Quantum Machine Learning

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.

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.

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.

Distributed quantum learning (DQL) has emerged as a promising paradigm to scale quantum-enhanced machine learning by interconnecting multiple quantum devices. However, for efficient real-world deployment, it is essential to characterize how DQL converges under practical scenarios while simultaneously safeguarding multi-device quantum infrastructures from evolving security threats. Addressing these aspects in an integrated manner is key to ensuring both performance and resilience in large-scale DQL systems. Therefore, this paper presents a new DQL study where our innovation lies in: (i) conducting a holistic convergence analysis for DQL under practical settings, i.e., partial device participation, non-convex loss functions, and heterogeneous data distributions, (ii) developing a novel multi-layered post-quantum cryptographic architecture with a quantum neural network-powered adaptive mechanism that monitors conditions, evaluates threats, and adjusts parameters across three National Institute of Standards and Technology (NIST)-compliant levels. Our theoretical framework and empirical validation reveal two key insights: (i) the derived convergence bound uncovers a fundamental trade-off between convergence rate, measurement shots, and the size of the participating device subset; and (ii) findings from our evaluations on a physical testbed modeling quantum control architectures expose the performance limitations of static post-quantum security, while confirming that our adaptive framework effectively mitigates these overheads to preserve overall system efficiency. Specifically, the hardware experiments demonstrate that our dynamic security mechanism reduces total security execution time by approximately 49% relative to static high-security baselines, while maintaining a threat detection accuracy of over 91%. Furthermore, extensive simulations validate our theoretical analysis.....

Kernel methods are typically formulated under the assumption of exact, noise-free access to the Gram matrix. However, in emerging settings such as quantum machine learning, each kernel entry must be inferred from noisy observations, and its accuracy depends on how a limited measurement budget is allocated. Despite this, existing approaches overwhelmingly rely on uniform allocation, which equalizes estimator variance but ignores the highly non-uniform dependence of kernelized classifiers on the Gram matrix. In this work, we introduce an adaptive measurement-allocation strategy for learning kernelized Support Vector Machines (SVMs) from noisy Bernoulli observations. Our approach combines two complementary principles: (i) geometric sensitivity, capturing how perturbations of individual kernel entries affect the classifier margin, and (ii) active-set instability, quantifying the probability of discrete changes in support-vector membership induced by measurement noise. These signals define a task-aware allocation scheme that concentrates measurements on the most decision-critical regions of the kernel matrix. We provide a theoretical analysis showing that the benefit of adaptive allocation is governed by the heterogeneity of the induced kernel importance structure, leading to distinct regimes in which adaptive or uniform strategies are preferable. Empirical evaluations on synthetic datasets demonstrate that adaptive allocation significantly improves support-vector recovery, margin estimation, and decision-function accuracy under fixed measurement budgets. A dual-coefficient stability criterion further enables early stopping, achieving near-optimal performance while using only a fraction of the measurement cost. Additional experiments on quantum kernels derived from real-world data reveal a regime-dependent behavior aligned with known phenomena such as kernel concentration. Together...

Photonic quantum computing is a promising platform for scalable quantum machine learning, but designing effective hybrid architectures remains challenging under hardware and optimization constraints. Existing approaches rely on manually tuned architectures that fail to account for the collaboration between classical preprocessing, phase encoding, and photonic circuit structure, limiting both accuracy and hardware compatibility. In this paper, we propose a neural architecture search framework for hybrid photonic quantum-classical models that combines genetic algorithm-based search with learnable quantum phase encoding to systematically explore the joint design space of classical and quantum components. Our framework encodes 19 hyperparameters across six gene groups and evolves a population of hybrid architectures using group-based crossover, per-gene mutation, and elitism, evaluating each candidate on a short training budget before full retraining of the best found design. We evaluate our framework on two image classification benchmarks, Digits and MNIST, achieving final validation accuracies of 99.44% and 98.78%, respectively, with first-principles execution time estimates on the Quandela Ascella photonic QPU projecting single-image inference at 67 ms (Digits) and 149 ms (MNIST). Our quantum contribution analysis further shows that the photonic layer extracts non-redundant features orthogonal to the classical pathway, providing a measurable accuracy advantage over classical-only baselines. Our results demonstrate that automated architecture search is both practical and impactful for hybrid photonic systems, opening the way for systematic design space exploration of quantum AI on photonic devices.

Unmanned aerial vehicles (UAVs) are cyber-physical systems whose attack surface spans networked avionics and on-board sensor fusion: a compromised GPS or battery module can mimic a benign mission segment and evade naive anomaly detectors. We present a leakage-free evaluation of quantum machine learning for UAV anomaly detection on the multi-sensor TLM:UAV benchmark. Three contributions support the study. (i) A group-aware temporal protocol (B2) partitions the dataset into ten contiguous TimeUS blocks and evaluates over ten seeds, eliminating the inflation produced by random stratified splits that mix neighbouring samples. (ii) A three-mode feature audit (full/loose/strict) quantifies how much accuracy stems from instantaneous physical signals versus contextual proxies (cumulative energy, battery state, GPS trajectory). (iii) A hybrid XGBoost + Data Reuploading (DRU) classifier is benchmarked against five paired non-linear controls (raw, PCA, polynomial-2, random-RBF, and an untrained DRU map) under identical budgets. The standalone DRU does not consistently match the strongest classical baseline across seeds; however, the trained-DRU hybrid is the only model whose mean F1 macro shifts upward from full to strict (+0.05), a directional signal that the per-seed standard deviations prevent from being interpreted as a statistically established difference. The trained-DRU hybrid also records the lowest mean false-alarm rate under proxy-free evaluation, subject to the inter-seed variance reported. We frame this as an incremental, reproducible quantum-enhanced hybrid benefit, and provide an open Qiskit 2.x implementation as a benchmark for cybersecurity analytics in NISQ-era aerospace systems.

Virtually all aspects of many-body atomic physics are challenging: experiments are technically demanding, datasets have become enormous, and the memory and CPU requirements for classical simulation of generic quantum systems often scale exponentially with system size. Machine learning (ML) methods are already assisting in each of these areas and are poised to become transformative. Here, we focus on two specific applications of ML to cold-atom-based quantum simulators. These devices generally generate data in the form of images; we first showcase denoising of raw images and then identify solitonic waves in Bose-Einstein condensates. In both of these examples, we comment on the interplay between performance, model complexity, and interpretability.

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

Machine learning has revolutionized numerous industrial domains. Despite recent advances, machine learning models remain vulnerable to adversarial threats. Adversarial machine learning is a field that studies these vulnerabilities to build robust machine learning models. Quantum machine learning is an interdisciplinary field that bridges quantum computing and classical machine learning. While quantum machine learning shows potentials to outperform classical machine learning in complex tasks such as regression, classification, and generative modeling, it remains vulnerable to adversarial attacks. Given the recent advancements in quantum computing and machine learning, the quantum adversarial machine learning field has emerged to study the vulnerabilities of quantum machine learning, possible attacks, and novel quantum-enhanced defense strategies. In this survey, we provide a detailed overview on quantum adversarial machine learning and explore the existing attacks and countermeasures. We also review the theoretical underpinnings of this area, emerging trends, and critical challenges.

Matrix product operator Born machines (MPO-BMs) are tractable tensor-network models for probabilistic modeling, but their efficient approximation capability remains unclear. We characterize this boundary from both negative and positive perspectives. First, we prove that KL approximation is NP-hard for MPO-BMs in the continuous setting, ruling out universal efficient approximation in the worst case. Second, for score-based variational inference, we show that, under a locality and spectral-gap conditions on the loss-induced Hamiltonian, structured targets (e.g., path-graph Markov random fields) admit MPO-BM approximations with polynomial bond dimension and provable KL guarantees. Third, under the same locality structure, we prove that polynomially many score queries suffice to estimate the induced Hamiltonian and obtain such guarantees. Our results provide a theoretical characterization of when MPO-BMs are fundamentally hard to approximate and when they become efficiently learnable.

Transfer learning under limited data is a challenging setting, where models must adapt to new tasks with minimal supervision. Prior work has primarily focused on improving absolute accuracy in transfer learning. However, empirical evidence comparing quantum and classical models in realistic transfer learning settings remains limited, especially in low-data regimes. In this work, we systematically study the robustness of quantum models under reduced training data. We evaluate multiple quantum and classical architectures across diverse transfer tasks and retraining configurations, and quantify robustness using accuracy degradation and relative performance retention (RPR). Our results show that, although classical models often achieve higher peak performance, they exhibit significantly larger degradation when training data is limited. In contrast, quantum models maintain more stable performance across data regimes, indicating improved robustness and data efficiency. These findings provide empirical evidence that quantum models can offer improved robustness in low-resource transfer learning scenarios.

Fast Weight Programmers (FWPs) encode temporal dependencies through dynamically updated parameters rather than recurrent hidden states. Quantum FWPs (QFWPs) extend this idea with variational quantum circuits (VQCs), but existing implementations rely on multi-qubit architectures that are difficult to scale on noisy intermediate-scale quantum (NISQ) devices and expensive to simulate classically. We propose gated QKAN-FWP, a fast-weight framework that integrates FWP with Quantum-inspired Kolmogorov-Arnold Network (QKAN) using single-qubit data re-uploading circuits as learnable nonlinear activation, known as DatA Re-Uploading ActivatioN (DARUAN). We further introduce a scalar-gated fast-weight update rule that stabilizes parameter evolution, supported by a theoretical analysis of its adaptive memory kernel, geometric boundedness, and parallelizable gradient paths. We evaluate the framework across time-series benchmarks, MiniGrid reinforcement learning, and highlight real-world solar cycle forecasting as our main practical result. In the long-horizon setting with 528-month input window and 132-month forecast horizon, our 12.5k-parameter model achieves lower scaled Mean Square Error (MSE), peak amplitude error, and peak timing error than a suite of classical recurrent baselines with up to 13x more parameters, including Long Short-Term Memory (LSTM) networks (25.9k-89.1k parameters), WaveNet-LSTM (167k), Vanilla recurrent neural network (11.5k), and a Modified Echo State Network (132k). To validate NISQ compatibility, we further deploy the trained fast programmer on IonQ and IBM Quantum processors, recovering forecasting accuracy within 0.1% relative MSE of the noiseless simulator at 1024 shots. These results position gated QKAN-FWP as a scalable, parameter-efficient, and NISQ-compatible approach to quantum-inspired sequence modeling.

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.

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 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.

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.

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.

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.

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.

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.

Quantum sensing technologies offer transformative potential for ultra-sensitive biomedical sensing, yet their clinical translation remains constrained by classical noise limits and a reliance on macroscopic ensembles. We propose a unifying generational framework to organize the evolving landscape of quantum biosensors based on their utilization of quantum resources. First-generation devices utilize discrete energy levels for signal transduction but follow classical scaling laws. Second-generation sensors exploit quantum coherence, extending precision with the coherence time up to the standard quantum limit, while third-generation architectures employ entanglement and spin squeezing to approach Heisenberg-limited precision. We define an emerging fourth generation characterized by the end-to-end integration of quantum sensing with quantum learning and variational circuits, enabling adaptive inference directly within the quantum domain. By introducing a bandwidth-matching analysis pairing the neural signal hierarchy with platform response bandwidths, classifying deployed clinical devices by precision-scaling class and sensor-tissue proximity, and outlining a staged physical-milestone roadmap toward learning-integrated sensor networks, we identify key technological bottlenecks and chart the transition from measuring physical observables to extracting structured biological information with quantum-enhanced intelligence.

Accurate financial volatility forecasting is crucial but challenged by the non-linear, highly correlated nature of market data. Recently, quantum computing has emerged as a promising paradigm for solving complex high-dimensional sampling problems. To harness this, we propose a novel hybrid framework combining the temporal representation power of classical neural networks with the distribution-learning capabilities of quantum models. Specifically, we integrate a Long Short-Term Memory (LSTM) network with a Quantum Circuit Born Machine (QCBM). The LSTM extracts dynamic features, while the QCBM acts as a learnable generative prior modeling complex market distributions to guide forecasting. Evaluated on 5-minute high-frequency data from the SSE Composite and CSI 300 indices, our model significantly outperforms a classical LSTM baseline across MSE, RMSE, and QLIKE metrics. Furthermore, by introducing a stochastic Drop-Prior" mechanism during training, the LSTM implicitly distills structured information from the quantum prior. This establishes a pragmatic paradigm of quantum-assisted training with classical-efficient inference", whereby the model retains its quantum-enhanced accuracy even when the quantum module is entirely disabled during deployment. This demonstrates a practical pathway for leveraging quantum computing to enhance classical models without real-time quantum inference latency.

Quantum generative modeling is a rapidly evolving discipline at the intersection of quantum computing and machine learning. Contemporary quantum machine learning is generally limited to toy examples or heavily restricted datasets with few elements. This is not only due to the current limitations of available quantum hardware but also due to the absence of inductive biases arising from application-agnostic designs. Current quantum solutions must resort to tricks to scale down high-resolution images, such as relying heavily on dimensionality reduction or utilizing multiple quantum models for low-resolution image patches. Building on recent developments in classical image loading to quantum computers, we circumvent these limitations and train quantum Wasserstein GANs on the established classical MNIST and Fashion-MNIST datasets. Using the complete datasets, our system generates full-resolution images across all ten classes and establishes a new state-of-the-art performance with a single end-to-end quantum generator without tricks. As a proof-of-principle, we also demonstrate that our approach can be extended to color images, exemplified on the Street View House Numbers dataset. We analyze how the choice of variational circuit architecture introduces inductive biases, which crucially unlock this performance. Furthermore, enhanced noise input techniques enable highly diverse image generation while maintaining quality. Finally, we show promising results even under quantum shot noise conditions.

Maximum likelihood prediction (MLP) is a core task at the heart of modern large language models. Here, we study a quantum version of this task for a simplified data model consisting of independent and identically distributed samples, as a first step. The quantum maximum likelihood predictor (QMLP) is obtained by embedding of empirical probability distributions into quantum states and performing a minimization of quantum relative entropy over a given class of states. We derive non-asymptotic performance guarantees for QMLP in terms of convergence rates and concentration inequalities, both in trace norm and quantum relative entropy. Our approach provides a unified framework to handle MLP within both classical and quantum LLMs. We also consider the related problem of quantum information projection and generalize the quantum Pythagorean theorem to mixture families specified by possibly non-self-adjoint linear constraints. We further show that the Pythagorean inequality continues to hold in the infinite-dimensional setting whenever the convex information-projection problem attains a finite minimum.

Quantum sensors offer significant advantages over classical devices in spatial resolution and sensitivity, enabling transformative applications across materials science, healthcare, and beyond. Their practical performance, however, is often constrained by unmodelled effects, including noise, imperfect state preparation, and non-ideal control fields. In this work, we report the first experimental implementation of a graybox modelling strategy for a solid-state open quantum system. The graybox framework integrates a physics-based system model with a data-driven description of experimental imperfections, achieving higher fidelity than purely analytical (whitebox) approaches while requiring fewer training resources than fully deep-learning blackbox models. We experimentally validate the method on the task of estimating a static magnetic field using a single-spin quantum sensor, performing Bayesian inference with a graybox model trained on prior experimental data. Using roughly 10,000 training datapoints, the graybox model yields several orders of magnitude improvement in mean squared error over the corresponding physics-only model, as well as significant improvement over a blackbox model with comparable size. These results are broadly applicable to a wide range of quantum sensing platforms, not limited to single-spin systems, and are particularly valuable for real-time adaptive protocols, where model inaccuracies can otherwise lead to suboptimal control and degraded performance.

The characterization of Hamiltonians and other components of open quantum dynamical systems plays a crucial role in quantum computing and other applications. Scientific machine learning techniques have been applied to this problem in a variety of ways, including by modeling with deep neural networks. However, the majority of mathematical models describing open quantum systems are linear, and the natural nonlinearities in learnable models have not been incorporated using physical principles. We present a data-driven model for open quantum systems that includes learnable, thermodynamically consistent terms. The trained model is interpretable, as it directly estimates the system Hamiltonian and linear components of coupling to the environment. We validate the model on synthetic two and three-level data, as well as experimental two-level data collected from a quantum device at Lawrence Livermore National Laboratory.

A recurring weakness in quantum machine learning (QML) is that reported ``quantum advantages'' are seldom tested against a \emph{capacity-matched} classical control, leaving it unclear whether a gain comes from the quantum substrate or from the architectural change that accompanies it. Our primary contribution is methodological: a protocol for attributing such gains honestly -- a capacity-matched classical bottleneck of identical parameter budget, transparent reporting of where quantum does \emph{not} help, and validation on real quantum hardware -- which we develop and apply through a concrete case study. That case study is Quantum Adaptive Self-Attention (QASA), a hybrid Transformer that replaces the value projection of a \emph{single} encoder layer with a 36-parameter parameterized quantum circuit (PQC), keeping all other layers classical. Across nine synthetic benchmarks and the real-world ETTh1 dataset, QASA improves on a full-capacity classical Transformer for chaotic and trend-dominated signals. To ask whether this is a genuinely \emph{quantum} effect, we introduce a control rarely applied in quantum machine learning -- a capacity-matched classical bottleneck with the same parameter budget -- and find that it matches the PQC on the error metrics. The gain is therefore attributable to the low-rank value-projection \emph{bottleneck} (an \emph{architectural parsimony} principle), not to quantumness; adding further quantum layers only degrades performance and trainability. We accordingly position the quantum layer not as a source of accuracy advantage but as a \emph{competitive} instantiation of this principle: its low-rank compression onto the signal's intrinsic dimensionality is matched by a classical bottleneck, so the gain is architectural rather than quantum.

This paper studies how spectral geometry emerges in quantum learning models and how it can be diagnosed with physically grounded probes. In graph-regularized quantum networks, training reorganizes the output similarity graph, increases the effective spectral dimension Delta S = +0.23, and reshapes the Laplacian spectrum. Edge-resolved two-boson interference directly probes this restructuring: the bosonic enhancement Delta P_uv correlates with the Fiedler edge split |Delta v_2| (r = -0.50), linking learned spectral partitions to interference signatures. A phase diagram shows a nonmonotonic dependence of performance on coupling strength gamma and noise delta, with graph regularization improving fidelity only in a restricted regime; hardware experiments confirm the predicted interference behavior within shot-noise uncertainty. We also analyze a hybrid quantum autoencoder and introduce Bloch-space drift as a geometric diagnostic of its latent representation. With an unsupervised benign-data threshold, the model achieves high ranking performance (ROC-AUC about 0.99) and negligible false-negative rates. Absolute Bloch drift strongly discriminates anomalies (ROC-AUC at least about 0.9), while consecutive drift is near random (ROC-AUC about 0.5), showing that detection arises from persistent state-space displacement rather than local fluctuations. Through the geometry of reduced single-qubit states and associated quantum Fisher information, these results show that learning-induced spectral organization appears as measurable quantum-state structure, establishing a unified spectral-geometric framework for diagnosing quantum learning systems with bosonic and Bloch probes.