Quantum Machine Learning

In this study, we developed and evaluated four conditional energy-based forecasting architectures: a classical Gaussian-Bernoulli CRBM, a hybrid quantum-classical QCRBM, a full-register QQRBM, and a lag-feature QFeatureQRBM with complete derivations of their conditional distributions, Contrastive-Divergence gradients, and hybrid training, bridging the energy-based formulation and the implementation-level quantum computation. Unlike prior comparisons, our evaluation enforces symmetric hyperparameter optimisation: classical and quantum-specific hyperparameters receive an equally thorough grid search across thirteen structured experiments. We test on two data classes, a Gaussian-process dataset (GP) generated with real financial data and the input-driven NARMA-10 nonlinear benchmark. Across both regimes we find no systematic evidence of a quantum advantage at the available sample size: no quantum architecture improves on the best classical baseline. The fully quantum QQRBM and QFeatureQRBM are significantly worse, whereas the hybrid QCRBM is statistically indistinguishable from the strongest classical CRBM on both datasets. A power analysis bounds this null result: at n = 12 only medium-to-large effects are detectable, so small advantages cannot be excluded. An iso-parameter (matched-budget) comparison reaches the same conclusion: the classical CRBM is lowest at three of the four budgets and no CRBM-vs-QCRBM difference is significant at any budget.

A central design principle in modern machine learning and artificial intelligence is to align a model's inductive bias with the structure of its input data. For matrix-valued inputs, relevant matrix-level relationships can be characterised through spectral values and spectral subspaces; however, common coordinate-wise rotation-gate data-encoding unitaries used in most quantum machine learning models do not explicitly construct such a matrix-level representation. We introduce Quantum Spectral Models (QSMs), in which we construct the generator of the data-encoding unitary directly from each input matrix. We study three QSM variants based on symmetric, global block, and non-overlapping patch-local block Hamiltonians. Their outputs admit truncated Fourier representations in which input-dependent spectral gaps supply candidate phase carriers, while spectral subspaces help determine their coefficients. We evaluate the QSMs and comparison quantum models on two matrix representations of Pendigits and two controlled synthetic tasks defined by spectral statistics. At the largest evaluated circuit depth, QSM variants lead the tested quantum models in mean test accuracy across all four benchmarks. The patch-local QSM leads on Pendigits, whereas the global block-Hamiltonian QSM leads on the controlled spectral tasks. Ablations show a task-dependent reversal: subspace-preserving controls perform better on Pendigits, whereas spectral-value-only controls lead among the tested ablations on the synthetic tasks. Together, these results shed new light on quantum machine-learning model design by showing how input-conditioned spectral representations can provide an analysable inductive bias, while offering a broader perspective on structure-aware model design in machine learning and artificial intelligence.

A central challenge in quantum machine learning is understanding the scaling behavior of parameterized quantum circuits (PQCs). In particular, it remains unclear how their performance on unseen data changes as the number of trainable parameters increases. Prior works have derived formal generalization guarantees for quantum models, but it is well-known that many such results do not fully characterize generalization behavior in practice. In this work, we show that gradient-based PQCs can exhibit improved performance on unseen data as model size increases, displaying the phenomenon of double descent. This contrasts with the traditional view that larger models lead to degraded generalization. We provide analytical results rigorously underpinning this behavior by leveraging add-one-in perturbation techniques and spectral properties of random matrices. We support these results with numerical experiments on re-uploading PQCs across several data sets and training set sizes, consistently observing the predicted double descent behavior. While other obstacles on the path toward practical quantum machine learning remain, our finding that deeper parameterized quantum circuits do not necessarily exhibit degraded performance provides reasons for cautious optimism.

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

Quantum machine learning (QML) algorithms in high energy physics (HEP) can efficiently represent and leverage long-range, high-order correlations in high-dimensional collider data, potentially with fewer parameters and favorable scaling relative to classical models. Deployment of QML in real-time collider applications such as trigger systems requires the ability to emulate and compile quantum circuits classically, then synthesize the resulting quantum gates onto low-latency hardware accelerators, namely field-programmable gate arrays (FPGAs). We present a study of variational quantum autoencoder models for real-time anomaly detection triggers in modern collider experiments. The models achieve performance comparable to state-of-the-art classical approaches and, after FPGA synthesis, satisfy resource usage and timing constraints consistent with trigger applications in future colliders. This work provides one of the first FPGA implementations of QML models for HEP triggers, enabling higher-capability models in today's classical data acquisition pipelines while advancing quantum readiness of collider experiment infrastructure.

Quantum federated learning enables distributed clients to train quantum neural networks without sharing local data, making it promising for privacy-aware intelligent services. Intelligent services in this context refer to privacy-sensitive distributed decision systems, such as fraud detection and genomic classification, where reliable and fair client-level learning is as important as the accuracy of the aggregate model. However, heterogeneous client data and noisy quantum optimization often cause unstable local updates, client drift, and unfair performance between clients. This paper proposes DUQFL-Prox, a drift-stable quantum federated learning framework based on deep-unfolded local optimization. Instead of using a fixed local optimizer, each client performs adaptive unfolded SPSA updates, while a proximal term keeps the local model close to the global model. A lightweight controller learns step-specific optimization parameters to improve post-aggregation performance. Experiments on financial fraud and genomic classification tasks show that DUQFL-Prox improves stability, generalization, and client fairness compared with standard QFL baselines. The results suggest that deep-unfolded quantum federated learning can support more reliable and fair intelligent services in heterogeneous distributed environments.

Quantum reservoir computing (QRC) uses fixed quantum dynamics as a high-dimensional temporal feature map and trains only a lightweight classical readout. QRC is attractive for near-term quantum machine learning, but its performance depends strongly on architecture choices such as input encoding, reservoir depth, entanglement topology, measurement features, state-reset policy, feature construction, and readout regularization. We introduce \method, a simulator-based benchmark that formulates QRC design as constrained black-box architecture search and evaluates whether large language models can act as proposal controllers for this search problem. The benchmark compares five policies under identical evaluation budgets: random search, evolutionary search, Bayesian/TPE optimization, a feedback-based LLM agent, and \hybrid, which combines LLM proposals with memory, mutation, crossover, duplicate avoidance, and exploration. On NARMA10, Mackey-Glass forecasting, and temporal parity, \hybrid{} is the most consistent policy: it ranks first on NARMA10 and temporal parity and second on Mackey-Glass, narrowly behind evolutionary search. Under a 25-evaluation budget and three seeds, \hybrid{} improves over random search on all tasks, including a 23.6% relative reduction in Mackey-Glass error. The results do not show that LLMs are universal QRC optimizers; rather, they show that generative models can be useful high-level controllers when embedded inside validated, reproducible hybrid search loops.

Quantum reservoir computing (QRC) uses the dynamics of a fixed or weakly tuned quantum system to transform temporal and sequential inputs into measured features, while training is typically confined to a classical readout. This separation reduces reliance on repeated quantum parameter updates and avoids the barren plateaus associated with variational circuit training. Its computational power is often attributed to the exponentially large Hilbert space of the quantum system. However, the memory, nonlinearity, and expressivity that determine what a reservoir can actually compute depend jointly on the input encoding, quantum evolution, observables, measurement, and readout, not on Hilbert space dimension alone. On hardware, these capabilities are further constrained by finite sampling, hardware noise, measurement backaction, and the cost of estimating observables, so a large state space alone does not guarantee useful computation. In this survey, we develop a common system model that connects these components and use it to organize QRC foundations, computational properties, reservoir architectures, operating protocols, and physical implementations. We examine spin, photonic, superconducting, bosonic, neutral atom, and other analog platforms, together with applications, software and high performance computing support, benchmarking, and reproducibility. The analysis distinguishes hardware demonstrations from simulations and identifies the assumptions and resources that govern comparisons across implementations. Current results do not establish a broad quantum advantage over well matched classical reservoirs. We therefore specify the resource accounting, benchmark standards, and theoretical criteria needed to evaluate claims of quantum advantage.

Quantum machine learning models define probabilistic input--output maps through coherent quantum evolution and measurement. While such models can exhibit computational advantages, their internal functioning and decision making generally resists interpretation in terms of stochastic trajectories through intermediate configurations. In contrast to classical (Markovian) stochastic processes, quantum dynamics generically violates the Chapman--Kolmogorov divisibility condition, preventing a decomposition into probabilistically meaningful intermediate transitions. We develop a probabilistic framework for representing quantum learning models as stochastic processes over configuration spaces where the dynamics are modeled as linear maps on probability distributions. Starting from a fixed POVM, arbitrary quantum channels induce transition kernels on the associated probability representation. For informationally complete POVMs, and in particular SIC-POVMs, these kernels are Markovian but generally quasi-stochastic, with non-classicality appearing as negativity. By contrast, projective spaces admit positive stochastic kernels but generally require non-Markovian dynamics due to the failure of Chapman--Kolmogorov divisibility. This yields a trade-off between negativity and dependence on past configurations, i.e. quantum dynamics can be represented either by Markovian quasi-stochastic maps or by positive stochastic processes with higher Markov order. We discuss how such representations of quantum dynamics can be interpreted as stochastic walks through a memory space in the spirit of Projective Simulation, a model of learning and agency in which decisions arise from random walks over an episodic memory network. We further outline how finite-order stochastic kernels can approximate such quantum deliberation processes and show in what regimes the classical machine learning model is recovered.

Quantum continual learning aims to train quantum models on sequential tasks without losing previously learned knowledge. However, variational quantum classifiers (VQCs) are prone to catastrophic forgetting under nonstationary task distributions. We propose quantum elastic weight consolidation (QEWC), a quantum Fisher information (QFI)-informed regularization method for mitigating forgetting. Unlike conventional elastic weight consolidation based on classical Fisher information (CFI), which measures parameter importance through measurement-dependent output statistics, QEWC uses QFI to quantify the intrinsic sensitivity of the parameterized quantum state. This gives an information-geometric view in which important parameters are identified by the local response of the quantum state manifold. We evaluate QEWC on VQCs trained on sequential binary classification tasks, including classical image-classification and quantum phase-classification tasks. Simulations show that sequential training without regularization causes severe forgetting, while both CFI-based EWC and QFI-based QEWC improve retention of previous tasks. Mechanistic analyses further show that the two methods impose different regularization geometries: CFI acts selectively on measurement-sensitive directions, whereas QFI imposes a denser state-geometric constraint over parameter space. Under depolarizing noise, CFI values are strongly suppressed by degraded measurement statistics, while QFI preserves a more stable sensitivity structure of the noisy parameterized quantum state. These results establish QEWC as a physically motivated approach for studying and mitigating forgetting in quantum continual learning through quantum-state geometry.

Quantum machine learning ideas are typically absent from traditional machine learning curricula and are instead introduced in upper-level courses on quantum information processing and quantum computing. We propose a route for bringing quantum ideas into the standard machine learning classroom directly after the introduction of binary linear classifiers. Specifically, we develop a pedagogical bridge between linear classifiers and single-qubit mixed-state classifiers by characterizing their geometric model structure. This characterization reveals that a single-qubit mixed-state model for binary classification can be viewed as the ``ellipsoidal version'' of a standard linear classifier: rather than learning a hyperplane that separates data, the model learns a hyperellipsoid.. We present this connection as an accessible bridge from familiar classical machine learning concepts to quantum machine learning, and encourage instructors to use it as a natural entry point for introducing quantum ideas in the undergraduate machine learning classroom.

Many datasets encountered across a wide range of domains possess rich geometric and topological structure that is difficult to capture using conventional vector-based representations. Quantum machine learning offers the possibility of processing high-dimensional data in Hilbert spaces, but its practical success depends critically on how classical data is encoded into quantum states. We introduce quantum topological data encoding (QTDE), a general framework for encoding topological information into quantum states via topology-driven quantum evolution. Our method generalises an existing topology-driven quantum encoding framework to higher-dimensional data. We test the proposed method on clique-complexes classification tasks, and provide preliminary evidence that topology-driven quantum representations can capture discriminative information beyond that available through direct comparisons of classical topological descriptors. The proposed quantum representations consistently outperform a baseline based on direct comparisons of the combinatorial Laplacians describing the underlying topological structure. We indicate several areas of application where the framework can be used to provide a more efficient and reliable data representation.

Most multimodal learning methods improve how heterogeneous representations are aligned and fused, while post-fusion enhancement remains less explored. We propose Parallel Quantum Feature Augmentation (PQFA), a hybrid quantum-classical framework that applies multiple shallow variational quantum circuits to fused multimodal features. Text and image representations extracted by frozen RoBERTa and ViT encoders are processed through bidirectional cross-attention, attentive pooling, and adaptive gated fusion. The fused feature is then amplitude-encoded into parallel quantum circuits, whose measurement readouts are concatenated with the classical representation for prediction. We evaluate PQFA on MM-IMDb and N24News through controlled comparisons using the same encoders, fusion backbone, data splits, projection dimension, and augmentation output width. PQFA consistently outperforms both the fusion backbone without quantum augmentation and a width-matched MLP augmentation baseline, while using approximately 2.2K augmentation parameters compared with 24.0K for the MLP branch. Missing-modality experiments further show improved robustness when textual or visual inputs are incomplete, with particularly clear gains when the more informative textual modality is severely degraded. Controlled ablations and feature-space analyses indicate that the improvement cannot be reproduced by random feature mappings, increased classical width, or untrained quantum transformations. Quantum-state diagnostics additionally show stable predictive performance across the tested simulated noise levels and distinct branch-specific transformations of the encoded states. These results establish PQFA as an effective and parameter-efficient strategy for post-fusion augmentation in hybrid quantum-classical multimodal learning.

Large-scale Vision-Language Models have demonstrated impressive transfer learning capabilities across a wide range of tasks. For few-shot classification, we observe that VLMs exhibit a notable ability to filter candidate categories and thus achieve high Top-K accuracy. However, they often struggle with fine-grained discrimination among visually similar categories, resulting in unsatisfactory Top-1 performance, as shown in Figure 1. Existing studies on VLM adapters generally focus on global alignment between visual and textual representations in the feature space, but fail to exploit semantically similar categories to refine fine-grained visual representations. Based on these observations, we propose a novel coarse-to-fine VLM fine-tuning approach for few-shot learning that leverages quantum computation, termed the Multi-Modal Quantum Adapter (MQAdapter). Specifically, MQAdapter first retrieves the Top-K category candidates most similar to the input image and uses them as semantic anchors. It then employs a cross-modal quantum learning mechanism to refine visual features under the guidance of these anchors. The core of this mechanism is the encoding of visual and textual features into quantum states. By leveraging quantum entanglement and superposition in a high-dimensional Hilbert space, MQAdapter effectively models higher-order cross-modal interactions, producing more discriminative representations than traditional Euclidean adapters. MQAdapter is parameter-efficient and can be integrated with various existing fine-tuning algorithms to achieve further performance gains. Evaluations on 15 datasets demonstrate the effectiveness of MQAdapter while requiring fewer trainable parameters.

Quantitative Structure-Activity Relationship ($\mathtt{QSAR}$) modeling is a foundational computational methodology in early-stage drug discovery, heavily relied upon for predicting compound toxicity, bioavailability, and therapeutic potential. However, classical methods often struggle to effectively map the highly complex, non-linear, and high-dimensional interactions inherent in molecular data, leading to reduced predictive accuracy and costly late-stage clinical failures. In this paper, we present a Quantum Multiple Kernel Learning ($\mathtt{QMKL}$) framework, dubbed Next-Gen $\mathtt{Q^2SAR}$, that leverages Quantum Support Vector Machines ($\mathtt{QSVMs}$) to overcome these classical limitations. By encoding molecular descriptors into exponentially large quantum Hilbert spaces, our approach substantially enhances the expressiveness of non-linear modeling. Benchmarking our quantum-enhanced framework on a dataset targeting the $\mathtt{DYRK1A}$ kinase (a critical target for Alzheimer's disease), the $\mathtt{QMKL}$-$\mathtt{SVM}$ achieves an impressive Area Under the Curve ($\mathtt{AUC}$) score of $0.8750$, significantly outperforming classical state-of-the-art Gradient Boosting models ($\mathtt{AUC} = 0.8037$). Furthermore, we establish a theoretical and empirical pathway toward resolving classical data bottlenecks through projected quantum kernels ($\mathtt{PQK}$) and measurement accelerators. As quantum computing architecture matures, this framework paves the way for autonomous cognitive architectures and self-improving drug discovery pipelines, promising to unlock deeper insights across vast chemical spaces and to accelerate the development of life-saving therapeutics.

Adversarial perturbations threaten machine learning classifiers, including variational quantum classifiers. We show that finite quantum measurement statistics (shot noise) act as a built-in defense against gradient-based test-time attacks whose cost scales unfavorably for the attacker. Because every gradient component must be inferred from repeated circuit executions under any unbiased gradient-estimation rule, white-box extraction consumes a dimension-dependent measurement budget that measurement grouping cannot remove in expressive circuits. Under stated assumptions, single-step attacks need at least quadratically many shots in the input dimension $d$, growing as $d^{5/2}$ under norm-concentration scaling, with a sufficient-budget analysis for iterative attacks via stochastic gradient Langevin dynamics. Simulations up to 784 input dimensions validate the law: the realized total budget is the $d^{5/2}$ geometric floor for plateau-mitigated models and grows as $d^{3.00}$ for the tested deep circuits, whose gradient norms decay with dimension absent barren-plateau mitigation; folding the measured gradient norm back in recovers the parameter-free $d^{3/2}$ shot-noise geometry. Against a matched classical baseline whose attack overhead is dimension-independent (the cheap-gradient principle of automatic differentiation), the quantum gradient cost ratio grows empirically as $d^{3.00}$, so the attacker's relative cost diverges as the model scales. Experiments on a 156-qubit IBM processor (ibm_boston, 4-qubit circuits, $d=12$) reproduce the effect: at matched budgets the device attack tracks the ideal within a few percent, with the high-shot gradient faithful to the exact one. The defense operates precisely when the forward map is classically hard to simulate: only then is a white-box attacker denied the simulate-and-backpropagate shortcut and must pay the measurement cost we quantify.

Data re-uploading parameterized quantum circuits (DRU-PQCs) are universal function approximators, yet their expressivity produces oscillatory, non-convex loss landscapes that resist gradient-based optimization. We show that the primary optimization bottleneck in DRU-PQCs is not insufficient capacity but a structural failure mode we term Fourier locking (FL): because encoding weights and entangling layers are nonlinearly coupled, random initialization on high-frequency targets collapses the encoding parameters into spurious local minima. Two Fisher diagnostics characterize FL. The input-space quantum Fisher information $F_x$ measures the effective frequency content of the encoded state; the Fisher discriminant ratio of the measured features measures their alignment with the class labels. In two independent 50-seed experiments, the locking is literal: trapped circuits hold $F_x$ frozen for the entire run, while escaping circuits migrate their frequency content (direct training: $r_{pb} = -0.48$; curriculum: $d = 1.34$; both $p < 0.001$). The replicated signature is this spectral mobility, not any endpoint value of $F_x$, and trapped circuits retain a fully non-degenerate parameter-space QFIM ($r_{pb} \approx 0$): the failure is spectral misalignment of a responsive state, not a loss of geometric sensitivity. A frequency-staged homotopy protocol that paces the target frequency ($f: 1.0 \to 3.0$) convexifies the early loss landscape; escaping circuits raise $F_x$ in step with the curriculum, and the escape rate triples (18% vs. 6%). Fourier locking is a frequency-alignment problem, and its remedy is frequency pacing.

Can a small quantum computer forecast a changing signal better than an ordinary classical method? Many studies say yes, but the classical methods they compare against are often left in a basic, untuned state while the quantum model is carefully optimised. We ask what happens when the classical competitor is given exactly the same care: the same size and the same amount of tuning effort. We study two popular reasons a quantum reservoir is thought to help, using exact simulations of small quantum systems (up to eleven qubits) on prediction tasks. In both cases the quantum advantage disappears once the comparison is fair. In the first, extra quantum measurements add nothing that a simple classical formula of the same size does not already provide. In the second, a feedback loop genuinely helps the quantum model, turning a useless setup into a working predictor, yet a well-tuned classical network still predicts slightly more accurately, and the gap is statistically reliable. Our point is not that quantum reservoirs can never win, but that two of their commonly cited advantages do not hold up against fair classical competitors at this scale. We provide these matched comparisons as a simple, reusable checklist for honest benchmarking. All results are fully reproducible from fixed random seeds.

Data scarcity and class imbalance are persistent challenges in machine learning that degrade model generalization and introduce predictive bias. We present a hybrid quantum-classical framework for synthetic data generation using a Quantum Circuit Born Machine (QCBM) to address these limitations. The proposed approach exploits quantum mechanical properties -- superposition and entanglement -- within a parameterized variational quantum circuit to model complex probability distributions that are difficult for classical generative methods to capture. Experiments are conducted on two tabular benchmark datasets: the Iris dataset and the Telco Customer Churn dataset. Preprocessing includes normalization and PCA-based dimensionality reduction to enable efficient basis encoding for quantum circuits. The QCBM is trained by minimizing Kullback-Leibler (KL) divergence between real and generated data distributions using a gradient-based parameter-shift optimization rule. Augmenting training data with QCBM-generated synthetic samples at 40-50% of the minority class improves F1-score by approximately 5-15% and minority-class recall by 10-25%. Cross-domain evaluations (Train on Synthetic, Test on Real; and Train on Real, Test on Synthetic) reveal a performance gap of only 3-10%, indicating strong distributional fidelity. Comparative analysis against classical oversampling methods -- SMOTE, Borderline-SMOTE, KMeansSMOTE, and SVM-SMOTE -- shows that QCBM achieves competitive classification performance and produces lower Maximum Mean Discrepancy (MMD) on the Telco dataset, suggesting superior structural similarity in certain imbalanced settings. These findings establish QCBM as a viable complementary tool for data augmentation, particularly for low-dimensional structured tabular data with class imbalance.

Privacy-preserving clustering is critical for analyzing sensitive data in healthcare, cybersecurity, and enterprise applications, where maintaining data confidentiality must be balanced with analytical performance. This paper presents Equivariant Quantum Clustering (EQC), a parameter-efficient framework that integrates symmetry-aware quantum circuits with differential privacy to improve the privacy-utility tradeoff. EQC employs p4m equivariant parameter sharing to reduce circuit complexity while preserving informative feature representations. The framework is evaluated on three privacy-sensitive datasets: NSL-KDD, CERT Insider Threat v6.2, and a synthetic MIMIC-III clinical dataset. On the NSL-KDD benchmark, EQC achieves 79.3% clustering accuracy while reducing membership inference attack success to 38.3% under a privacy budget of ε = 1.0 and δ = 10^-5, outperforming representative classical and quantum baselines. Ablation studies indicate that the performance gains primarily arise from parameter-efficient circuit design combined with differential privacy. The results demonstrate that EQC provides a practical quantum-ready framework for secure and privacy-preserving clustering across heterogeneous sensitive datasets.

Nonlinear dynamics is ubiquitous in nature, ranging from chemical pattern formation to ocean circulation, yet its simulation on quantum computers is fundamentally limited by the unitary nature of quantum evolution. We propose the quantum Koopman method, a data-driven framework that embeds nonlinear dynamics into a learned linear representation and implements the resulting evolution using shallow quantum circuits. This method learns Koopman observables from trajectory data, projects the lifted dynamics onto a finite-dimensional subspace, and decomposes the corresponding non-unitary propagator into parallel spectral channels. We utilize the Koopman method on a superconducting processor to simulate three distinct nonlinear systems, comprising reaction-diffusion dynamics, fluid motion on a sphere, and satellite-derived observations of Gulf Stream currents, employing up to 32 parallel circuits of 10 qubits. These quantum simulations capture the dominant multiscale patterns and statistical signatures of the underlying dynamics, and reveal a transition from performance limited by hardware noise in weakly nonlinear systems to performance limited by finite-dimensional Koopman representations as nonlinear scale interactions increase. This transition identifies a practical boundary for quantum-amenable nonlinear dynamics, establishing a hardware-validated route for simulating moderately nonlinear dynamics on near-term quantum hardware.

Quantum diffusion models provide a physics-consistent route to generative learning by formulating noising and denoising directly on quantum states. However, applying such models to classical high-dimensional data is constrained by the qubit cost of state encoding and the computational burden of simulating large density operators. We propose a scalable hybrid generative pipeline that combines a classical autoencoder for dimensionality reduction with a mixed-state quantum denoising diffusion probabilistic model (MSQuDDPM) operating in the learned latent space. The autoencoder compresses data into compact latent codes that can be embedded into a small-qubit Hilbert space, after which the quantum diffusion model learns a generative distribution over latent density operators and decodes samples back to the original domain. Algorithmically, we simplify the reverse dynamics by predicting an estimate of the clean state $ρ_0$ at timestep $t$ and computing the one-step reverse update via an analytic backward propagation rule, rather than learning an explicit predictor for $ρ_{t-1}$. We demonstrate the proposed approach on MNIST image generation and discuss how mixed-state quantum diffusion can serve as a practical backbone for hybrid quantum--classical generative modeling under realistic qubit budgets.

Given that quantum computers are naturally suited to simulate the behavior of quantum many-body systems, an immediate question arises: can one formulate physically motivated quantum machine learning (QML) tasks that exhibit learning separations? We address this problem by studying the learnability of quantum many-body dynamics from the perspective of probably approximately correct (PAC)-learning. Concretely, we devise a supervised learning problem where the training set consists of specifications of randomized stabilizer probe states, evolution times sampled uniformly from a polynomially large time interval $[0,T]$, coupled with expectation values of certain observables evaluated on the resulting time-evolved state under an unknown Hamiltonian. For this learning task, we provide an efficient quantum procedure whose training phase learns the underlying Hamiltonian from short-time training samples, and whose deployment phase combines Hamiltonian simulation with the classical shadows protocol to perform inference on a newly given data point. By contrast, the existence of $O(\mathsf{poly}(n))$-time instances ensures classical hardness: by embedding a $\mathsf{BQP}$-complete computation into the polynomially long time-dynamics of a low-intersection variant of the Feynman-Kitaev clock Hamiltonian construction, we show that, for a certain family of input distributions, no randomized classical polynomial-time algorithm can fulfill our learning condition, unless $\mathsf{BQP}\subseteq\mathsf{P/poly}$. Furthermore, we show that the classically hard instance maintains quantum learnability. We also give an interpretation of our results in learning-assisted certified quantum simulation. Taken together, our results demonstrate a rigorous learning separation for a natural ML task based on Hamiltonian evolution, while building connections between quantum learning theory, quantum simulation, and QML.

Parameterized quantum circuits (PQCs) are increasingly used as policies and value functions in quantum reinforcement learning, yet it remains unclear when and why quantum policies generalize. We give a PAC-Bayesian account in which generalization is governed not by the raw number of circuit parameters, but by the effective dimension of the Fisher geometry induced by the circuit. This quantity is inflated by entanglement, making entangling connectivity an independent axis of complexity.In controlled experiments that fix the number of trainable rotations and vary only entanglement, we find that circuits with larger Fisher effective dimension exhibit larger train-test gaps, while parameter count is a weak predictor. The resulting bound acts primarily as a ranking certificate: it correctly orders circuits with identical parameter count, which parameter-counting bounds cannot do. We validate this mechanism across supervised classification, quantum contextual bandits, and value-function generalization, where entangled circuits consistently generalize worse than non-entangled circuits of equal parameter count, with gaps shrinking as sample size increases.Our strongest evidence comes from low-variance decision models, including single-observable classifiers, value heads, and one-step policies. In end-to-end multi-step policy learning, entanglement effects remain statistically significant but high return variance leaves the full ordering only partially resolved. Partial-correlation analysis shows that Fisher effective dimension screens off entangling pattern, and controls for training accuracy, readout, and optimizer rule out major optimization confounders. The effect also persists on an IBM Heron quantum processor under real noise. Overall, our results reframe quantum policy design around an entanglement--generalization trade-off rather than expressivity alone.

Quantum convolutional neural networks (QCNNs) combine the power of quantum computing and classical CNN for computational speedup in classification tasks. However, noise levels on state-of-the-art quantum devices remain too high for practical QCNN execution. In addition, despite the reliable surface code providing a method for error rates below a threshold value, they have a prohibitively large qubit cost. Recently introduced bivariate bicycle (BB) codes are of particular interest for their high error threshold, constant encoding rate, and linear code distance. Through simulation with realistic hardware noise sources, we demonstrate that a 4-qubit unprotected QCNN fails to converge and exhibits a worse learning rate compared to numerical simulations. Addressing both limitations, we propose a distance-4 BB quantum error-correction (QEC) technique for QCNNs. In doing so, we validate that our low-overhead QEC technique for QCNNS represents a step toward practical QCNNs.

Canonical quantization provides a systematic procedure for constructing quantum models from classical Hamiltonians. Here, we apply this principle to a fundamental computational primitive of machine learning: the neuron. Specifically, by viewing a neuron as a composition of an energy function and an activation function, we quantize this model by replacing the energy function with a quantum Hamiltonian and applying the activation function to it through matrix functional calculus. This results in an activation observable that can be measured on an input quantum state. We investigate the use of these quantized neurons for function approximation, where the objective is to learn an unknown observable from labeled quantum data. For this purpose, we develop hybrid quantum-classical algorithms for training and evaluation, including procedures for measuring the activation observable and estimating gradients of the squared loss error. Our algorithms for gradient estimation rely on basic primitives like classical random sampling, the Hadamard test, and Hamiltonian simulation, and those for measuring an activation observable rely on quantum algorithms known as the power of one qumode and Schroedingerization. Numerical experiments demonstrate that our quantized neurons exhibit enhanced expressive capabilities relative to corresponding classical neurons on representative learning tasks. Our work establishes canonical quantization as a principled framework for constructing quantum machine learning primitives and provides a foundation for developing neural architectures tailored to quantum data.

The geometric and topological structure of quantum cost landscapes (QCLs) governs the optimization and thus the predictive power of variational quantum algorithms (VQAs). We systematically analyze ravines - low-cost paths connecting local minima - using an adapted version of the nudged elastic band (NEB) algorithm, a method originating from theoretical chemistry. By training quantum neural networks (QNNs) to classify the concentratable entanglement of quantum states, we apply the NEB algorithm and numerically identify ravine structures in QCLs of hardware-efficient ansatzes. Beyond visualizing these ravines, we construct an ensemble prediction framework by averaging predictions from QNNs parameterized along the low-cost NEB path. We introduce a resource-light pre-training metric which quantifies local-prediction variability and serves as a strong performance indicator for VQAs, even beyond the scope of this study. When base classifiers are drawn from circuit and weight initializations exhibiting high local-prediction variability, the quantum-based NEB ensembles outperform both classical and naive quantum alternatives. Moreover, a complexity analysis shows that leveraging the ravine-like structure of QCLs with the QNN NEB approach substantially reduces computational costs compared to naive QNN ensembling. A depth and qubit scaling analysis indicates that ravines persist across both scalings, and that, despite the expected growth in resource requirements with the qubit scaling, the NEB approach also accelerates convergence over the naive alternative.

Quantum computing has emerged as a promising computational paradigm for machine learning (ML), with the potential to offer computational advantages over classical approaches. At this stage, the evidence supporting the performance and advantages of quantum machine learning (QML) models relative to classical models is insufficient. To address this gap, this paper presents an empirical study on the performance of QML models and their classical counterparts. We compare seven model pairs spanning supervised learning and reinforcement learning. Our results indicate that the evaluated quantum machine learning models do not yet surpass the classical baselines in overall prediction performance, policy stability, or training time. Nevertheless, QML remains a promising approach for filtering noise and controlling false positives. Our research findings summarize the challenges facing quantum machine learning across hardware environments, training efficiency, and convergence stability, providing a foundation for research into the robustness and parameter optimization of QML. This work is publicly available at https://github.com/Z-537-437/QML.

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

The emergence of powerful deep generative models based on diffusion and flow matching has enabled the learning and modeling of complex distributions. Learning quantum distributions, however, remains challenging due to the inherent difficulty of accurately modeling the meaningful physical properties of quantum states. We propose Quantum Flow Matching (QFM), a novel generative model designed to learn quantum distribution by utilizing spin Wigner function and flow matching. By converting density matrix into the spin Wigner function and leveraging functional flow matching to learn distributions in function space, QFM enables accurate and effective learning of multi-qubit quantum distributions. We demonstrate the effectiveness of our method by evaluating physical quantities such as trace, purity, and entanglement entropy of the generated quantum states, accurately capturing the underlying physics of the given quantum distributions.