum simulation platform, and the results show that QDS-SNN achieves 99.72% accuracy on the GTSRB dataset in only 6 time steps -- outperforming the MS-ResNet baseline by 1.32% while reducing energy consumption by 55.77%. In the TSRD dataset, it achieves 97.90% accuracy while reducing energy use to 52.68% of the baseline. These results demonstrate that QDS-SNN offers a high-performance, energy-efficient solution for traffic sign recognition in intelligent transportation systems.

Scene Graph Generation (SGG) requires relational reasoning over objects and their interactions, but performance is often limited by severe long-tail predicate imbalance. Classical SGG models frequently rely on dataset statistics, leading to biased predictions toward frequent relations rather than fine-grained semantic predicates. Although existing debiasing strategies improve mean recall, predicate classification in current frameworks still often depends on large classical decision modules with high parameter cost. This work introduces a hybrid quantum predicate classifier for SGG by replacing the classical predicate head in Causal Feature Enhancement Network (CFEN) with a Quantum Predicate Head (QP-Head) trained using weighted cross-entropy. To the best of our knowledge, this is among the first studies to evaluate a hybrid quantum architecture for scene graph predicate classification on Visual Genome 150. We study the effect of qubit count, encoding strategy, entangling structure, and circuit depth on relational prediction. The best 4-qubit QP-Head uses Amplitude Embedding and Strongly Entangling Layers to compress 4096-dimensional pair features into a 16-dimensional quantum-compatible representation, corresponding to a 256$\times$ reduction. It achieves an mR@100 of 57.25%, compared with 41.1% for the classical CFEN reference, while using only 96 trainable quantum parameters. Scaling to 8 qubits maintains strong long-tail performance, reaching an mR@100 of 55.38% with 384 quantum parameters, while the depth analysis shows a trade-off between expressibility and runtime overhead. These results suggest that compact hybrid quantum predicate heads can support parameter-efficient long-tail relational classification in complex visual reasoning tasks.

Understanding and anticipating scientific change requires models that distinguish between endogenous consolidation and exogenous diffusion of scientific concepts. Using the quantum computing subtree of concepts in OpenAlex, we construct a temporally resolved concept co-occurrence network and track each concept pair through its upstream citation lineage and downstream diffusion. We train LightGBM models on distributional and diversity-aware features to predict four outcomes: endogenous reinforcement, exogenous diffusion, their ratio, and diffusion entropy. After controlling for overall publication growth of the scientific body, endogenous reinforcement proves largely unpredictable in the primary quantum-computing benchmark. In contrast, exogenous diffusion and entropy are strongly predictable ($R^2$ up to $0.78à) and are driven by upstream heterogeneity, citation breadth, and distributional dispersion, as shown by SHAP analyses; replications on robotics, advanced materials, and neuro implants confirm that exogenous diffusion remains the top-ranked target across fields ($R^2_test \sim 0.60-0.87$), while endogenous predictability rises markedly in neuro implants (R^2_test = 0.83), indicating that the quantum-computing asymmetry does not generalise uniformly. Case studies reveal that sharp entropy increases coincide with the opening of new conceptual frontiers, while entropy collapses signal technological convergence or paradigm displacement. These results demonstrate that conceptual diffusion is governed by stable structural regularities embedded in semantic and citation environments. By identifying early diversity-based signals of cross-domain uptake, the approach provides a scalable foundation for anticipatory scientometrics, technology foresight, and innovation-oriented policy analysis in rapidly evolving research fields.

Training quantum neural networks (QNNs) on quantum hardware is currently bottlenecked by the cost of gradient estimation: standard parameter-shift methods require a number of circuit evaluations that grows quadratically with the number of trainable parameters, making hardware-based optimisation impractical beyond small system sizes. In this work, we introduce a training framework that reduces this cost to logarithmic in the number of qubits, making gradient-based QNN optimisation feasible on near-term hardware at increasing scales. Our framework combines three co-designed ingredients: (i) a structured, subspace-preserving Butterfly circuit architecture with $O(n \log n)$ parameters and logarithmic depth; (ii) a layer-wise training strategy that confines on-hardware optimisation to one small, well-structured layer at a time; and (iii) a parallelised parameter-shift rule that exploits the commuting structure within each Butterfly layer to extract all gradients in a constant number of circuit executions. Together these reduce the number of distinct circuit evaluations per optimisation step from $O(n^2)$ to $O(\log n)$. We validate the framework on clinical data imputation using the MIMIC-III electronic health record dataset, a demanding benchmark sensitive to optimisation instability and model variance. Hybrid classical-quantum models are trained directly on IonQ Forte Enterprise trapped-ion hardware at 16 qubits without performance degradation relative to ideal or noisy simulation and via tensor-network simulation at 32 qubits, with 32-qubit inference executed on hardware. The resulting models match or exceed strong classical neural baselines in downstream patient survival prediction while exhibiting reduced variance across runs, demonstrating that the proposed framework enables practical, scalable QNN training under realistic hardware constraints.

Large machine learning models benefit substantially from multimodal inputs that provide a complementary view of the same example. We introduce QUIVER (QUantum-Informed Views for Enhanced Representations, a paradigm that enriches classical data-driven features with a quantum Fisher view: a geometrically motivated, basis-independent summary of higher-order correlations captured by a variational quantum circuit (VQC) trained to perform the same task. Unlike classical feature augmentation, the quantum Fisher information matrix encodes the intrinsic geometry of the learned quantum state manifold. While this feature map, motivated by quantum information theory, is ordinarily non-trivial to model classically, it can surface statistical structure that additional classical data or model capacity finds difficult to learn. This makes the quantum Fisher view a genuinely complementary modality rather than a redundant one. We demonstrate that QUIVER improves standard performance metrics on two benchmark datasets from very different fields: QM9 for predicting molecule properties, and JetClass for predicting jet flavor at the Large Hadron Collider (LHC). The core contribution, however, is domain-agnostic: the quantum Fisher view can be fused into a broad class of model architectures via targeted modifications to the base architecture, to incorporate information about the quantum geometry of the problem. These results demonstrate that quantum-geometric features, extracted from simulated variational circuits, can deliver measurable value for standard machine learning tasks, well before the advent of fault-tolerant quantum hardware.

Quantum LDPC code discovery requires searching large algebraic design spaces while reliably certifying the parameters and equivalence classes of any candidates found. We introduce an LLM-guided evolutionary workflow in which language models mutate Python programs that generate bivariate-bicycle and perturbed bivariate-bicycle code ansätze. Across five campaigns, the system performed approximately 1{,}650 evolutionary iterations, screened about $2 \times 10^5$ candidate codes, and required ${\sim}140$ hours of computation and ${\sim}$US$400 in LLM inference cost. Candidate codes are evaluated through a staged validation pipeline combining $\mathrm{GF}(2)$ rank computation, distance estimation and certification, mixed-integer linear programming, BLISS Tanner-graph deduplication, decomposability analysis, and local-Clifford equivalence checks. At block length $n \leq 360$, the workflow identifies 465 distinct candidate codes: 97 CSS bivariate-bicycle codes and 368 non-CSS perturbed variants. The CSS search recovers known high-performing codes and finds new finite-length representatives, including an indecomposable [[288,16,12]] code and higher-weight codes with up to $k = 50$ at distance $d = 8$. The non-CSS search produces perturbed codes matching the gross-code figure of merit at [[144,12,12]], along with additional high-distance candidates reported as certified values or upper bounds according to MILP status. Overall, these results show that LLM-guided program evolution can serve as a practical tool for structured quantum-code discovery when paired with independent evaluation.

Machine learning has accelerated quantum chemistry but is hindered by the prohibitive cost of generating high fidelity training data. Multifidelity machine learning (MFML) mitigates this overhead by systematically combining abundant low fidelity data with sparse high fidelity data. In spite of its success, standard MFML schemes rely on pre-defined scaling factors to determine sparse data ratio across fidelities, often generating redundant multifidelity data resulting in a loss of efficiency. Here, we introduce an adaptive on-the-fly multifidelity framework for machine learning that autonomously determines training dataset composition. By dynamically querying training samples at each fidelity, the algorithm saturates model accuracy at lower fidelities before moving up to more expensive reference calculations. We benchmark the novel adaptive-MFML across diverse chemical properties including the computational chemistry gold standard coupled cluster energies, and the more chemically challenging excitation energies. In our numerical experiments we show that our adaptive algorithm reduces data generation costs by up to a factor of 30 compared to single fidelity methods and improves upon standard MFML by up to a factor of 5. The mitigation of data redundancy establishes a high-accuracy low-cost pathway for sustainable cost-aware machine learning in quantum chemistry.

External regret certifies stability only against replacing one's behavior by a fixed alternative. In a quantum game, this misses a natural physical move: a player can apply a local completely positive trace-preserving (CPTP) map to the state it actually received or prepared. We introduce coherent swap regret as the regret benchmark against all such local CPTP deviations, and give an algorithm achieving $O(\sqrt{dT\log d})$ coherent swap regret via entropic mirror ascent on the CPTP Choi slice with a fixed-point play rule. The main result is a three-level deviation-class landscape. Replacement channels recover ordinary external regret at rate $Θ(\sqrt{T\log d})$. Unital channels, including unitary deviations and mixtures of unitaries, have zero minimax regret. Deterministic measurement-and-preparation channels already force $Ω(\sqrt{dT\log d})$ regret in the moderate-horizon regime, and this rate is also sufficient for all CPTP deviations. Thus the hardness comes from non-unital use of the recommendation register, not from quantum coherence alone. As an application, decentralized full-information learning in finite quantum games reaches an $\varepsilon$-approximate separable quantum correlated equilibrium after $T=O(\max_i d_i\log d_i/\varepsilon^2)$ rounds. We identify these equilibria with channel-proofness of mediated quantum recommendation protocols, give an SDP audit for local CPTP exploitability applicable to arbitrary finite-dimensional states, and include a probing-bandit extension with pseudo-regret $O(d^{4/3}T^{2/3}(\log d)^{1/3})$ under Haar-random pure-state probes.

Training Variational Quantum Circuits (VQCs) under Noisy Intermediate-Scale Quantum (NISQ) constraints introduces severe computational limitations: classical statevector simulation memory scales exponentially ($\mathcal{O}(2^n)$), and global cost functions suffer from barren plateaus where gradient variance decays exponentially ($\mathcal{O}(1/2^n)$). This paper introduces and evaluates the Quantum Algorithm for Distributed Reduction of Entanglements (QADR), a hybrid quantum-classical machine learning framework that decomposes a global $n$-qubit VQC into localized sub-circuits operating approximately within the causal light cones of individual target qubits. QADR reduces classical simulation memory scaling from $\mathcal{O}(2^n)$ to $\mathcal{O}(n \cdot 2^{2d+1})$ for a light cone radius $d$, while naturally mitigating global barren plateaus. We benchmark QADR against standard global VQCs, Support Vector Machines (SVM), and two customized classical parameter-matched neural networks (CANN and PMNN) on the MNIST dataset and the high-dimensional NASA IMS wind turbine drivetrain diagnostic task. QADR demonstrates excellent scalability, operating successfully at $n_{\text{features}}=2000$ where standard global VQCs crash due to memory exhaustion, while matching or exceeding the performance of optimized classical architectures.

Full waveform inversion (FWI) reconstructs heterogeneous material properties from receiver data but remains computationally demanding. Physics-informed neural networks (PINNs) and their domain-decomposed variants (FBPINNs) offer a mesh-free alternative but face convergence challenges when representing complex velocity fields. We present a hybrid quantum-classical FBPINN for acoustic FWI, bringing together quantum computing and classical machine learning, in which the decomposed wavefield network and the global velocity network are implemented as classical-to-quantum pipelines terminating in parameterized quantum circuits (PQCs). The PQCs are realized as differentiable JAX statevector simulators, enabling end-to-end automatic differentiation through the classical PINN, the quantum circuit, and the physics-informed loss. On a geophysical anomaly benchmark, the quantum hybrid reaches a lower L1 velocity error than the primary classical FBPINN baseline in approximately 8x fewer training iterations, despite using approximately 33% fewer trainable parameters, and it outperforms all 15 classical hyperparameter variants tested. A second benchmark (checkerboard) demonstrates the generality of the inversion pipeline, confirming that the quantum hybrid architecture can recover structured spatial variations beyond the localized anomaly benchmark. Our framework is broadly applicable to wave-based inverse problems beyond geophysics, including medical ultrasound tomography and non-destructive evaluation.

Transistor scaling is approaching a quantum-mechanical limit, as thin gate oxides induce electron leakage through quantum tunneling. Unlike conventional digital systems, AI inference can tolerate such errors provided their structure is modeled correctly. In this paper, we introduce quantum tunneling-aware machine learning (QTAML). We derive the deployment-time weight-error distribution from first principles using the Wentzel-Kramers-Brillouin (WKB) approximation and show that it has structure that generic Gaussian noise models miss: an exact affine mean drift, a per-bit variance hierarchy dominated by the most-significant bit, and a per-layer dependence on $\|W_\ell\|_\infty$ and the trained-network Jacobian. We package these three structural properties into a single deployment-time algorithm, Tunneling-Aware Compensation (TAC), that combines closed-form mean correction with an optimal layer-adaptive bit-budget allocation derived from the WKB variance decomposition. Across four convolutional architectures at $p_\mathrm{flip}$=0.10 and a transformer encoder at $p_\mathrm{flip}$=0.05, TAC reaches $95\%$ of clean accuracy with 3.4$\times$ to 33.6$\times$ less ECC overhead than Uniform-MSP, the natural baseline derived from the same physics. The closed-form saturation ratio $ρ^*$ predicts these gains in advance, and on heterogeneous architectures WKB-derived scoring outperforms magnitude-based allocation by up to 24 percentage points at small budgets. The algorithm requires no retraining, no labels, and no inference-time overhead. We also verify the WKB-derived distributional theorems to Monte Carlo precision. These results connect WKB tunneling physics with noise-aware deep learning and suggest a principled path toward hardware--software co-design beyond conventional scaling limits.

Two recent results have reshaped quantum Gaussian processes (QGPs). On the one hand, \citet{lowe2025assessing} rule out the exponential speedups claimed by HHL-based QGP regression in the typical, well-conditioned regime; on the other, an independent line of work shows that highly expressive quantum kernels suffer posterior pathologies that break Bayesian optimization. We show that these seemingly unrelated phenomena are governed by the same quantity: the normalized spectral entropy $S(K)/\log n$ of the kernel Gram matrix. We prove a Cauchy--Schwarz tail bound on Nyström approximation error, a finite-sample variance-contraction identity in terms of Bach's degrees of freedom $d_σ(K)$, and a characterization of the \emph{target-dependent} optimal entropy via the intrinsic dimension of the target in the kernel eigenbasis. Empirically, the diagnostic is kernel-agnostic: hardware-efficient, matchgate, IQP \emph{and} RBF/Matérn/RFF/deep-kernel families all collapse onto identical $S/\log n$ curves on dequantization, ECE, and variance-contraction panels. The NLL sweet spot lives at high entropy for smooth targets and at low entropy for band-limited quantum-data targets. The diagnostic transfers from simulator to IBM Heron hardware with median absolute error $3.2\%$ and mean $5.2\%$ in $S/\log n$ across $24$ configurations at $n_q = 4$, with matchgate and IQP within $5\%$ mean and a single HE configuration returning a $30\%$ outlier that drops to $0.5\%$ on rerun (attributed to calibration drift); the same diagnostic transfers to a second Heron backend (mean error $2.7\%$) and to a $n_q = 6$ scale-up on the original backend (mean error $1.7\%$). No error mitigation is applied throughout.

Many practically relevant applications of quantum machine learning involve classical data, for which performance depends critically on how inputs are embedded into quantum states. Yet the use of a fixed embedding circuit ansatz remains standard practice. We propose an energy-based generative learning framework that synthesizes gate sequences to optimize embedding structures and refine data-tailored parameters, using a fidelity-based surrogate objective to guide the search toward improved class distinguishability. Empirically, the method improves classification performance across diverse settings, while also revealing datasets where architecture search within the present embedding family yields only limited additional gains. We explain this saturation by deriving bounds on the achievable empirical risk in terms of the Wasserstein distance in the input space, showing that classical data geometry provides an \emph{a priori} diagnostic for regimes in which substantial gains from embedding optimization are unlikely. The results establish a practically useful and theoretically motivated framework for searching effective quantum data embeddings through generative optimization, with the attainable gains diagnosed through the geometry of the underlying classical data.

We investigate the computational complexity of neural network verification in quantised settings. We distinguish three classes of Feedforward Neural Networks (FNNs): rational FNNs with exact rational weights, quantised FNNs whose weights come from a finite-width arithmetic, and dynamically quantised FNNs in which rational networks are evaluated with respect to a given finite-width arithmetic. We consider two types of specifications used in the literature. Linear programming (LP) specifications are conjunctions of linear constraints, while bit-vector (BV) specifications allow reasoning at the bit level and can express non-linear constraints. Our results give a complexity landscape of these verification problems. For quantised FNNs with fixed arithmetic precision, we show that verification under both LP and BV specifications remains NP-complete, matching the complexity of the rational case. For dynamically quantised FNNs with BV specifications, we establish upper bounds, complementing a previously known PSPACE-hardness result.

Traditional cryptography, rooted in problems, e.g., integer factorisation or discrete log, is inevitably vulnerable to a fully operational quantum computer. Although it remains an engineering frontier, the looming threat extends to encrypted data stored today, which could be decrypted in the future with quantum capabilities. To safeguard against this eventuality, the backbone of the modern quantum-safe cryptography is the Shortest Vector Problem (SVP). We enhance Laarhoven's treatment of Ajtai et al.'s sieving as a genetic algorithm (GA) for the SVP by incorporating domain-informed SVP representation and crossover while naturally extending application to the module lattices.

Many applications in quantum simulation, quantum chemistry, and quantum machine learning require not a single quantum state but an ensemble of states characterizing the heterogeneity of a target system. Preparing such ensembles state-by-state is prohibitive in both variational and fault-tolerant settings, thereby motivating a generative modeling approach. We introduce latent-conditioned parameterized quantum circuits (LPQCs), a hybrid quantum-classical framework in which classical neural networks map a latent variable sampled from a prior distribution to the parameters of a parameterized quantum circuit. We prove that LPQCs are universal approximators for probability measures over density operators in the 1-Wasserstein distance, extending classical universal approximation theorems to the quantum-distribution setting. We additionally introduce a multimodal latent prior and a mixture-of-experts circuit architecture, and show empirically that the latent-conditioned parameterization alleviates the barren plateau problem during optimization, a behavior for which we provide rigorous partial guarantees. Numerical experiments validate the framework on a synthetic multi-cluster ensemble of mixed quantum states and on a QM9-derived ensemble of 3-D molecular structures. In these tasks, LPQC outperforms recent quantum generative baselines and matches the generation quality of a classical neural-network baseline, while requiring an output dimension that grows only linearly with the number of qubits rather than exponentially. By leveraging classical expressivity in the latent space, LPQCs offer a tractable route to quantum generative modeling.

Artificial Intelligence has achieved remarkable success across diverse application domains. However, its vulnerability to adversarial attacks poses significant challenges to reliability, security, and trustworthiness. Adversarial machine learning demonstrates that even highly accurate models can be manipulated through carefully crafted perturbations, raising serious concerns in safety critical systems such as healthcare, finance, and autonomous technologies. In parallel, quantum computing has emerged as a transformative paradigm capable of addressing complex computational problems through principles such as superposition, entanglement, and quantum interference. The convergence of these fields has led to the emergence of quantum artificial intelligence, which explores how quantum techniques can enhance learning efficiency, scalability, and robustness. This chapter provides a comprehensive overview of adversarial machine learning and existing defense strategies, followed by an accessible introduction to quantum computing and quantum machine learning models. It further presents conceptual frameworks for quantum-enhanced adversarial robustness, emphasizing quantum optimization, feature mapping, and hybrid quantum classical architectures. Practical applications, key challenges, and future research directions are also discussed to support the development of secure and trustworthy AI systems.

Logical operations are essential for quantum computation within quantum error-correcting codes. However, discovering their physical realizations is challenging, especially for non-additive codes that lack a stabilizer description. We present a general learning-based framework that, given only an encoding circuit, constructs physical implementations of logical operations while enforcing structural properties such as transversality or shallow depth. Our approach is validated by rediscovering known logical operations of standard stabilizer codes. We then extend it to a co-design procedure, dubbed variational early fault-tolerant quantum computing (VarEFTQC), which tailors non-additive encodings to a given noise model and enforces desired logical gate sets, such as transversal IQP-type families or low-depth universal sets. A software library implements the complete learning pipeline, including loss-function variants, ansatz families, and optimization routines. Together, these results position VarEFTQC as a proof-of-concept framework for discovering hardware-adapted logical gadgets for early fault-tolerant quantum computing.

The rapid growth of computer vision and increasingly complex image recognition tasks has exposed fundamental computational limitations of classical machine learning models, motivating the exploration of quantum computing as an emerging new paradigm. This paper presents a comprehensive benchmarking study of classical and quantum machine learning models for image recognition on the MNIST handwritten digit dataset, evaluating both traditional models, a Classical Support Vector Machine (CSVM) and a Quantum Support Vector Machine (QSVM), and deep neural network models, a Classical Convolutional Neural Network (CCNN) and a Quantum Convolutional Neural Network (QCNN), across four performance dimensions: classification accuracy, computational runtime, parameter count, and memory requirements. Experiments are conducted as functions of both feature dimensionality and sample size, and across CPU and GPU execution environments, providing a controlled, multidimensional comparison to address gaps in prior work. For the SVM-based models, QSVM consistently outperforms CSVM in accuracy, reaching $\sim$ 0.90 versus $\sim$ 0.85 at 1,000 samples, with a higher computational cost. A feature count of 10 qubits and a sample size in the range of 200 -- 500 emerge as practical operating points that balance accuracy and runtime. For the neural network models, CCNN and QCNN achieve comparable classification accuracy, both exceeding 0.96 at 64 features and 60,000 samples, yet QCNN offers substantially superior parameter and memory efficiency, requiring $\sim$ 94% fewer parameters and $\sim$ 75% less memory than CCNN at higher feature counts, while incurring higher runtime. Across both model families, quantum models consistently outperform classical models by greater margins in accuracy as feature dimensionality or sample size increases.

The 2024-2025 Nobel and Turing awards recognised AI and quantum science simultaneously. Yet no deployed system has brought these streams together for the public. This paper presents QSignAI, a production-deployed platform demonstrating a bidirectional AI-quantum relationship in a real-time event participation system. We address three questions: can quantum-randomness generation via a two-source extractor be embedded in an AI-driven social platform with acceptable latency; can an AI bot make quantum phenomena perceptually legible to general audiences; and does the combined system work in practice? A conversational bot routes each participant's first message through a quantum pipeline comprising a Toeplitz two-source extractor over independent single-qubit Hadamard measurements on SV1 and DM1 simulators, plus a 2-qubit Bell state, producing a unique quantum-randomness-seeded identity signature per participant. The first two questions are answered through system architecture and qualitative deployment evidence from live events; the third through successful production deployment. The current deployment uses cloud quantum simulators; physical QPU randomness is the near-term extension. Measurable benchmarks are identified as priority future work.

We construct and evaluate group-equivariant neural networks for the prediction of the two-dimensional $Q$-tensor order parameter of nematic liquid crystals from synthetically generated microscopic textures. Seven architectures, equivariant to cyclic groups $C_k$ of order $k$ for $k=4,\,8,\,16,\,32,\,64,\,128,\, 256$, are built using a combination of weight-sharing constraints, equivariant activations and regularization techniques. To do this, we construct rotation-like permutation matrix groups with elements $\varrho_{C_k}(g)$ that act on row-wise vectorized images, thereby approximating a $\frac{2π}{k}$ rotation of the circular subdomain on square images. We show that all seven equivariant models satisfy the $Q$-tensor equivariance constraint to within single-precision floating point accuracy. Comparing against approximate parameter-matched non-equivariant benchmarks, with and without data augmentation, we find that the equivariant models consistently achieve lower errors and generalize more robustly to unseen defect configurations. Performance increases with group order, suggesting that the incorporation of finer rotational symmetry leads to lower errors.

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 adapt Microsoft's QuantumKatas -- a well-established quantum computing curriculum -- from Q# to Qiskit, the most widely-adopted quantum computing framework, and package it with an evaluation framework for systematic LLM assessment. The resulting benchmark comprises 350 tasks across 26 categories, spanning fundamental gates through advanced algorithms (Grover's, Simon's, Deutsch-Jozsa), error correction, key distribution, and quantum games. Each task includes a natural language prompt, canonical solution, and deterministic test verification via classical circuit simulation. By building on the QuantumKatas' proven pedagogical design rather than creating tasks from scratch, we inherit a principled difficulty progression and comprehensive concept coverage while contributing the framework adaptation, evaluation infrastructure, and empirical analysis. We evaluate 16 LLMs across 7 prompting configurations -- a total of 39,200 model runs -- to demonstrate the benchmark's utility. Three key findings emerge: (1) the benchmark effectively differentiates model capabilities, with best-configuration pass rates ranging from 32.3% to 83.1% and a 26.1 pp average gap between frontier and open-source models; (2) models perform well at implementing known algorithms (SimonsAlgorithm 82.1%, BasicGates 81.6%) but struggle with problem encoding (SolveSATWithGrover 34.4%, DistinguishUnitaries 40.0%); and (3) chain-of-thought prompting shows a modestly bimodal effect -- it is the best strategy for three models (two of them explicitly reasoning-tuned per vendor documentation) but degrades performance for the rest, leaving it mid-pack in aggregate (56.3% mean) behind few-shot-5 (57.8%). We release the benchmark, evaluation framework, and baseline results to support research on LLM capabilities in quantum computing.

We present a Multi-task Soft Actor-Critic (SAC) Reinforcement Learning framework designed for open-system quantum control across diverse Hamiltonians, which learns optimal pulse sequences while simultaneously discovering problem-specific evolution time T and number of control pulse segments N. Experimental results across 51 Hamiltonian variations demonstrate that the multi-task SAC model is able to generate control pulses that can drive a system, under environment noise, from its initial state to its target state with high fidelities, establishing essential foundations for universal quantum control applicable to realistic noisy quantum devices. Through progressive expansion of the training Hamiltonian set, we investigate if a single multi-task model trained using a given number of sample Hamiltonians can successfully accomplish state-transfer tasks for Hamiltonians drawn from the same Hamiltonian space but not encountered during training. In addition, our Robustness Infidelity Measure (RIM) analysis reveals that SAC trained policies exhibit superior robustness to pulse amplitude perturbations and decoherence rate variations compared to GRAPE-optimized controls.

We train a pair of autoregressive models to construct zero-mean control variates to mitigate the sign problem in quantum Monte Carlo simulations. The two autoregressive networks are confined to the positive- and negative-sign sectors with strictly disjoint support, and each is exactly normalized over its sector. Their difference is therefore structurally zero-mean, providing an unbiased auxiliary observable whose correlation with the sign estimator controls the variance reduction. We implement the method within the stochastic series expansion framework, which we extend to frustrated lattices by developing an incremental loop-topology update. Sign-ergodic sampling is achieved through a twist channel, which is the unique sign-changing mechanism on non-bipartite lattices. We implement the control variates as autoregressive transformers with an end-of-sequence parity mask that enforces exact sign-sector resolution, while the incremental loop-count change and cumulative frustration parity are incorporated as topological features. On the triangular-lattice Heisenberg antiferromagnet, we benchmark the method in the small-$N$ limit. The control variate reduces the standard error of the average sign by up to an order of magnitude and that of the energy estimator by a factor of three to five, remaining effective even when the average sign drops below $10^{-3}$. This work lays out the framework and provides a proof-of-principle demonstration that autoregressive control variates can effectively mitigate the sign problem. Scaling to larger systems with physics-informed architectures is the subject of future work.

The growing complexity of quantum programming frameworks has exposed a critical limitation in existing large language model (LLM)-based code assistants: general-purpose models hallucinate PennyLane-specific gate names, misplace device configurations, and produce structurally invalid circuits when faced with specialized quantum coding challenges. We present PennySynth, a retrieval-augmented generation framework that addresses this gap by conditioning LLM inference on a curated knowledge base of 13,389 PennyLane instruction-code pairs, built via a three-stage extraction, verification, and deduplication pipeline over official PennyLane repositories, community GitHub sources, and QHack competition archives. PennySynth introduces a code-aware embedding strategy using st-codesearch-distilroberta-base, trained for natural-language-to-code retrieval, increasing average retrieval cosine similarity from 0.45 to 0.726 compared to a general-purpose baseline. Evaluated across 74 challenges spanning three years of the QHack competition (2022, 2023, 2024), PennySynth achieves 64%, 68%, and 52% pass@5 on QHack 2022, 2023, and 2024, respectively, improving over Claude Sonnet 4.6 without retrieval by +28, +25, and +28 percentage points. We further introduce a quantum-adapted CodeBLEU metric that upweights qml.* token patterns and show that structural code similarity and functional correctness capture distinct aspects of quantum code quality. Controlled ablations reveal that code-aware embeddings are the primary driver of retrieval performance, while dataset expansion and source composition provide additional gains when retrieval quality is sufficiently precise.

Quantum machine learning (QML) is moving from research prototypes to deployed cloud services. As QML enters regulated industries, the integrity of the quantum stage becomes a practical concern on two fronts: noisy hardware drifts at the channel level between recalibrations, and an adversary with control over the execution environment can substitute the declared quantum channel with a behaviorally similar but mathematically distinct one. Neither concern is covered by existing QML verification work on pulse-level noise, input drift, input-perturbation robustness, or device identity. We introduce QML-PipeGuard, a contract-based framework addressing both concerns under a single mathematical machinery. It characterizes a QML pipeline at runtime by its behavioral fingerprint, the vector of observable expectation values under a tomographically structured measurement family, and operates in two modes: drift-aware monitoring that absorbs benign calibration changes within a calibrated tolerance, and adversarial detection that catches channel substitution as a violation of an informationally complete observable contract. The framework contributes a pipeline-composition treatment of the encoder-ansatz-measurement channel with a QML-specific threat model (tight frame-bound C=sqrt(3) for the single-qubit Pauli family), a finite-shot sample-complexity bound, and a tolerance decomposition separating adversarial and natural-drift contributions. We validate the framework end-to-end on a two-qubit QSVM pipeline on the IBM Heron r2 processor (ibm_fez), with a sample-complexity validation on a noise-matched simulator. The prescribed measurement budget (about 1.4e4 shots) fits in a single batched job, the sneaky channel is detected with a wide safety margin while evading the weak contract, and the typical hardware drift sits within tolerance.

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.

Fermi-Dirac machines were proposed recently as an approach to solving semidefinite optimization problems on quantum computers. Here, we reinterpret them as canonical quantizations of classical neurons. By viewing a classical neuron as an activation function applied to a parameterized classical Hamiltonian, we quantize this model by replacing classical variables with operators whose eigenvalues encode their possible values. This follows the standard approach to canonical quantization in quantum mechanics. Crucially, when the Hamiltonian consists of commuting operators, our construction reduces exactly to a classical neuron. More generally, our approach yields an activation observable, defined as an activation function applied to a parameterized quantum Hamiltonian. The output of this quantized neuron is a random variable with expectation value equal to that of the activation observable with respect to an input state. We develop efficient hybrid quantum-classical algorithms for evaluating outputs and gradients of our quantized neurons, enabling evaluation and training. These algorithms rely on basic primitives that include random sampling, Hamiltonian simulation, and the Hadamard test. We also quantize a whole host of other activation functions, including the smooth rectified linear unit (ReLU), sigmoid linear unit, Gaussian-smoothed ReLU, and Gaussian error linear unit (GeLU), which are known to be useful for deep learning applications. Numerical experiments indicate that neurons based on quantum Hamiltonians can learn functions that classical neurons cannot. We further define a computational decision problem based on Fermi-Dirac neurons and prove that it is BQP-complete, providing complexity-theoretic evidence against efficient classical simulation. Finally, we generalize our approach to continuous quantum variables and sketch two different ways of composing these neurons into networks.

Quantum machine learning is often motivated by the idea that quantum systems can expose useful high-dimensional structure that is difficult to access with classical models. We isolate one central component of this claim: the fixed data-encoding map. Amplitude, angle, and basis encoding are evaluated as deterministic feature maps for classical supervised learning under matched output dimensionality and strong classical controls. The benchmark compares these encodings against raw linear models, random Fourier features, polynomial features, PCA, RBF SVMs, and shallow neural networks across diverse classical datasets. Rather than treating performance as a single endpoint, we analyze the geometry of each representation through effective rank, condition number, centered kernel alignment, predictive performance, and practical overhead. The resulting picture is mechanistic: amplitude encoding can remove magnitude information through unit-sphere normalization, angle encoding can become geometrically redundant with raw linear features, and basis encoding can impose a binary Hamming geometry that is poorly aligned with smooth decision structure. These findings do not argue against quantum computation, however, they show that fixed quantum-inspired encoding geometry alone is not a reliable source of machine-learning advantage on classical data.

Statistical downscaling is a crucial component of the weather modeling field, where high-resolution outputs must be reconstructed from coarse-resolution inputs with the full cost of dynamical refinement. In this work, we investigate a hybrid quantum-classical corrective diffusion model for probabilistic statistical downscaling of weather fields. The proposed model inserts variational quantum circuit layers into the most compressed bottleneck of the diffusion UNet while leaving the regression branch fully classical. This placement tests whether quantum circuits can act as compact nonlinear feature maps for latent-channel mixing. We evaluate intra-channel and cross-channel ansätze on 10m wind components. On the 2020 validation set, the hybrid models remain stable, preserve the large-scale spatial organization of the generated wind fields, and improve both MAE and CRPS relative to a classical corrective diffusion model in several configurations. Structural diagnostics further show that the hybrid variants preserve kinetic-energy spectra and windspeed distributions similar to its classical counterpart while producing controlled changes in tail behavior, extreme-windspeed localization, and joint wind field components structure. Backend studies on the 2020 validation set show negligible impact from simulated device noise at the tested circuit scale, whereas real-hardware deployment remains limited by qubit availability and execution fidelity. The 2021 out-of-distribution test shows that these in-distribution gains do not transfer uniformly under temporal shift, revealing a generalization gap that motivates future mitigation through stabilization and regularization. These results show that bottleneck-level quantum hybridization can make a nontrivial contribution to weather statistical downscaling, while also highlighting that circuit scale and hardware deployment remain key limiting factors.

Accurate classification of microscopic blood cells is still a critical task in medical image analysis, where subtle variations and limited data can challenge conventional deep learning models. As such, we investigate in this work the potential of Hybrid Quantum-Classical Neural Networks (HQNNs) to enhance feature representation and improve classification performance in this domain. We propose a modular architecture combining a pre-trained ResNet-50 backbone with a low-dimensional latent bottleneck and a variational quantum circuit, enabling a direct comparison between quantum-enhanced and purely classical transformation mechanisms. To isolate the contribution of the quantum component, we evaluate three architectures: a HQNN model, a Classical Matched Model with an additional nonlinear transformation layer of comparable capacity, and a baseline model without an intermediate transformation stage. Experiments conducted on two publicly available blood cell datasets, namely the Blood Cell Images dataset and the PBC dataset, demonstrate that HQNNs consistently achieve superior or more balanced performance across evaluation metrics. In the Blood Cell Images Dataset, the proposed approach improves macro F1-score by up to 3.7% compared to classical baselines, while improving the F1-score from 98.54% to 98.69% in the more challenging 8-class scenario with near-saturated performance. Additional evaluation on IBM quantum hardware shows that the model remains robust under noise, with only a modest performance degradation relative to simulated results. These results indicate that quantum feature transformations can enhance discriminative representations, particularly in challenging classification scenarios, and highlight the practical potential of HQNN models for medical imaging tasks.

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.