Quantum Machine Learning

We introduce a hybrid quantum-classical pipeline, based on neutral-atom reservoir computing, for medical image classification, focusing on the binary classification task of polyp detection. To deal effectively with the high dimensionality, we integrate a guided auto-encoder. This pipeline learns compact and discriminative representations of image data that are also well-suited for quantum reservoir computing. A key challenge in such systems is the non-differentiable nature of quantum measurements, which creates a 'gradient barrier' for standard training. We overcome this barrier by incorporating a differentiable surrogate model that emulates the quantum layer, enabling end-to-end backpropagation through the entire system. This guided training process is jointly optimized for classification accuracy and for faithful image recovery from the auto-encoder. The learned latent representations are encoded as pulse detuning parameters within a Rydberg Hamiltonian, and quantum embeddings are subsequently obtained through expectation values. These embeddings are then passed to a linear classifier. Our simulations show that this method outperforms some traditional approaches that use PCA or unguided autoencoders. We also conduct ablation studies to assess the impact of various quantum and training parameters, demonstrating the robustness and flexibility of our proposed pipeline for real-world medical imaging applications, even in the current NISQ era.

Quantum machine learning has emerged as a promising tool for pattern recognition, yet many audio-focused approaches still treat spectrograms as generic images and do not explicitly exploit their time-frequency structure. We propose Q-Patch, a quantum feature map tailored to audio that encodes local time-frequency patches from mel-spectrograms into quantum states using shallow, hardware-efficient circuits with adjacency-aware entanglement. Each selected patch is summarized by a compact four-dimensional acoustic descriptor and mapped to a four-qubit circuit with depth at most three, enabling practical quantum kernel construction under near-term constraints. We evaluate Q-Patch on an audio spoofing detection task using a controlled, balanced protocol and compare it with size-matched classical baselines. Q-Patch improves discrimination between bona fide and spoofed samples, achieving an area under the receiver operating characteristic curve (AUROC) of 0.87, compared with 0.82 for a radial basis function support vector machine (RBF-SVM) trained on the same patch-level features. Kernel-space analysis further reveals a clear class structure, with cross-class similarity around 0.615 and within-class self-similarity of 1.00. Overall, Q-Patch provides a practical framework for incorporating time-frequency-aware representations into quantum kernel learning for audio authenticity assessment in low-resource settings.

Variational quantum circuits with angle encoding implement truncated Fourier series, and architectures arranging $N$ qubits with $L$ encoding layers each -- sharing encoding budget $E = NL$ -- generate identical frequency spectra, identical frequency redundancy, and require the same minimum parameter count for coefficient control. Despite this equivalence, trainability varies substantially with architecture shape $(N,L)$ at fixed $E$. We identify structural rank deficiency of the coefficient matching Jacobian $J$ as the mechanism responsible. For serial single-qubit architectures, we prove $\mathrm{rank}(J) \leq 2L+1$ regardless of parameter count $P$, with $\dim(\ker J) \geq P-(2L+1)$ growing without bound -- a phenomenon we term \emph{structural gradient starvation}: a growing fraction of parameters become structurally decoupled from the loss as $P$ increases at fixed $L$. Parallel architectures avoid this via independent phase trajectories, ensuring $σ_{\min}(J^{(\mathrm{par})}) > 0$ generically for $P \leq 2E+1$, so no parameter lies in $\ker J$. For practitioners, we further show that the two natural routes to increasing parameter count have fundamentally different effects: adding feature map (FM) layers monotonically strengthens the Jacobian QFIM eigenvalue spectrum and achieves $R^2 \geq 0.95$ with $1.6$--$2.2\times$ fewer parameters than adding trainable blocks across all tested architectures, while trainable blocks improve training only through the classical interpolation mechanism with no quantum-specific benefit.

Large language models (LLMs) have transformed artificial intelligence, yet classical architectures impose a fundamental constraint: every trainable parameter demands classical memory that scales unfavourably with model size. Quantum computing offers a qualitatively different pathway, but practical demonstrations on real hardware have remained elusive for models of practical relevance. Here we show that Cayley-parameterised unitary adapters -- quantum circuit blocks inserted into the frozen projection layers of pre-trained LLMs and executed on a 156-qubit IBM Quantum System Two superconducting processor -- improve the perplexity of Llama 3.1 8B, an 8-billion-parameter model in widespread use, by 1.4% with only 6,000 additional parameters and end-to-end inference validated on real Quantum Processing Unit (QPU). A systematic study on SmolLM2 (135M parameters), chosen for its tractability, reveals monotonically improving perplexity with unitary block dimension, 83% recovery of compression-induced degradation, and correct answers to questions that both classical baselines fail -- with a sharp noise-expressivity phase transition identifying the concrete path to quantum utility at larger qubit scales.

Parity (XOR) classification requires detecting discrete, high-order feature interactions that smooth classical kernels cannot efficiently capture. We study how quantum kernel advantage depends on parity complexity, the number of features entering the XOR rule, and find a clear threshold behavior. We pair a ZZ quantum feature map with binary {0, pi} encoding (features median thresholded before circuit input) to expose parity structure. A binary encoding ablation, RBF SVM trained on the identical {0, pi} features, separates encoding from circuit effects: at low complexity (n = 5 features), binary RBF achieves 83.4% +/- 1.7% and the quantum kernel 81.2% +/- 1.9%, showing encoding drives performance there. At high complexity (n = 11 features, 11 qubits, r = 3 ZZ repetitions), all classical methods collapse to near-random (approx. 50%), binary RBF reaches only 54.3% +/- 1.1%, and the quantum ZZ kernel achieves 66.3% +/- 3.2% (mean +/- std, 10 seeds), a +12.0 percentage-point margin over the binary ablation and approx. 7x higher kernel-target alignment (0.094 +/- 0.020 vs. 0.013 +/- 0.001). These results identify parity complexity as a concrete axis along which genuine quantum kernel advantage, not attributable to encoding alone, emerges.

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.

Nonstabilizerness, commonly referred to as magic, is a fundamental resource underpinning quantum advantage. In this paper, we propose a magic-informed quantum architecture search (QAS) technique that enables control over a quantum resource within the general framework of circuit design. Inspired by the AlphaGo approach, we tackle the problem with a Monte Carlo Tree Search technique equipped with a Graph Neural Network (GNN) that estimates the magic of candidate quantum circuits. The GNN model induces a magic-based bias that steers the search toward either high- or low-magic regimes, depending on the target objective. We benchmark the proposed magic-informed QAS technique on both the structured ground-state energy problem and on the more general quantum state approximation problem, spanning different sizes and target magic levels. Experimental results show that the proposed technique effectively influences the magic across the search tree and notably also on the resulting final circuit, even in regimes where the GNN operates on out-of-distribution instances. Although introducing a problem-agnostic magic bias could, in principle, constrain the search dynamics, we observe consistent improvements in solution quality across all problems tested.

Distributed quantum algorithms offer a promising pathway to scale variational quantum algorithms beyond the constraints of noisy intermediate-scale quantum hardware. However, existing approaches implicitly assume a trusted entanglement-sharing layer across quantum processors. We show that this assumption introduces a fundamental vulnerability: adversarial perturbations of shared entanglement induce structured gate-level noise that directly impacts quantum learning. We develop a framework that maps entanglement-level perturbations to gate-level noise via an explicit Kraus representation. To quantify their impact, we introduce Kraus expressibility, a metric that generalizes unitary expressibility to noisy quantum channels. We then establish a trade-off between Kraus expressibility and trainability of noisy quantum circuits through gradient variance analysis. Our analysis reveals that an adversary can manipulate Kraus expressibility to maintain sufficiently large cost gradients (avoiding barren plateaus) while systematically biasing optimization toward incorrect solutions. We validate these findings through numerical simulations, demonstrating adversarial degradation of expressibility and trainability.

Quantum machine learning increasingly relies on pure-state representations, motivating generative models that sample directly in quantum representation space rather than perturbing classical inputs and re-encoding. We introduce Stochastic Schrödinger Diffusion Models (SSDMs), a score-based generative framework that defines diffusion, scores, and reverse-time sampling intrinsically on the complex projective manifold $\mathbb{CP}^{d-1}$ under the Fubini--Study metric. SSDMs combine a Riemannian Ornstein--Uhlenbeck forward diffusion with a stochastic Schrödinger realization, and learn reverse-time dynamics driven by the Riemannian score. Our central technical contribution is a local-time learning objective that exploits the local Euclidean OU limit of intrinsic manifold diffusions in Fubini-Study normal coordinates to obtain an analytic teacher score, bypassing the intractable transition densities that limit existing Riemannian score-based models. Across synthetic, physics-inspired (TFIM, XXZ), and quantum feature-state benchmarks up to $14$ qubits, SSDMs match target pure-state ensembles by orders of magnitude on MMD and observable statistics over both ambient Euclidean and matched Riemannian score-based baselines, and improve representation-level diagnostics for downstream quantum kernel methods.

While parameterized quantum computations have shown success in standard reinforcement learning (RL), whether these advantages adapt to hierarchical RL (HRL) remains a critical open question. This work demonstrates that variational quantum circuits (VQCs) can effectively enhance HRL agents based on the option-critic architecture. Evaluated in standard environments, a hybrid HRL agent with a quantum feature extractor outperforms classical baselines while using fewer parameters. We also identify an architectural bottleneck: using VQCs for option-value estimation severely degrades learning. Further ablations reveal how quantum circuit design affects performance. Our work establishes design principles for parameter-efficient hybrid HRL agents.

We present an experimental study of energy-to-solution (ETS) of hybrid quantum-classical applications, enabled by direct instrumentation of power consumption of a Forte Enterprise trapped-ion quantum processor. We apply this methodology to a hybrid quantum-classical pipeline for quantum fine-tuning of foundational AI models, and validate the approach end-to-end on quantum hardware. Despite noise and limited qubit counts, the resulting models achieve accuracy competitive with and exceeding classical baselines such as logistic regression and support vector classifiers. Our results show that QPU energy consumption scales approximately linearly with qubit number for shallow circuits, while classical simulation exhibits exponential scaling, indicating a break-even for ETS around 34 qubits. The classification error improvement of the best quantum fine-tuned model over the best classical fine-tuned model considered in this study is around 24%. We further contextualize these findings with comparisons to tensor network methods. This work establishes energy-to-solution as a measurable and scalable metric for evaluating quantum applications and provides experimental evidence of favorable energy-accuracy trade-offs.

While tensor networks have their traditional application in simulating quantum systems, in the recent decade they have gathered interest as machine learning models. We combine the experience from both fields and derive how quantum constraints placed on a tensor network manifest a change in capabilities. To this end, we employ a method of inference of classical tensor networks on a quantum computer to define a hybrid architecture. This hybrid tensor network is a practical unified framework for it's classical and quantum tensor network edge cases. We identify post-selection as the important property on which this interpolation hinges. The amount of post-selection corresponds to the level to which quantum constraints are enforced on the tensor network. On this basis, we propose a new hyperparameter which controls the transition between the hybrid and the quantum tensor network. In the comparison of classical and quantum tensor networks it complements the bond dimension. Quantum machine learning is improved by using the hyperparameter to allocate the practically limited post-selection to the quantum model in a trainable manner.

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.

High-fidelity circuit execution on noisy intermediate-scale quantum devices is bottlenecked by compilation pipelines that disregard complex, correlated noise. To address this, this methodology article proposes a quantum machine learning control (QMLC) framework for generative quantum circuit synthesis from gate-set tomography (GST) data that bypasses the traditional two-step pipeline of characterizing native quantum gates via GST followed by unitary decomposition algorithms. Instead, a generative concept space is directly learnt from GST data, enabling conditional synthesis of quantum circuits on a desired output distribution. Our approach tokenizes GST germ circuits and embeds them into a structured latent space using a curriculum-learning-motivated strategy, starting with short circuits and progressively incorporating longer ones with diverse output statistics. The embedded sequences are processed by a set-vision transformer with permutation-invariant pooling, producing k-seed vectors that represent the learned concept space of the quantum device. Aggregating data across multiple circuits makes this latent representation inherently context-aware, capturing the shared physical noise environment (e.g., crosstalk, drift) that isolated gate metrics miss. We propose an unconditional diffusion model to sample from the concept space. During inference, a user provides a target measurement distribution, and the model generates a corresponding circuit. To ensure fidelity and robustness, the output is denoised using a diffusion model that operates on the target conditional covariance matrix. This end-to-end framework is a step towards context-aware, hardware-native circuit synthesis directly from raw GST data, which offers a new paradigm for integrating quantum control and compilation. The QMLC framework is particularly suited for near-term quantum devices with complex calibration procedures.

Quantum machine learning is a promising field for efficiently learning features of a dataset to perform a specified task, such as classification. Interval bound propagation (IBP) is a popular certified training method in classical machine learning, where the lower and upper bounds are tracked throughout the model. These bounds are used during training to ensure that the model is certified to predict the correct label even under adversarial perturbations. While IBP is successful in classical domain, there are limited certified training efforts in quantum domain. In this paper, we present quantum interval bound propagation (QIBP) to establish a certified training routine for quantum machine learning, certifying the accuracy of models under adversarial perturbations. We implement QIBP using both interval and affine arithmetic to explore the tradeoffs between the two implementations in terms of accuracy and other design considerations. Extensive evaluation demonstrates that the resulting certified trained models have robust decision boundaries, guaranteed to predict the correct class for the samples within the trained adversarial robustness bounds.

Edge detection refers to identifying points in a digital image where intensity changes sharply, indicating object boundaries or structural features. Corners are locations where gray-level intensity changes abruptly in multiple directions and are widely used in feature extraction, object tracking, and 3D modeling. In this study, we present a quantum implementation of Sobel-based edge detection and Harris-style corner detection. Two quantum image encoding methods - Flexible Representation of Quantum Images (FRQI) and Quantum Probability Image Encoding (QPIE) - are used to encode the input data and are comparatively analyzed. The proposed approach introduces a quantum gradient computation scheme based on lag-2 differences, enabling the evaluation of gradient-like features in superposition. To improve detection quality and reduce false positives, a classical post-processing step is applied to candidate corner points identified by the quantum circuit. Results show that the proposed quantum circuits produce outputs consistent with classical Sobel and Harris operators. Furthermore, the QPIE-based configuration yields more stable and coherent results than FRQI, especially under limited measurement shots. While gradient computation can be performed efficiently at the circuit level, the overall cost remains dominated by state preparation, measurement, and classical post-processing. All experiments are conducted under noiseless simulation, and performance on NISQ hardware may be affected by noise and measurement limitations. Therefore, this work demonstrates a functional and scalable quantum realization of classical edge and corner detection methods rather than an end-to-end speedup.

Operator learning enables fast surrogate modelling of high-dimensional dynamical systems, but existing approaches face two fundamental limitations: the quadratic cost of dense neural layers and unreliable uncertainty quantification in safety-critical settings. We propose Conformalized Quantum DeepONet Ensembles, a framework that addresses both challenges simultaneously. Using Quantum Orthogonal Neural Networks (QOrthoNNs), we characterize the resource regime in which their established $\widetilde{\mathcal{O}}(n)$ hidden-layer running-time scaling improves on the $\mathcal{O}(n^2)$ cost of a classical dense layer. To quantify uncertainty, we combine ensemble predictions with split conformal calibration. For a new input-output function pair jointly exchangeable with the calibration pairs, we prove a finite-sample, distribution-free lower bound on the expected fraction of covered query locations. As a secondary proof-of-concept, we explore hybrid classical-quantum architectures and superposed execution to manage ensemble runtime and hardware requirements. Experiments on synthetic operator benchmarks and real-world power-system dynamics show accurate predictions under ideal simulation and empirical coverage near the target under both ideal conditions and selected compact-circuit simulations with depolarizing or device-calibrated composite noise. Together, these results connect resource-aware scalability analysis with finite-sample uncertainty guarantees for quantum operator learning.

Quantum machine learning integrates the strengths of quantum computing and machine learning, enabling models to learn complex features using fewer parameters than their classical counterparts. Due to the increasing complexity of quantum machine learning models, it is necessary to verify that the implementation of these models satisfy the design specification and be free of bugs and faults. Mutation testing is a promising avenue to identify faulty quantum circuits that do not meet design specifications or contain defects by intentionally inserting faults into the quantum circuit. It is necessary to define mutation operations to inject faults into quantum circuits to ensure that a test suite is robust enough to evaluate an implementation against its design specification. In this paper, we extend mutation testing to quantum machine learning applications, primarily quantum neural network models. Specifically, this paper makes two important contributions. We define new mutation operations for efficient fault insertion compared to state-of-the-art approaches. We also present a directed mutation generation technique to reduce redundant mutant circuits. Extensive experimental evaluation demonstrates that our approach generates a more diverse and representative set of mutants, effectively addressing faults that traditional techniques fail to expose.

Despite rapid recent advances in quantum machine learning, the field is in many ways stuck. Existing approaches can exhibit serious limitations, and we still lack learning frameworks that are simple, interpretable, scalable, and naturally suited to quantum data. To address this, here we introduce quantum Gaussian processes, a Bayesian framework for learning from quantum systems through priors over unknown quantum transformations. We show that, under suitable conditions, unitary quantum stochastic processes define Gaussian processes, thereby enabling regression, classification, and Bayesian optimization directly on quantum data. The key ingredient in this framework is sufficient knowledge of a quantum process's structure and symmetries to define an informative prior through its corresponding quantum kernel, effectively injecting a strong, physics-informed inductive bias into the learning model. We then prove that matchgate, or free-fermionic, evolutions give rise to provable and scalable quantum Gaussian processes, providing the first family in our framework where the unknown unitary acts non-trivially on all qubits. Finally, we demonstrate accurate long-range extrapolation, phase-diagram learning in many-body systems, and sample-efficient Bayesian optimization in a quantum sensing task. Our results identify quantum Gaussian processes as a promising route toward simpler and more structured forms of quantum learning.

Machine learning models can learn from data samples to carry out various tasks efficiently. When data samples are adversarially manipulated, such as by insertion of carefully crafted noise, it can cause the model to make mistakes. Quantum machine learning models are also vulnerable to such adversarial attacks, especially in image classification using variational quantum classifiers. While there are promising defenses against these adversarial perturbations, such as training with adversarial samples, they face practical limitations. For example, they are not applicable in scenarios where training with adversarial samples is either not possible or can overfit the models on one type of attack. In this paper, we propose an adversarial training-free defense framework that utilizes a quantum autoencoder to purify the adversarial samples through reconstruction. Moreover, our defense framework provides a confidence metric to identify potentially adversarial samples that cannot be purified the quantum autoencoder. Extensive evaluation demonstrates that our defense framework can significantly outperform state-of-the-art in prediction accuracy (up to 68%) under adversarial attacks.

Quantum machine learning (QML) provides a promising framework for leveraging quantum-mechanical effects in learning tasks. However, its vulnerability to adversarial perturbations remains a major challenge for practical deployment. In QML systems, small perturbations applied to classical inputs can propagate through the quantum encoding stage and distort the resulting quantum state, thereby degrading model performance. In this work, we propose a defense mechanism that replaces the conventional quantum encoding stage of a QML model with passive steering-based controlled state preparation, which guides the encoded state toward a controlled intermediate state. By tuning the steering strength and the number of steering iterations, the proposed method suppresses the influence of adversarial perturbations while maintaining high clean accuracy and improving adversarial accuracy. Experimental results demonstrate that the passive steering-based defense consistently improves adversarial accuracy across different QML models and datasets under gradient-based adversarial attacks, achieving adversarial accuracy improvements of up to 40.19%.

Semantic segmentation in remote sensing is commonly addressed using classical deep learning architectures such as U-Net, which require a large number of parameters to model complex spatial relationships. Quantum machine learning (QML) provides an alternative representation paradigm by mapping classical features into quantum states, but its direct application to high-dimensional images remains challenging under near-term quantum hardware constraints. In this work, we propose HQ-UNet, a hybrid quantum-classical U-Net architecture that integrates a compact parameterized quantum circuit at the bottleneck of a classical U-Net. The proposed design uses a non-pooling quantum convolutional module to enrich highly compressed encoder features before decoding, while keeping the quantum component shallow and parameter-efficient. Experiments on the LandCover.ai dataset show that HQ-UNet achieves a mean IoU of 0.8050 and an overall accuracy of 94.76%, outperforming the classical U-Net baseline. These results suggest that compact quantum bottlenecks can enhance feature representation for remote sensing image segmentation under near-term quantum constraints. This highlights the potential of hybrid quantum-classical designs as a promising direction for parameter-efficient dense prediction in Earth observation.

Classical continuous-space neural networks fundamentally struggle to lock into exact mathematical symmetries, such as modular arithmetic and non-commutative algebra. To approximate these discrete logical rules, they often rely on massive parameter scaling, resulting in stochastic instability even after delayed generalization phenomena known as grokking. Here, we introduce the Universal Quantum Transformer (UQT), a fundamentally novel, quantum-native computing architecture that uses the physical properties of multi-qubit systems as a universal inductive bias for exact mathematical and algebraic reasoning. Rather than translating classical neural mechanisms, our framework relies entirely on parameterized geometric phase embedding and $SU(2)$ wave-interference. We demonstrate that the quantum attention circuit, operating on a highly compact 5-qubit substrate, perfectly learns two highly distinct formal classes: cyclic modular arithmetic ($\mathbb{Z}_{11}$) and non-Abelian algebra (the $S_4$ permutation group). While classical attention-based networks exhibit stochastic instability at convergence, the UQT achieves mathematically exact, deterministic generalization. We refer to this phenomenon as crystallization: a step beyond the well-known phenomenon of grokking. Crucially, this framework yields massive computational and memory advantages by theoretically bypassing the quadratic bottleneck of classical self-attention, and by logarithmically compressing the required representation dimension to eliminate the massive over-parameterization inherent to classical networks. Finally, we deploy this architecture on noisy intermediate-scale quantum (NISQ) hardware, proving its viability on current IBM Quantum computers. These results establish parameterized quantum topology as a universally superior physical substrate for exact artificial intelligence.

We present a quantum feature-selection framework based on a higher-order unconstrained binary optimization (HUBO) formulation that explicitly incorporates multivariate dependencies beyond standard quadratic encodings. In contrast to QUBO-based approaches, the proposed model includes one-, two-, and three-body interaction terms derived from mutual-information measures, enabling the objective function to capture feature relevance, pairwise redundancy, and higher-order statistical structure within a unified energy model. To suppress trivial all-selected solutions, we further include structured linear penalties that promote sparsity while preserving informative variables. The resulting HUBO instances are optimized with digitized counterdiabatic quantum optimization on IonQ Forte and compared against noiseless quantum simulation as well as two classical dimensionality-reduction baselines: SelectKBest based on mutual information and principal component analysis (PCA). We evaluate the proposed workflow on two benchmark classification datasets, namely the Gallstone dataset and the Spambase dataset, and analyze both predictive performance and selected-subset structure. The results show good qualitative agreement between hardware executions and noiseless simulations, supporting the feasibility of implementing higher-order feature-selection Hamiltonians on current trapped-ion processors. In addition, the quantum approach yields competitive classification performance while producing compact and informative feature subsets, highlighting the potential of higher-order quantum optimization for machine-learning preprocessing tasks.

We investigate variational quantum classifiers (VQCs) for land-cover classification from multispectral satellite imagery, adopting a feature-map perspective in which the quantum circuit defines a nonlinear data embedding while the readout determines how this representation is exploited. Using the EuroSAT-MS dataset, we perform a systematic one-vs-one evaluation across all class pairs under a controlled experimental protocol, comparing classical baselines (logistic regression, SVMs, neural networks) with VQCs employing both linear readout and quantum-kernel SVM strategies. Our results show that, while VQCs with linear readout do not outperform strong classical baselines such as RBF-SVM, the same trained quantum feature map can significantly improve performance when reused within a kernel-based decision framework. A qubit-count sweep further reveals saturation effects consistent with the mismatch between exponential Hilbert space dimension and linear parameter scaling. Overall, our findings highlight that the effectiveness of quantum models depends critically on the interplay between representation and readout, and that meaningful gains may arise from combining learned quantum feature maps with classical decision mechanisms rather than seeking direct replacement of classical models.

This paper presents Quantum Gatekeeper, a context-bound image steganography framework where successful payload recovery depends on both cryptographic decryption and the reconstruction of a precise extraction path. The system integrates lossless least significant bit (LSB) embedding with a deterministic variational quantum circuit (VQC)-derived gate key, multi-factor contextual binding, and authenticated encryption. Payload extraction is contingent upon four requisite factors: a password, a shared secret, a user-supplied context string, and a reference image signature. Any deviation in these factors causes the system to read from an incorrect pixel sequence or fail authentication, resulting in silent rejection rather than partial disclosure. The proposed method derives a gatecontrolled extraction key from a seed-conditioned variational circuit, with parameters generated via cryptographic hash expansion and context-dependent image features. To ensure encode/decode consistency, the cryptographic key path is generated via exact statevector simulation; concurrently, IBM superconducting quantum hardware is utilized to evaluate the statistical behavior of the circuit family under physical noise. We introduce a dual-region image layout to resolve the nonce bootstrapping dependency, separating header recovery from payload recovery through independently derived keys. Experimental results confirm successful end-to-end message embedding and recovery on PNG images, demonstrating deterministic success under correct conditions and failure otherwise. The framework supports both text and image payloads; in the image-in-image configuration, a secret image is resized to a fixed resolution prior to embedding, enabling exact pixel-level recovery under correct contextual reconstruction.

Loading high dimensional distributions is an important task for utilizing quantum computers on applications ranging from machine learning to finance. The high dimensionality leads to a curse of dimensionality, representing a d-dimensional distribution with k resolution requires dk qubits and an unstructured parameterized circuit would express a unitary in an exponential operator space in the number of qubits, leading to vanishing gradients and poor convergence guarantees even at high depth. Vine copula decompositions are widely used to represent high dimensional distributions classically, showing high quality approximation in many important applications, such as financial modeling. We present Qvine, a vine structured ansatz for quantum circuits, that mirrors the vine decomposition to construct scalable quantum circuits with efficient trainability while achieving similarly high quality approximation for amplitude encoding distributions. For regular vines (R-vines), we show that the circuit depth scales at most quadratic in the dimension of the distribution, while for D-vines, as well as many practical R-vines, the circuit depth scales linear in the dimension. For 3-dimensional and 4-dimensional Gaussians and empirical joint stock price return distributions for selected stocks, our experiments show Qvines achieve high quality loading.

Quantum computing remains in the Noisy Intermediate-Scale Quantum (NISQ) era, where the performance is highly constrained to noise. Addressing the limitation often requires hardware-facing capabilities beyond gate-sequence circuit specification, including mid-circuit measurement and classical feedback for quantum error correction (QEC), precise timing control for dynamical decoupling (DD), and pulse-level waveform access for calibration. OpenQASM-3 was introduced to expose exactly these capabilities, providing a hardware-level programming interface. However, despite the rapid progress of large language models in code generation, there is still no dataset specifically designed to train and evaluate LLMs on OpenQASM-3 programs that involve its advanced hardware-oriented features. To address this gap, we introduce QASM-Eval, the first comprehensive dataset designed to train and evaluate LLMs on OpenQASM-3. Rather than focusing on quantum algorithm design or reasoning, QASM-Eval explicitly targets the language's hardware-facing features. QASM-Eval comprises an expert-verified test set of 100 tasks and a training set of 4,000 tasks, systematically covering classical logic, timing scheduling, pulse control, and complex real-world workflows. To automatically validate generated programs, we check syntax, quantum states and program timeline using an extended verifier. Our evaluation reveals that while state-of-the-art LLMs struggle heavily in OpenQASM-3 coding tasks, targeted fine-tuning on QASM-Eval yields significant gains. QASM-Eval provides a crucial benchmark and training foundation to accelerate the development of reliable LLM assistants for hardware-facing quantum programming in NISQ era. Data and code: https://github.com/fuzhenxiao/QASM-Eval

In the context of quantum secure scenarios, existing research on mobile edge devices and intelligent computing and edge (ICE) systems based on the Non-Orthogonal Multiple Access (NOMA) communication model have overlooked the energy consumption overhead of Post-Quantum Cryptography (PQC) modules, and the high complexity of traditional resource allocation algorithms fails to meet the demands of real-time decision-making. To address these challenges, this paper proposes a lightweight agentic AI framework designed for online joint optimization within ICE-enabled mobile devices. The scheme constructs a multi-stage stochastic Mixed Integer Nonlinear Programming (MINLP) model that incorporates static power-consumption constraints for PQC modules. Based on Lyapunov optimization theory, the long-term optimization problem is decoupled, and a linear complexity algorithm is proposed to solve the nonconvex challenges of NOMA power allocation . Simulation results verify that the proposed scheme significantly improves computational throughput while ensuring system queue stability and energy consumption constraints. Compared with traditional Successive Convex Approximation (SCA) algorithms, the complexity is reduced to $\mathcal{O}(N)$, achieving a speedup of approximately 46 times when the number of devices $N=35$, thereby meeting the real-time decision-making requirements in dynamic wireless environments.

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.

We solve the time-dependent Schrödinger equation by learning the score function, the gradient of the log-probability density, on Bohmian trajectories. In Bohm's formulation of quantum mechanics, particles follow deterministic paths under the classical potential supplemented by a quantum potential depending on the score function of the evolving density. These non-crossing Bohmian trajectories form a continuous normalizing flow governed by the score. We parametrize the score with a neural network and minimize a self-consistent Fisher divergence between the network and the score of the resulting density. We prove that the zero-loss minimizer of this self-consistent objective recovers Schrödinger dynamics for nodeless wave functions, a condition naturally met in quantum vibrations of atoms. We demonstrate the approach on wavepacket splitting in a double-well potential and anharmonic vibrations of a Morse chain. By recasting real-time quantum dynamics as a self-consistent score-driven normalizing flow, this framework opens the time-dependent Schrödinger equation to the rapidly advancing toolkit of modern generative modeling.

We introduce HAML (Hamiltonian Adaptation via Meta-Learning), a framework for fast online adaptation of effective Hamiltonian models of superconducting quantum processors. HAML proceeds in two phases. A supervised training phase uses an ensemble of simulated devices to learn an offline map from control inputs and device parameters to effective Hamiltonian coefficients. An online adaptation phase then uses a small number of hardware-accessible measurements to identify the unknown parameters of a new device. By training directly against effective two-qubit coefficients extracted from full multi-mode simulations, HAML implicitly learns the reduction from full multi-mode Hamiltonians to effective qubit descriptions without invoking perturbation theory. We further show that a variance-maximizing greedy selection of measurement configurations boosts online adaptation efficiency. We demonstrate HAML on a transmon-coupler-transmon system, recovering effective two-qubit coefficients across a wide range of operating regimes, including parameter regions where Schrieffer-Wolff perturbation theory (SWPT) breaks down. This establishes a scalable, sample-efficient approach to Hamiltonian reduction and characterization for near-term quantum processors, with direct implications for calibration, control, and error mitigation.

We provide evidence of quantum kernel advantage under noiseless simulation in binary insurance classification on MIMIC-CXR chest radiographs using quantum support vector machines (QSVM) with frozen embeddings from three medical foundation models (MedSigLIP-448, RAD-DINO, ViT-patch32). We propose a two-tier fair comparison framework in which both classifiers receive identical PCA-q features. At Tier 1 (untuned QSVM vs. untuned linear SVM, C = 1 both sides), QSVM wins minority-class F1 in all 18 tested configurations (17 at p < 0.001, 1 at p < 0.01). The classical linear kernel collapses to majority-class prediction on 90-100% of seeds at every qubit count, while QSVM maintains non-trivial recall. At q = 11 (MedSigLIP-448 plateau center), QSVM achieves mean F1 = 0.343 vs. classical F1 = 0.050 (F1 gain = +0.293, p < 0.001) without hyperparameter tuning. Under Tier 2 (untuned QSVM vs. C-tuned RBF SVM), QSVM wins all seven tested configurations (mean gain +0.068, max +0.112). Eigenspectrum analysis reveals quantum kernel effective rank reaches 69.80 at q = 11, far exceeding linear kernel rank, while classical collapse remains C-invariant. A full qubit sweep reveals architecture-dependent concentration onset across models. Code: https://github.com/sebasmos/qml-medimage

Quantum error mitigation (QEM) is essential for extracting reliable results from near-term quantum devices, yet practical deployments must balance mitigation strength against runtime overhead under time-varying noise. We introduce \emph{GSC-QEMit}, a telemetry-driven, \textbf{context--forecast--bandit} framework for \emph{adaptive} mitigation that switches between lightweight suppression and heavier intervention as drift evolves. GSC-QEMit composes three coupled modules: (G) a Growing Hierarchical Self-Organizing Map (GHSOM) that clusters streaming telemetry into operating contexts; (S) an uncertainty-aware subsampled Gaussian-process forecaster that predicts short-horizon fidelity degradation; and (C) a cost-aware contextual multi-armed bandit (CMAB) that selects mitigation actions via Thompson sampling with explicit intervention cost. We evaluate GSC-QEMit on benchmark circuit families (GHZ, Quantum Fourier Transform, and Grover search) under nonstationary noise regimes simulated in Qiskit Aer, using an instrumented testbed where action labels correspond to graded mitigation intensity. Across Clifford, non-Clifford, and structured workloads, GSC-QEMit improves average logical fidelity by \textbf{+9.0%} relative to unmitigated execution while reducing unnecessary heavy interventions by reserving them for inferred noise spikes. The resulting policies exhibit a favorable fidelity--cost trade-off and transfer across the evaluated workloads without circuit-specific tuning.

In the noisy intermediate-scale quantum (NISQ) regime, quantum devices contain hardware-specific noise sources which restrict device-invariant error mitigation strategies. We explore transfer learning approaches to apply noise models learned on one quantum device to a different device with the help of a small amount of data. We create a real-hardware dataset from two IBM quantum devices, ibm_fez (source) and ibm_marrakesh (target), comprising 170 noisy and ideal circuit output distributions, with device calibration features added. We train a residual neural network on the source device to map noisy to ideal outcomes. The zero-shot transfer test shows a KL divergence of 1.6706 (up from 0.3014), establishing device specificity. With K = 20 fine-tuning samples, KL drops to 1.1924 (28.6% improvement over zero-shot), recovering 34.9% of the gap between zero-shot and in-domain KL. Ablation studies reveal that the major cause of mismatches across devices is CX gate error, followed by readout error. The results show quantum noise can be learned and fine-tuned with minimal samples, and provide a plausible approach to cross-device quantum error mitigation.

In this work, we extend the class of previously introduced non-Euclidean neural quantum states (NQS) which consists only of Poincare hyperbolic GRU, to new variants including Poincare RNN as well as Lorentz RNN and Lorentz GRU. In addition to constructing the new non-Euclidean hyperbolic NQS ansatzes, we generalize the results of our earlier work regarding the definitive outperformances delivered by hyperbolic Poincare GRU NQS when benchmarked against their Euclidean counterparts in the Variational Monte Carlo (VMC) experiments involving the Heisenberg $J_1J_2$ and $J_1J_2J_3$ models. Here, using larger systems consisting of 100 spins, we find that all four hyperbolic RNN/GRU NQS variants always outperform their respective Euclidean counterpart with the same architecture. In our experiments, among the four hyperbolic NQS, Lorentz RNN stands out in particular because despite having almost three times fewer parameters, it is capable of surpassing the more complex Poincare GRU and Lorentz GRU to emerge as the best overall hyperbolic NQS ansatz on many instances involving different $J_2$ and ($J_2, J_3$) couplings. Given the findings from this work showing that the four newly constructed hyperbolic RNN/GRU NQS ansatzes are able to outperform the well-established Euclidean RNN/GRU NQS in Heisenberg spin models, we establish the utility and efficiency of the hyperbolic Poincare RNN/GRU and Lorentz RNN/GRU NQS for future variational studies of quantum many-body systems, especially those exhibiting a hierarchical structure in the form of the different degrees of nearest-neighbor interactions.

Large language model tutors are easy to build in a notebook and hard to run in a real course. We describe ITAS (Intelligent Teaching Assistant System), a multi-agent tutoring system that a graduate quantum computing course used for a semester at Old Dominion University. The system has three layers. The teaching layer is a Spoke-and-Wheel of three parallel specialist agents (Video, Code, Guidance) followed by a Synthesizer, plus a separate autograder that evaluates both the correctness and the approach of checkpoint submissions. The operational layer is four Cloud Run microservices with session state in Cloud SQL and interaction events streamed through Pub/Sub to BigQuery. The feedback layer is a narrow-scope conversational agent that answers instructor questions over per-lesson pseudonymized event streams, addressing what we call the Blind Instructor Problem: LLM tutors accumulate more data about students than the instructor can reach through routine channels. The architecture is a direct response to specific failures of an earlier prototype, and we describe which of those fixes carried forward and which were dropped for this iteration. We report on a pilot deployment (five students, one course, one semester) interpreted as system-behavior evidence rather than learning-outcome evidence: the teaching layer handled 334 chat turns without the task-boundary hallucinations that domain consolidation would have risked, the operational layer captured 10,628 events across five modules, and the feedback layer surfaced two findings the instructor acted on mid-semester. We do not claim the pilot generalizes. We do claim that the system as described is one workable answer to the question of what an LLM-based ITS needs to look like end-to-end to run in a real course.

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.

Variational quantum circuits (VQCs) are a leading approach to quantum machine learning on near-term devices, yet it remains unclear which circuit architecture yields the best accuracy-parameter trade-off on classical tabular data. We present a systematic empirical comparison of four VQC families -- multi-layer fully-connected (FC-VQC), residual (ResNet-VQC), hybrid quantum-classical transformer (QT), and fully quantum transformer (FQT) -- across five regression and classification benchmarks. Our key findings are: \textbf{(i)}~FC-VQCs achieve 90-96% of the $R^2$ of attention-based VQCs while using 40-50% fewer parameters, and consistently outperform equal-capacity MLPs (mean $R^2{=}0.829$ vs.\ MLP$_{720}$'s $0.753$ on Boston Housing, 3-seed average); \textbf{(ii)}FC-VQC's Type4 inter-block connectivity provides partial cross-token mixing that approximates the role of attention -- explicit quantum self-attention yields only marginal gains on most datasets while significantly increasing parameter count; \textbf{(iii)}expressibility saturates at circuit depth${\approx}\,3$, explaining why shallow VQCs already cover the Hilbert space effectively; \textbf{(iv)}~LayerNorm on the fully quantum transformer improves classification accuracy, suggesting normalization is important when all operations are quantum; \textbf{(v)}~in our noise study on Boston Housing, FQT degrades gracefully under depolarizing noise while QT collapses. All results are validated across three random seeds. These findings provide practical architectural guidance for deploying VQCs on near-term quantum hardware.

Variational quantum circuits train poorly on chaotic forecasting, usually blamed on barren plateaus (exponentially vanishing gradients). Using an exactly simulable four-qubit variational quantum physics-informed circuit fit to Lorenz-63, we show the barren-plateau explanation fails: the failure is an architectural capacity ceiling fixed by the circuit time-encoding, not its trainable depth. Four measurements support this. (i) A McClean-comparable gradient-variance estimator sits at the local-cost Haar/2-design scale 2^(-2n)=3.9e-3 at n=4; on structurally live parameters it decays about ninefold with depth then saturates there, large enough to train, not an exponential collapse. (ii) At a common budget of 200 optimiser iterations (600, in three stages, for layer-wise), gradient descent, layer-wise, and SPSA reach the same order of magnitude of loss, so no optimiser unlocks a better basin. (iii) The output-Jacobian rank saturates at 33 from five layers on, so depth buys no new output directions. (iv) A Fourier analysis explains why: the qubit-1 phase encoding acts on the initial |0> and is inert, so the maximum accessible frequency is 2.5/t_max=0.83 Hz, identical at every depth and about 4.4x below the narrowest Lorenz component bandwidth. The corrected band has dimension 1+2x5=11 per observable, and 3x11=33 equals the measured rank ceiling exactly, unifying the two diagnostics. A trained depth sweep agrees: mean loss improves with depth then flattens once the rank saturates. We correct our earlier preprint diagnosis, which compared unnormalised gradient norms to the McClean threshold, and place the advantage of fixed reservoirs and classical echo-state networks in architecture, not quantum mechanics.

Joint measurements on multiple copies of a quantum state provide access to nonlinear observables such as $\operatorname{tr}(ρ^t)$, but whether replica number marks a sharp information-theoretic resource boundary has remained unclear. For every fixed order $t\ge 3$, existing protocols show that $\lceil t/2\rceil$ replicas already suffice for polynomial-sample estimation of $\operatorname{tr}(ρ^t)$, yet it has remained open whether one fewer replica must necessarily incur a sample-complexity barrier growing with the dimension. We prove that this is indeed the case in the sample/copy-access model with replica-limited joint measurements: any protocol restricted to $\lceil t/2\rceil-1$ replicas requires dimension-growing sample complexity, while $\lceil t/2\rceil$ replicas suffice by prior work. Thus the exact replica threshold for fixed-order pure moments is $\lceil t/2\rceil$. Equivalently, for fixed-order pure moments, one additional coherent replica is not merely useful but marks the exact threshold between polynomial-sample estimation and a dimension-growing regime in the replica-limited model. We further show that the same threshold law extends to a broad family of observable-weighted moments $\operatorname{tr}(Oρ^t)$, including Pauli observables and other observables with bounded operator norm and macroscopic trace norm. Coherent replica number therefore acts as a genuinely discrete resource for nonlinear quantum-state estimation.

The integration of quantum machine learning with classical deep learning offers promising avenues for medical image analysis by mapping data into high-dimensional Hilbert spaces. However, effectively unifying these distinct paradigms remains challenging due to common optimization asymmetries. In this paper, a novel hybrid quantum-classical architecture for breast cancer diagnosis based on a dual-branch feature-extraction pipeline is proposed. Our framework extracts and unifies complementary representations from classical models and quantum circuits, exploring both trainable and deterministic (non-trainable) quantum paradigms. To integrate these embeddings, three progressive feature fusion strategies are introduced: Static Hybrid Fusion (SHF) for offline extraction, Dynamic Hybrid Fusion (DHF) for end-to-end co-adaptation, and a novel Temperature-Scaled Hybrid Fusion (TSHF). The TSHF strategy incorporates a learnable scalar, inspired by multimodal learning, that dynamically balances hybrid gradient dynamics and resolves optimization bottlenecks. Empirical validation on the BreastMNIST dataset confirms our hypothesis that unifying diverse feature representations creates a richer data context. The TSHF strategy, specifically when pairing a ResNet backbone with a trainable quantum circuit, achieved a peak accuracy of 87.82%, F1-score of 91.77%, and an AUC-ROC of 89.08%, outperforming purely classical baselines. These results demonstrate that the proposed hybrid framework improves classification accuracy and threshold reliability, providing a stable, high-performance architecture for the clinical deployment of quantum-enhanced diagnostic tools.

Deep reinforcement learning (RL) for quantum circuit optimization faces three fundamental bottlenecks: replay buffers that ignore the reliability of temporal-difference (TD) targets, curriculum-based architecture search that triggers a full quantum-classical evaluation at every environment step, and the routine discard of noiseless trajectories when retraining under hardware noise. We address all three by treating the replay buffer as a primary algorithmic lever for quantum optimization. We introduce ReaPER$+$, an annealed replay rule that transitions from TD error-driven prioritization early in training to reliability-aware sampling as value estimates mature, achieving $4-32\times$ gains in sample efficiency over fixed PER, ReaPER, and uniform replay while consistently discovering more compact circuits across quantum compilation and QAS benchmarks; validation on LunarLander-v3 confirms the principle is domain-agnostic. Furthermore we eliminate the quantum-classical evaluation bottleneck in curriculum RL by introducing OptCRLQAS which amortizes expensive evaluations over multiple architectural edits, cutting wall-clock time per episode by up to $67.5\%$ on a 12-qubit optimization problem without degrading solution quality. Finally we introduce a lightweight replay-buffer transfer scheme that warm-starts noisy-setting learning by reusing noiseless trajectories, without network-weight transfer or $ε$-greedy pretraining. This reduces steps to chemical accuracy by up to $85-90\%$ and final energy error by up to $90\%$ over from-scratch baselines on 6-, 8-, and 12-qubit molecular tasks. Together, these results establish that experience storage, sampling, and transfer are decisive levers for scalable, noise-robust quantum circuit optimization.

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.

With the growing synergy between deep learning and quantum computing, Quantum Neural Networks (QNNs) have emerged as a promising paradigm by leveraging quantum parallelism and entanglement. However, testing QNNs remains underexplored due to their complex quantum dynamics and limited interpretability. Developing a mutation testing technique for QNNs is promising while requires addressing stochastic factors, including the inherent randomness of mutation operators and quantum measurements. To tackle these challenges, we propose QuanForge, a mutation testing framework specifically designed for QNNs. We first introduce statistical mutation killing to provide a more reliable criterion. QuanForge incorporates nine post-training mutation operators at both gate and parameter levels, capable of simulating various potential errors in quantum circuits. Finally, a mutant generation algorithm is formalized that systematically produces effective mutants, thereby enabling a robust and reliable mutation analysis. Through extensive experiments on benchmark datasets and QNN architectures, we show that QuanForge can effectively distinguish different test suites and localize vulnerable circuit regions, providing insights for data enhancement and structural assessment of QNNs. We also analyze the generation capabilities of different operators and evaluate performance under simulated noisy conditions to assess the practical feasibility of QuanForge for future quantum devices.

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.

In a global derivatives market with notional values in the hundreds of trillions of dollars, the accuracy and efficiency of pricing models are of fundamental importance, with direct implications for risk management, capital allocation, and regulatory compliance. In this work, we employ the Black-Scholes-Merton (BSM) framework not as an end in itself, but as a controlled benchmark environment in which to rigorously assess the capabilities of quantum machine learning methods. We propose a fully quantum approach to option pricing based on Quantum Neural Networks (QNNs), and, to the best of our knowledge, present one of the first implementations of such a methodology on currently available quantum hardware. Specifically, we investigate whether QNNs, by exploiting the geometric structure of Hilbert space, can effectively approximate option pricing functions. Our implementation utilizes a compact 2-qubit QNN architecture evaluated across multiple state-of-the-art quantum processors, including IBM Fez, IQM Garnet, IonQ Forte, and Rigetti Ankaa-3. This cross-platform study reveals distinct hardware-dependent performance characteristics while demonstrating that accurate pricing approximations can be achieved consistently across different devices despite the constraints of Noisy Intermediate-Scale Quantum (NISQ) hardware. The results provide empirical evidence that QNN-based approaches constitute a viable framework for derivative pricing. While the analysis is conducted within the BSM setting, the broader significance lies in the potential extension of these methods to more realistic and computationally demanding models, including local volatility, stochastic volatility, and interest rate frameworks commonly used in practice.

Barren-plateau results have established exponential gradient suppression as a widely cited obstacle to the scalability of variational quantum algorithms. When and whether these results extend to a given objective has been addressed through loss-specific arguments, but a general structural characterization has remained open. We show that the objective itself admits a fixed-observable representation if and only if the loss is affine in the measured statistics, thereby identifying the exact boundary of the standard concentration-based proof template. Existing transfer results for non-affine losses achieve this reduction under additional assumptions; our characterization implies that such a reduction is not structurally available for a class of non-affine objectives, placing them outside the automatic reach of the existing proof template. Beyond the affine regime, a chain-rule decomposition reveals three governing factors -- model responsivity, loss-side signal, and transmittance -- and induces a loss-class dichotomy: bounded-gradient losses inherit suppression, while amplification-capable losses can in principle counteract it. In the exponentially wide setting, both classes fail, but for different structural reasons. When the interface is instead designed at polynomial width -- exposing coarse-grained statistics rather than individual bitstring probabilities -- the exponential-dimensional obstruction is relaxed and the dichotomy plays a genuine role. In a numerical demonstration on a charge-conserving quantum system, the amplification-capable objective produces resolved gradients several orders of magnitude larger than affine and inheriting baselines at comparable shot budgets. Over the tested interval, its scaling trend is statistically distinguished from the exponential trend of both alternatives. The boundary is affine; what lies beyond it is a representation-design problem.

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.

Quantum kernel methods have been proposed as a promising approach for leveraging near-term quantum computers for supervised learning, yet rigorous benchmarks against strong classical baselines remain scarce. We present a comprehensive empirical study of quantum kernel support vector machines (QSVMs) across nine binary classification datasets, four quantum feature maps, three classical kernels, and multiple noise models, totalling 970 experiments with strict nested cross-validation. Our analysis spans four phases: (i) statistical significance testing, revealing that none of 29 pairwise quantum-classical comparisons reach significance at $α= 0.05$; (ii) learning curve analysis over six training fractions, showing steeper quantum slopes on six of eight datasets that nonetheless fail to close the gap to the best classical baseline; (iii) hardware validation on IBM ibm_fez (Heron r2), demonstrating kernel fidelity $r \geq 0.976$ across six experiments; and (iv) seed sensitivity analysis confirming reproducibility (mean CV 1.4%). A Kruskal-Wallis factorial analysis reveals that dataset choice dominates performance variance ($\varepsilon^2 = 0.73$), while kernel type accounts for only 9%. Spectral analysis offers a mechanistic explanation: current quantum feature maps produce eigenspectra that are either too flat or too concentrated, missing the intermediate profile of the best classical kernel, the radial basis function (RBF). Quantum kernel training (QKT) via kernel-target alignment yields the single competitive result -- balanced accuracy 0.968 on breast cancer -- but with ~2,000x computational overhead. Our findings provide actionable guidelines for quantum kernel research. The complete benchmark suite is publicly available to facilitate reproduction and extension.

Reconfigurable intelligent surfaces (RISs) modify signal reflections to enhance wireless communication capabilities. Classical RIS phase optimization is highly non convex and challenging in dynamic environments due to high interference and user mobility. Here we propose a hierarchical multi-objective quantum metalearning algorithm that switches among specific quantum paths based on historical success, energy cost, and current data rate. Candidate RIS control directions are arranged as switch paths between quantum neural network layers to minimize inference, and a scoring mechanism selects the top performing paths per layer. Instead of merely storing past successful settings of the RIS and picking the closest match when a new problem is encountered, the algorithm learns how to select and recombine the best parts of different solutions to solve new scenarios. In our model, high-dimensional RIS scenario features are compressed into a quantum state using the tensor product, then superimposed during quantum path selection, significantly improving quantum computational advantage. Results demonstrate efficient performance with enhanced spectral efficiency, convergence rate, and adaptability.

Breast cancer diagnosis through thermographic image analysis remains a critical challenge in medical AI, with classical deep learning approaches facing limitations in complex thermal pattern classification tasks. This paper presents a novel Hybrid Quantum Neural Network (HQNN) architecture that integrates quantum computing principles with classical convolutional neural networks for enhanced breast cancer classification. Our approach employs parameterized quantum circuits with multi-head attention mechanisms for quantum-aware feature encoding, coupled with classical convolutional layers for comprehensive pattern recognition. The quantum component utilizes a 4qubit variational circuit with strongly entangling layers, while the classical component incorporates advanced attention mechanisms for feature fusion. Experimental validation on breast cancer thermographic data demonstrates substantial performance improvements over state-of-the-art classical architectures, with the quantum-enhanced approach exhibiting superior convergence dynamics and enhanced feature representation capabilities. Our findings provide evidence for quantum advantage in medical image classification through classical simulation, establishing a framework for quantum-classical hybrid systems in healthcare applications. The methodology addresses key challenges in quantum machine learning deployment while maintaining computational feasibility on near-term quantum devices.

Quantum error mitigation (QEM) provides a practical route for estimating reliable observables on noisy intermediate-scale quantum (NISQ) devices. Traditional QEM strategies, including zero-noise extrapolation (ZNE) and Clifford data regression (CDR), rely on noise scaling or global regression, and their performance is constrained by the exponential growth of the system degrees of freedom. We construct a graph-enhanced mitigation (GEM) framework, which incorporates physical information into the model representation. In this work, quantum circuits are encoded as attributed graphs. Hardware-level physical information is mapped to node and edge features: local noise parameters such as calibration parameters $T_1$, $T_2$, and readout errors are encoded at nodes, while coupling-related information such as two-qubit gate errors is encoded as edge features. Graph neural networks are used to model how errors propagate along the physical coupling structure and build up into non-local correlations. This allows the model to capture local interactions and part of the resulting non-local correlations across qubits. A dual-branch affine correction is applied to maintain consistency with physical constraints. Experiments on 10-qubit and 16-qubit random circuits executed on superconducting quantum processors show that GEM provides a level of accuracy comparable to CDR at small scales, while yielding lower mean absolute error and improved stability in zero-shot transfer to larger systems. Results of the traditional QEM strategy indicate that global regression methods remain effective in low-dimensional settings but become less reliable as system degrees of freedom grow. In contrast, GEM makes use of local physical structures to show better scalability and generalization, while preserving the overall error propagation patterns. This work provides a practical scalable approach to QEM for NISQ devices.

Quantum feature maps offer expressive embeddings for classical learning tasks, and augmenting sparse identification of nonlinear dynamics (SINDy) with such features is a natural but unexplored direction. We introduce \textbf{Q-SINDy}, a quantum-kernel-augmented SINDy framework, and identify a specific failure mode that arises: \emph{coefficient cannibalization}, in which quantum features absorb coefficient mass that rightfully belongs to the polynomial basis, corrupting equation recovery. We derive the exact cannibalization-bias formula $Δξ_P = (P^\top P)^{-1}P^\top Q\,\hatξ_Q$ and prove that orthogonalizing quantum features against the polynomial column space at fit time eliminates this bias exactly. The claim is verified numerically to machine precision ($<10^{-12}$) on multiple systems. Empirically, across six canonical dynamical systems (Duffing, Van der Pol, Lorenz, Lotka-Volterra, cubic oscillator, Rössler) and three quantum feature map architectures (ZZ-angle encoding, IQP, data re-uploading), orthogonalized Q-SINDy consistently matches vanilla SINDy's structural recovery while uncorrected augmentation degrades true-positive rates by up to 100%. A refined dynamics-aware diagnostic, $R^2_Q$ for $\dot X$, predicts cannibalization severity with statistical significance (Pearson $r=0.70$, $p=0.023$). An RBF classical-kernel control across 20 hyperparameter configurations fails more severely than any quantum variant, ruling out feature count as the cause. Orthogonalization remains robust under depolarizing hardware noise up to 2% per gate, and the framework extends without modification to Burgers' equation.

Quantum machine learning offers a promising new paradigm for computational biology by leveraging quantum mechanical principles to enhance cancer classification, biomarker discovery, and bioinformatics diagnostics. In this study, we apply QML to identify subtype specific biomarkers for lung adenocarcinoma (LUAD) and lung squamous cell carcinoma (LUSC), the two predominant forms of non-small cell lung cancer. Our methodology involves a two-phase process: in Phase 1, differential expression analysis and methylation analysis between tumor and normal samples allows us to identify LUAD-specific and LUSC-specific genes, revealing potential prognostic biomarkers for cancer subtypes. Phase 2 focuses on developing a quantum classifier capable of distinguishing between LUAD and LUSC tumors, as well as between tumor and normal samples. This classifier not only enhances diagnostic precision but also demonstrates the quantum advantage in processing large-scale multiomic datasets. Our results consistently demonstrated that Sample3, representing the combined gene set, achieved the highest overall predictive performance in all metrics. These results demonstrate that QML provides an effective and scalable approach for biomarker discovery and subtype specific cancer classification. GO enrichment analysis highlighted the significant involvement of genes in synaptic signaling, ion channel regulation, and neuronal development. In the quantum phase, KEGG analysis further identified enrichment in cancer-associated pathways, including neurotrophin, MAPK, Ras, and PI3KAkt signaling, with key genes such as NGFR, NTRK2, and NTF3 suggesting a central role in neurotrophinmediated oncogenic processes. Our findings highlight the growing potential of quantum computing to advance precision oncology and next-generation biomedical analytics.

Interpretable machine learning techniques are becoming essential tools for extracting physical insights from complex quantum data. We build on recent advances in variational autoencoders to demonstrate that such models can learn physically meaningful and interpretable representations from a broad class of unlabeled quantum datasets. From raw measurement data alone, the learned representation reveals rich information about the underlying structure of quantum phase spaces. We further augment the learning pipeline with symbolic methods, enabling the discovery of compact analytical descriptors that serve as order parameters for the distinct regimes emerging in the learned representations. We demonstrate the framework on experimental Rydberg-atom snapshots, classical shadows of the cluster Ising model, and hybrid discrete-continuous fermionic data, revealing previously unreported phenomena such as a corner-ordering pattern in the Rydberg arrays. These results establish a general framework for the automated and interpretable discovery of physical laws from diverse quantum datasets. All methods are available through qdisc, an open-source Python library designed to make these tools accessible to the broader community.

Learning with large-scale datasets and information-critical applications, such as in High Energy Physics (HEP), demands highly complex, large-scale models that are both robust and accurate. To tackle this issue and cater to the learning requirements, we envision using a federated learning framework with a quantum-enhanced model. Specifically, we design a hybrid quantum-classical long-shot-term-memory model (QLSTM) for local training at distributed nodes. It combines the representative power of quantum models in understanding complex relationships within the feature space, and an LSTM-based model to learn necessary correlations across data points. Given the computing limitations and unprecedented cost of current stand-alone noisy-intermediate quantum (NISQ) devices, we propose to use a federated learning setup, where the learning load can be distributed to local servers as per design and data availability. We demonstrate the benefits of such a design on a classification task for the Supersymmetry(SUSY) dataset, having 5M rows. Our experiments indicate that the performance of this design is not only better that some of the existing work using variational quantum circuit (VQC) based quantum machine learning (QML) techniques, but is also comparable ($Δ\sim \pm 1\%$) to that of classical deep-learning benchmarks. An important observation from this study is that the designed framework has $<$300 parameters and only needs 20K data points to give a comparable performance. Which also turns out to be a 100$\times$ improvement than the compared baseline models. This shows an improved learning capability of the proposed framework with minimal data and resource requirements, due to the joint model with an LSTM based architecture and a quantum enhanced VQC.

AI-driven methods have demonstrated considerable success in tackling the central challenge of accurately solving the Schrödinger equation for complex many-body systems. Among neural network quantum state (NNQS) approaches, the NNQS-SCI (Selected Configuration Interaction) method stands out as a state-of-the-art technique, recognized for its high accuracy and scalability. However, its application to larger systems is severely constrained by a hybrid CPU-GPU architecture. Specifically, centralized CPU-based global de-duplication creates a severe scalability barrier due to communication bottlenecks, while host-resident coupled-configuration generation induces prohibitive computational overheads. We introduce QiankunNet-cuSCI, a fully GPU-accelerated SCI framework designed to overcome these bottlenecks. It first integrates a distributed, load-balanced global de-duplication algorithm to minimize redundancy and communication overhead at scale. To address compute limitations, it employs specialized, fine-grained CUDA kernels for exact coupled configuration generation. Finally, to break the single-GPU memory barrier exposed by this full acceleration, it incorporates a GPU memory-centric runtime featuring GPU-side pooling, streaming mini-batches, and overlapped offloading. This design enables much larger configuration spaces and shifts the bottleneck from host-side limitations back to on-device inference. Our evaluation demonstrates that our work fundamentally expands the scale of solvable problems. On an NVIDIA A100 cluster with 64 GPUs, our work achieves up to 2.32X end-to-end speedup over the highly-optimized NNQS-SCI baseline while preserving the same chemical accuracy. Furthermore, it demonstrates excellent distributed performance, maintaining over 90% parallel efficiency in strong scaling tests.

We present PINNACLE, an open-source computational framework for physics-informed neural networks (PINNs) that integrates modern training strategies, multi-GPU acceleration, and hybrid quantum-classical architectures within a unified modular workflow. The framework enables systematic evaluation of PINN performance across benchmark problems including 1D hyperbolic conservation laws, incompressible flows, and electromagnetic wave propagation. It supports a range of architectural and training enhancements, including Fourier feature embeddings, random weight factorization, strict boundary condition enforcement, adaptive loss balancing, curriculum training, and second-order optimization strategies, with extensibility to additional methods. We provide a comprehensive benchmark study quantifying the impact of these methods on convergence, accuracy, and computational cost, and analyze distributed data parallel scaling in terms of runtime and memory efficiency. In addition, we extend the framework to hybrid quantum-classical PINNs and derive a formal estimate for circuit-evaluation complexity under parameter-shift differentiation. Results highlight the sensitivity of PINNs to architectural and training choices, confirm their high computational cost relative to classical solvers, and identify regimes where hybrid quantum models offer improved parameter efficiency. PINNACLE provides a foundation for benchmarking physics-informed learning methods and guiding future developments through quantitative assessment of their trade-offs.

The impossibility of simultaneously cloning non-orthogonal states lies at the foundations of quantum theory. Even when allowing for approximation errors, cloning an arbitrary unknown pure state requires as many initial copies as needed to fully learn the state. Rather than arbitrary unknown states, modern quantum learning theory often considers structured classes of states and exploits such structure to develop learning algorithms that outperform general-state tomography. This raises the question: How do the sample complexities of learning and cloning relate for such structured classes? We answer this question for an important class of states. Namely, for $n$-qubit stabilizer states, we show that the optimal sample complexity of cloning is $Θ(n)$. Thus, also for this structured class of states, cloning is as hard as learning. To prove these results, we use representation-theoretic tools in the recently proposed Abelian State Hidden Subgroup framework and a new structured version of the recently introduced random purification channel to relate stabilizer state cloning to a variant of the sample amplification problem for probability distributions that was recently introduced in classical learning theory. This allows us to obtain our cloning lower bounds by proving new sample amplification lower bounds for classes of distributions with an underlying linear structure. Our results provide a more fine-grained perspective on No-Cloning theorems, opening up connections from foundations to quantum learning theory and quantum cryptography.