Quantum Machine Learning

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%.

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.

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

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: (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); (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; (iii)expressibility saturates at circuit depth${\approx}\,3$, explaining why shallow VQCs already cover the Hilbert space effectively; (iv)~LayerNorm on the fully quantum transformer improves classification accuracy, suggesting normalization is important when all operations are quantum; (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.

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.

Node embeddings act as the information interface for graph neural networks, yet their empirical impact is often reported under mismatched backbones, splits, and training budgets. This paper provides a controlled benchmark of embedding choices for graph classification, comparing classical baselines with quantum-oriented node representations under a unified pipeline. We evaluate two classical baselines alongside quantum-oriented alternatives, including a circuit-defined variational embedding and quantum-inspired embeddings computed via graph operators and linear-algebraic constructions. All variants are trained and tested with the same backbone, stratified splits, identical optimization and early stopping, and consistent metrics. Experiments on five different TU datasets and on QM9 converted to classification via target binning show clear dataset dependence: quantum-oriented embeddings yield the most consistent gains on structure-driven benchmarks, while social graphs with limited node attributes remain well served by classical baselines. The study highlights practical trade-offs between inductive bias, trainability, and stability under a fixed training budget, and offers a reproducible reference point for selecting quantum-oriented embeddings in graph learning.

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.

Multi-task learning (MTL) improves generalization and data efficiency by jointly learning related tasks through shared representations. In the widely used hard-parameter-sharing setting, a shared backbone is combined with task-specific prediction heads. However, task-specific parameters can grow rapidly with the number of tasks. Therefore, designing multi-task heads that preserve task specialization while improving parameter efficiency remains a key challenge. In Quantum Machine Learning (QML), variational quantum circuits (VQCs) provide a compact mechanism for mapping classical data to quantum states residing in high-dimensional Hilbert spaces, enabling expressive representations within constrained parameter budgets. We propose a parameter-efficient quantum multi-task learning (QMTL) framework that replaces conventional task-specific linear heads with a fully quantum prediction head in a hybrid architecture. The model consists of a VQC with a shared, task-independent quantum encoding stage, followed by lightweight task-specific ansatz blocks enabling localized task adaptation while maintaining compact parameterization. Under a controlled and capacity-matched formulation where the shared representation dimension grows with the number of tasks, our parameter-scaling analysis demonstrates that a standard classical head exhibits quadratic growth, whereas the proposed quantum head parameter cost scales linearly. We evaluate QMTL on three multi-task benchmarks spanning natural language processing, medical imaging, and multimodal sarcasm detection, where we achieve performance comparable to, and in some cases exceeding, classical hard-parameter-sharing baselines while consistently outperforming existing hybrid quantum MTL models with substantially fewer head parameters. We further demonstrate QMTL's executability on noisy simulators and real quantum hardware, illustrating its feasibility.

Synthetic Aperture Radar (SAR) data is inherently complex-valued, while quantum machine learning (QML) models operate in complex Hilbert spaces. This similarity suggests that using both the magnitude and phase of SAR data in quantum encoding should help automatic target recognition in SAR images. In this study, we test this assumption by comparing five encoding strategies for quantum models: magnitude-only encoding, joint magnitude-phase encoding, in-phase and quadrature encoding, preprocessed phase encoding, and a purely quantum architecture. All approaches are evaluated under a unified experimental setup on the MSTAR benchmark dataset. Surprisingly, we find that magnitude-only encoding performs better than phase-inclusive encodings in hybrid quantum-classical models. It achieves 99.57 percent accuracy on the 3-class task and 71.19 percent accuracy on the 8-class task, outperforming complex-valued alternatives under the same framework. Adding phase information provides little or no improvement and can sometimes degrade performance. However, in purely quantum models with only 184 to 224 trainable parameters and no classical neural-network layers, phase information becomes much more important, improving accuracy by up to 21.65 percentage points. These findings show that the usefulness of phase information depends not only on the data, but also on the architecture used to process it. Hybrid models can compensate for missing phase information through their classical components, while pure quantum models rely more strongly on phase information for class discrimination. The results provide practical guidance for encoding complex-valued data in quantum machine learning and highlight the importance of jointly designing encoding strategies and model architectures for current quantum systems.

Broadly applicable quantum advantage, particularly in classical data processing and machine learning, has been a fundamental open problem. In this work, we prove that a small quantum computer of polylogarithmic size can perform large-scale classification and dimension reduction on massive classical data by processing samples on the fly, whereas any classical machine achieving the same prediction performance requires exponentially larger size. Furthermore, classical machines that are exponentially larger yet below the required size need superpolynomially more samples and time. We provide evidence for these quantum advantages in real-world applications, including single-cell RNA sequencing and movie review sentiment analysis, demonstrating four to six orders of magnitude reduction in size with fewer than 60 logical qubits. These quantum advantages are enabled by quantum oracle sketching, an algorithm for accessing the classical world in quantum superposition using only random classical data samples. Combined with classical shadows, our algorithm circumvents the data loading and readout bottleneck to construct succinct classical models from massive classical data, a task provably impossible for any classical machine that is not exponentially larger than the quantum machine. These quantum advantages persist even when classical machines are granted unlimited time or if BPP = BQP, and rely only on the correctness of quantum mechanics. Together, our results establish machine learning on classical data as a broad and natural domain of quantum advantage and a fundamental test of quantum mechanics at the complexity frontier.

Designing quantum neural networks (QNNs) that are both accurate and deployable on NISQ hardware is challenging. Handcrafted ansatze must balance expressivity, trainability, and resource use, while limited qubits often necessitate circuit cutting. Existing quantum architecture search methods primarily optimize accuracy while only heuristically controlling quantum and mostly ignore the exponential overhead of circuit cutting. We introduce QNAS, a neural architecture search framework that unifies hardware aware evaluation, multi objective optimization, and cutting overhead awareness for hybrid quantum classical neural networks (HQNNs). QNAS trains a shared parameter SuperCircuit and uses NSGA-II to optimize three objectives jointly: (i) validation error, (ii) a runtime cost proxy measuring wall clock evaluation time, and (iii) the estimated number of subcircuits under a target qubit budget. QNAS evaluates candidate HQNNs under a few epochs of training and discovers clear Pareto fronts that reveal tradeoffs between accuracy, efficiency, and cutting overhead. Across MNIST, Fashion-MNIST, and Iris benchmarks, we observe that embedding type and CNOT mode selection significantly impact both accuracy and efficiency, with angle-y embedding and sparse entangling patterns outperforming other configurations on image datasets, and amplitude embedding excelling on tabular data (Iris). On MNIST, the best architecture achieves 97.16% test accuracy with a compact 8 qubit, 2 layer circuit; on the more challenging Fashion-MNIST, 87.38% with a 5 qubit, 2 layer circuit; and on Iris, 100% validation accuracy with a 4 qubit, 2 layer circuit. QNAS surfaces these design insights automatically during search, guiding practitioners toward architectures that balance accuracy, resource efficiency, and practical deployability on current hardware.

Crime pattern analysis is critical for law enforcement and predictive policing, yet the surge in criminal activities from rapid urbanization creates high-dimensional, imbalanced datasets that challenge traditional classification methods. This study presents a quantum-classical comparison framework for crime analytics, evaluating four computational paradigms: quantum models, classical baseline machine learning models, and two hybrid quantum-classical architectures. Using 16-year crime statistics, we systematically assess classification performance and computational efficiency under rigorous cross-validation methods. Experimental results show that quantum-inspired approaches, particularly QAOA, achieve up to 84.6% accuracy, while requiring fewer trainable parameters than classical baselines, suggesting practical advantages for memory-constrained edge deployment. The proposed correlation-aware circuit design demonstrates the potential of incorporating domain-specific feature relationships into quantum models. Furthermore, hybrid approaches exhibit competitive training efficiency, making them suitable candidates for resource-constrained environments. The framework's low computational overhead and compact parameter footprint suggest potential advantages for wireless sensor network deployments in smart city surveillance systems, where distributed nodes perform localized crime analytics with minimal communication costs. Our findings provide a preliminary empirical assessment of quantum-enhanced machine learning for structured crime data and motivate further investigation with larger datasets and realistic quantum hardware considerations.

Efficient data loading remains a bottleneck for near-term quantum machine learning. Existing schemes (angle, amplitude, and basis encoding) either underuse the exponential Hilbert-space capacity or require circuit depths that exceed the coherence budgets of noisy intermediate-scale quantum hardware. We introduce shot-based quantum encoding (SBQE), a data embedding strategy that distributes the hardware's native resource, shots, according to a data-dependent classical distribution over multiple initial quantum states. By treating the shot counts as a learnable degree of freedom, SBQE produces a mixed-state representation whose expectation values are linear in the classical probabilities and can therefore be composed with nonlinear activation functions. We show that SBQE is structurally equivalent to a multilayer perceptron whose weights are realized by quantum circuits, and we describe a hardware-compatible implementation protocol. Benchmarks on three image datasets, with 10 independent initializations per model, show that SBQE achieves 89.1% +- 0.9% test accuracy on Semeion (reducing error by 5.3% relative to amplitude encoding and matching a width-matched classical network), 80.95% +- 0.10% on Fashion MNIST (exceeding amplitude encoding by +2.0% and a linear multilayer perceptron by +1.3%), and 90.25% +- 0.18% on MNIST (exceeding amplitude encoding by 2.1 percentage points and the width-matched classical network by 0.3), all without any data-encoding gates.

Learning quantum states from measurement data is a central problem in quantum information and computational complexity. In this work, we study the problem of learning to generate mixed states on a finite-dimensional lattice. Motivated by recent developments in mixed state phases of matter, we focus on arbitrary states in the trivial phase. A state belongs to the trivial phase if there exists a shallow preparation channel circuit under which local reversibility is preserved throughout the preparation. We prove that any mixed state in this class can be efficiently learned from measurement access alone. Specifically, given copies of an unknown trivial phase mixed state, our algorithm outputs a shallow local channel circuit that approximately generates this state in trace distance. The sample complexity and runtime are polynomial (or quasi-polynomial) in the number of qubits, assuming constant (or polylogarithmic) circuit depth and gate locality. Importantly, the learner is not given the original preparation circuit and relies only on its existence. Our results provide a structural foundation for quantum generative models based on shallow channel circuits. In the classical limit, our framework also inspires an efficient algorithm for classical diffusion models using only a polynomial overhead of training and generation.

Learning from quantum data using classical machine learning models has emerged as a promising paradigm toward realizing quantum advantages. Despite extensive analyses on their performance, clean and fully labeled quantum data from the target domain are often unavailable in practical scenarios, forcing models to be trained on data collected under conditions that differ from those encountered at deployment. This mismatch highlights the need for new approaches beyond the common assumptions of prior work. In this work, we address this issue by employing an unsupervised domain adaptation framework for learning from imperfect quantum data. Specifically, by leveraging classical representations of quantum states obtained via classical shadows, we perform unsupervised domain adaptation entirely within a classical computational pipeline once measurements on the quantum states are executed. We numerically evaluate the framework on quantum phases of matter and entanglement classification tasks under realistic domain shifts. Across both tasks, our method outperforms source-only non-adaptive baselines and target-only unsupervised learning approaches, demonstrating the practical applicability of domain adaptation to realistic quantum data learning.

Integrating quantum circuits into deep learning pipelines remains challenging due to heuristic design limitations. We propose Q-DIVER, a hybrid framework combining a large-scale pretrained EEG encoder (DIVER-1) with a differentiable quantum classifier. Unlike fixed-ansatz approaches, we employ Differentiable Quantum Architecture Search to autonomously discover task-optimal circuit topologies during end-to-end fine-tuning. On the PhysioNet Motor Imagery dataset, our quantum classifier achieves predictive performance comparable to classical multi-layer perceptrons (Test F1: 63.49%) while using approximately \textbf{50$\times$ fewer task-specific head parameters} (2.10M vs. 105.02M). These results validate quantum transfer learning as a parameter-efficient strategy for high-dimensional biological signal processing.

Large language models have recently shown potential in bridging the gap between classical machine learning and quantum machine learning. However, the lack of standardized, high-quality datasets and robust translation frameworks limits progress in this domain. We introduce Q-Bridge, an LLM-guided code translation framework that systematically converts CML implementations into executable QML variants. Our approach builds on a self-involving pipeline that iteratively expands a verified seed codebase into a large-scale dataset, CML-2-QML, integrating verifiable and unverifiable code pairs. The Q-Bridge model is fine-tuned using supervised LoRA adaptation for scalable and memory-efficient training, achieving faithful and interpretable quantum code generation across diverse architectures. Empirical analysis confirms the feasibility of direct CML-to-QML translation and reveals consistent structural alignment between classical and quantum paradigms. Case studies further demonstrate that Q-Bridge can maintain deterministic correctness and also enable creative architectural exploration. This work establishes the first reproducible framework and dataset for LLM-driven quantum code translation, offering a foundation for scalable quantum AI development.

A faithful description of chemical processes requires exploring extended regions of the molecular potential energy surface (PES), which remains challenging for strongly correlated systems. Transferable deep-learning variational Monte Carlo (VMC) offers a promising route by efficiently solving the electronic Schrödinger equation jointly across molecular geometries at consistently high accuracy, yet its stochastic nature renders direct exploration of molecular configuration space nontrivial. Here, we present a framework for highly accurate ab initio exploration of PESs that combines transferable deep-learning VMC with a cost-effective estimation of energies, forces, and Hessians. By continuously sampling nuclear configurations during VMC optimization of electronic wave functions, we obtain transferable descriptions that achieve zero-shot chemical accuracy within chemically relevant distributions of molecular geometries. Throughout the subsequent characterization of molecular configuration space, the PES is evaluated only sparsely, with local approximations constructed by estimating VMC energies and forces at sampled geometries and aggregating the resulting noisy data using Gaussian process regression. Our method enables accurate and efficient exploration of complex PES landscapes, including structure relaxation, transition-state searches, and minimum-energy pathways, for both ground and excited states. This opens the door to studying bond breaking, formation, and large structural rearrangements in systems with pronounced multi-reference character.

This article presents an argument for why quantum computers could unlock new methods for machine learning. We argue that spectral methods, in particular those that learn, regularise, or otherwise manipulate the Fourier spectrum of a machine learning model, are often natural for quantum computers. For example, if a generative machine learning model is represented by a quantum state, the Quantum Fourier Transform allows us to manipulate the Fourier spectrum of the state using the entire toolbox of quantum routines, an operation that is usually prohibitive for classical models. At the same time, spectral methods are surprisingly fundamental to machine learning: A spectral bias has recently been hypothesised to be the core principle behind the success of deep learning; support vector machines have been known for decades to regularise in Fourier space, and convolutional neural nets build filters in the Fourier space of images. Could, then, quantum computing open fundamentally different, much more direct and resource-efficient ways to design the spectral properties of a model? We discuss this potential in detail here, hoping to stimulate a direction in quantum machine learning research that puts the question of ``why quantum?'' first.

Generalization is a central concept in machine learning theory, yet for quantum models, it is predominantly analyzed through uniform bounds that depend on a model's overall capacity rather than the specific function learned. These capacity-based uniform bounds are often too loose and entirely insensitive to the actual training and learning process. Previous theoretical guarantees have failed to provide non-uniform, data-dependent bounds that reflect the specific properties of the learned solution rather than the worst-case behavior of the entire hypothesis class. To address this limitation, we derive the first PAC-Bayesian generalization bounds for a broad class of quantum models by analyzing layered circuits composed of general quantum channels, which include dissipative operations such as mid-circuit measurements and feedforward. Through a channel perturbation analysis, we establish non-uniform bounds that depend on the norms of learned parameter matrices; we extend these results to symmetry-constrained equivariant quantum models; and we validate our theoretical framework with numerical experiments. This work provides actionable model design insights and establishes a foundational tool for a more nuanced understanding of generalization in quantum machine learning.

The Random Forest model is one of the popular models of Machine learning. We present a quantum algorithm for testing (forecasting) process of the Random Forest machine learning model for the Regression problem. The presented algorithm is more efficient (in terms of query complexity or running time) than the classical counterpart.

The development of new drugs is a tedious, time-consuming, and expensive process, for which the average costs are estimated to be up to around $2.5 billion. The first step in this long process is the design of the new drug, for which de novo drug design, assisted by artificial intelligence, has blossomed in recent years and revolutionized the field. In particular, generative artificial intelligence has delivered promising results in drug discovery and development, reducing costs and the time to solution. However, classical generative models, such as generative adversarial networks (GANs), are difficult to train due to barren plateaus and prone to mode collapse. Quantum computing may be an avenue to overcome these issues and provide models with fewer parameters, thereby enhancing the generalizability of GANs. We propose a new style-based quantum GAN (QGAN) architecture for drug design that implements noise encoding at every rotational gate of the circuit and a gradient penalty in the loss function to mitigate mode collapse. Our pipeline employs a variational autoencoder to represent the molecular structure in a latent space, which is then used as input to our QGAN. Our baseline model runs on up to 15 qubits to validate our architecture on quantum simulators, and a 156-qubit IBM Heron quantum computer in the five-qubit setup is used for inference to investigate the effects of using real quantum hardware on the analysis. We benchmark our results against classical models as provided by the MOSES benchmark suite.

Quantum computers provide a super-exponential speedup for performing a Fourier transform over the symmetric group, an ability for which practical use cases have remained elusive so far. In this work, we leverage this ability to unlock spectral methods for machine learning over permutation-structured data, which appear in applications such as multi-object tracking and recommendation systems. It has been shown previously that a powerful way of building probabilistic models over permutations is to use the framework of non-Abelian harmonic analysis, as the model's group Fourier spectrum captures the interaction complexity: "low frequencies" correspond to low order correlations, and "high frequencies" to more complex ones. This can be used to construct a Markov chain model driven by alternating steps of diffusion (a group-equivariant convolution) and conditioning (a Bayesian update). However, this approach is computationally challenging and hence limited to simple approximations. Here we construct a quantum algorithm that encodes the exact probabilistic model -- a classically intractable object -- into the amplitudes of a quantum state by making use of the Quantum Fourier Transform (QFT) over the symmetric group. We discuss the scaling, limitations, and practical use of such an approach, which we envision to be a first step towards useful applications of non-Abelian QFTs.

We propose a Quantum Federated Autoencoder for Anomaly Detection, a framework that leverages quantum federated learning for efficient, secure, and distributed processing in IoT networks. By harnessing quantum autoencoders for high-dimensional feature representation and federated learning for decentralized model training, the approach transforms localized learning on edge devices without requiring transmission of raw data, thereby preserving privacy and minimizing communication overhead. The model leverages quantum advantage in pattern recognition to enhance detection sensitivity, particularly in complex and dynamic IoT network traffic. Experiments on a real-world IoT dataset show that the proposed method delivers anomaly detection accuracy and robustness comparable to centralized approaches, while ensuring data privacy.

Variational Quantum Algorithms (VQAs) have been extensively researched for applications in Quantum Machine Learning (QML), Optimization, and Molecular simulations. Although designed for Noisy Intermediate-Scale Quantum (NISQ) devices, VQAs are predominantly evaluated classically due to uncertain results on noisy devices and limited resource availability. Raising concern over the reproducibility of simulated VQAs on noisy hardware. While prior studies indicate that VQAs may exhibit noise resilience in specific parameterized shallow quantum circuits, there are no definitive measures to establish what defines a shallow circuit or the optimal circuit depth for VQAs on a noisy platform. These challenges extend naturally to Variational Quantum Classification (VQC) algorithms, a subclass of VQAs for supervised learning. In this article, we propose a relative entropy-based metric to verify whether a VQC model would perform similarly on a noisy device as it does on simulations. We establish a strong correlation between the average relative entropy difference in classes, transpilation circuit depth, and their performance difference on a noisy quantum device. Our results further indicate that circuit depth alone is insufficient to characterize shallow circuits. We present empirical evidence to support these assertions across a diverse array of techniques for implementing VQC, datasets, and multiple noisy quantum devices.