Quantum Machine Learning

Also known as QML

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Quantum machine learning studies how quantum states, measurements, and computation can support learning from classical or quantum data for tasks such as prediction, generation, sensing, and decision-making. Common approaches include variational quantum circuits and hybrid neural networks, quantum kernels and Gaussian processes, generative models, and learning-theoretic tools such as classical shadows and PAC bounds. Researchers test these methods on image and time-series tasks, molecular prediction, quantum-state and many-body dynamics learning, and reinforcement learning, while addressing data encoding, measurement cost, noise, trainability, and generalization. Evidence remains mixed: particular structured or quantum-data problems may benefit, but broad computational advantage over carefully tuned classical methods is not established and depends on fair, resource-matched evaluation.

Latest papers

256 papers32 papers in the last four weeks, up 7% on the four weeks before. 0.2% of all new papers.

Mar 19, 2026

End-to-End QGAN-Based Image Synthesis via Neural Noise Encoding and Intensity Calibration

Quantum Generative Adversarial Networks (QGANs) offer a promising path for learning data distributions on near-term quantum devices. However, existing QGANs for image synthesis avoid direct full-image generation, relying on classical post-processing or patch-based methods. These approaches dilute the quantum generator's role and struggle to capture global image semantics. To address this, we propose ReQGAN, an end-to-end framework that synthesizes an entire N=2^D-pixel image using a single D-qubit quantum circuit. ReQGAN overcomes two fundamental bottlenecks hindering direct pixel generation: (1) the rigid classical-to-quantum noise interface and (2) the output mismatch between normalized quantum statistics and the desired pixel-intensity space. We introduce a learnable Neural Noise Encoder for adaptive state preparation and a differentiable Intensity Calibration module to map measurements to a stable, visually meaningful pixel domain. Experiments on MNIST and Fashion-MNIST demonstrate that ReQGAN achieves stable training and effective image synthesis under stringent qubit budgets, with ablation studies verifying the contribution of each component.

Xue Yang, Rigui Zhou, Shizheng Jia +5

Shanghai Maritime University · Agency for Science, Technology and Research · Singapore University of Technology and Design +1

Quantum Generative Modeling Image Generation Quantum Machine Learning Quantum State Preparation

Mar 17, 2026

Hybrid Classical-Quantum Transfer Learning with Noisy Quantum Circuits

Quantum transfer learning combines pretrained classical deep learning models with quantum circuits to reuse expressive feature representations while limiting the number of trainable parameters. In this work, we introduce a family of compact quantum transfer learning architectures that attach variational quantum classifiers to frozen convolutional backbones for image classification. We instantiate and evaluate several classical-quantum hybrid models implemented in PennyLane and Qiskit, and systematically compare them with a classical transfer-learning baseline across heterogeneous image datasets. To ensure a realistic assessment, we evaluate all approaches under both ideal simulation and noisy emulation using noise models calibrated from IBM quantum hardware specifications, as well as on real IBM quantum hardware. Experimental results show that the proposed quantum transfer learning architectures achieve competitive and, in several cases, superior accuracy while consistently reducing training time and energy consumption relative to the classical baseline. Among the evaluated approaches, PennyLane-based implementations provide the most favorable trade-off between accuracy and computational efficiency, suggesting that hybrid quantum transfer learning can offer practical benefits in realistic NISQ era settings when feature extraction remains classical.

D. Martín-Pérez, F. Rodríguez-Díaz, D. Gutiérrez-Avilés +2

Data Science and Big Data Lab, Pablo de Olavide University, Seville, Spain · Department of Computer Science, University of Seville, Seville, Spain

Quantum Machine Learning Hybrid Quantum-Classical ML Image Classification Variational Quantum Circuits

Mar 16, 2026

Photonic Quantum-Enhanced Knowledge Distillation

Photonic quantum processors naturally produce intrinsically stochastic measurement outcomes, offering a hardware-native source of structured randomness that can be exploited during machine-learning training. Here we introduce Photonic Quantum-Enhanced Knowledge Distillation (PQKD), a hybrid quantum photonic--classical framework in which a programmable photonic circuit generates a compact conditioning signal that constrains and guides a parameter-efficient student network during distillation from a high-capacity teacher. PQKD replaces fully trainable convolutional kernels with dictionary convolutions: each layer learns only a small set of shared spatial basis filters, while sample-dependent channel-mixing weights are derived from shot-limited photonic features and mapped through a fixed linear transform. Training alternates between standard gradient-based optimisation of the student and sampling-robust, gradient-free updates of photonic parameters, avoiding differentiation through photonic hardware. Across MNIST, Fashion-MNIST and CIFAR-10, PQKD traces a controllable compression--accuracy frontier, remaining close to teacher performance on simpler benchmarks under aggressive convolutional compression. Performance degrades predictably with finite sampling, consistent with shot-noise scaling, and exponential moving-average feature smoothing suppresses high-frequency shot-noise fluctuations, extending the practical operating regime at moderate shot budgets.

Kuan-Cheng Chen, Shang Yu, Chen-Yu Liu +10

Department of Electrical and Electronic Engineering, Imperial College London, South Kensington, London, SW7 2AZ, England, United Kingdom. · Imperial Centre for Quantum Engineering, Science and Technology, Imperial College London, South Kensington, London, SW7 2AZ, England, United Kingdom. · JIJ, Rutherford Appleton Laboratory, Harwell Campus, Didcot, OX11 0QX, United Kingdom. +9

Knowledge Distillation Quantum Machine Learning Hybrid Quantum-Classical ML Photonic Computing

Mar 15, 2026

IQP Born Machines under Data-dependent and Agnostic Initialization Strategies

Quantum circuit Born machines based on instantaneous quantum polynomial-time (IQP) circuits are natural candidates for quantum generative modeling, both because of their probabilistic structure and because IQP sampling is provably classically hard in certain regimes. Recent proposals focus on training IQP-QCBMs using Maximum Mean Discrepancy (MMD) losses built from low-body Pauli-

Z

correlators, but the effect of initialization on the resulting optimization landscape remains poorly understood. In this work, we address this by first proving that the MMD loss landscape suffers from barren plateaus for random full-angle-range initializations of IQP circuits. We then establish lower bounds on the loss variance for identity and an unbiased data-agnostic initialization. We then additionally consider a data-dependent initialization that is better aligned with the target distribution and, under suitable assumptions, yields provable gradients and generally converges quicker to a good minimum (as indicated by our training of circuits with 150 qubits on genomic data). Finally, as a by-product, the developed variance lower bound framework is applicable to a general class of non-linear losses, offering a broader toolset for analyzing warm-starts in quantum machine learning.

Sacha Lerch, Joseph Bowles, Ricard Puig +3

Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland · Centre for Quantum Science and Engineering, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland · Xanadu, Toronto, ON, M5G 2C8, Canada +3

Quantum Circuit Born Machines Quantum Machine Learning Quantum Generative Modeling Variational Quantum Circuits Barren Plateaus

Mar 13, 2026

Filtered Spectral Projection for Quantum Principal Component Analysis

Quantum principal component analysis (qPCA) is commonly formulated as the extraction of eigenvalues and eigenvectors of a covariance-encoded density operator. Yet in many qPCA settings the practical goal is simpler: projection onto the dominant spectral subspace. Here we introduce a projection-first framework, the Filtered Spectral Projection Algorithm (FSPA), which bypasses explicit eigenvalue estimation while preserving the relevant spectral structure. FSPA amplifies any nonzero warm-start overlap with the leading subspace and remains robust in small-gap and near-degenerate regimes, without artificial symmetry breaking in the absence of bias. We show that FSPA achieves an oracle complexity

\mathcal{O}((\log(1/ε)+\log(1/|a_1|^2))/\log(λ_1/λ_2))

,which is tight by a matching lower bound, establishing it as anoptimal projection primitive. We derive a convergence rate for degenerate spectra, give a circuit resource analysis with

n+\mathcal{O}(1)

qubit overhead independent of system dimension, and extend the method to threshold spectral projection, Threshold-FSPA, which converges in

\mathcal{O}(\log(1/ε))

calls when the threshold lies between eigenvalues. In the density matrix exponentiation access model, FSPA gives an exponential copy-complexity advantage over classical methods. For classical datasets, we show that for amplitude-encoded centered data the ensemble density matrix

ρ=\sum_i p_i|ψ_i\rangle\langleψ_i|

equals the covariance matrix. Numerical tests on chemistry density matrices, noisy circuit outputs, Breast Cancer Wisconsin, handwritten Digits, and 1--4-qubit scalability confirm the theory. A minimal Qiskit implementation validates magnitude invariance, signal amplification, and no spurious symmetry breaking. These results establish FSPA as an optimal and deployable quantum spectral projection primitive.

Sk Mujaffar Hossain, Satadeep Bhattacharjee

Indo-Korea Science and Technology Center (IKST), Bengaluru 560064, India

Principal Component Analysis Quantum Machine Learning Spectral Methods

Mar 13, 2026

Embedded Quantum Machine Learning in Embedded Systems: Feasibility, Hybrid Architectures, and Quantum Co-Processors

Embedded quantum machine learning (EQML) seeks to bring quantum machine learning (QML) capabilities to resource-constrained edge platforms such as IoT nodes, wearables, drones, and cyber-physical controllers. In 2026, EQML is technically feasible only in limited and highly experimental forms: (i) hybrid workflows where an embedded device performs sensing and classical processing while offloading a narrowly scoped quantum subroutine to a remote quantum processing unit (QPU) or nearby quantum appliance, and (ii) early-stage "embedded QPU" concepts in which a compact quantum co-processor is integrated with classical control hardware. A practical bridge is quantum-inspired machine learning and optimisation on classical embedded processors and FPGAs. This paper analyses feasibility from a circuits-and-systems perspective aligned with the academic community, formalises two implementation pathways, identifies the dominant barriers (latency, data encoding overhead, NISQ noise, tooling mismatch, and energy), and maps them to concrete engineering directions in interface design, control electronics, power management, verification, and security. We also argue that responsible deployment requires adversarial evaluation and governance practices that are increasingly necessary for edge AI systems.

Somdip Dey, Syed Muhammad Raza

School of Engineering and Computing, Regent College London, London, United Kingdom

Quantum Machine Learning Hybrid Quantum-Classical ML Edge ML

Mar 11, 2026

Quantum entanglement provides a competitive advantage in adversarial games

Whether uniquely quantum resources confer advantages in fully classical, competitive environments remains an open question. Competitive zero-sum reinforcement learning is particularly challenging, as success requires modelling dynamic interactions between opposing agents rather than static state-action mappings. Here, we conduct a controlled study isolating the role of quantum entanglement in a quantum-classical hybrid agent trained on Pong, a competitive Markov game. An 8-qubit parameterised quantum circuit serves as a feature extractor within a proximal policy optimisation framework, allowing direct comparison between separable circuits and architectures incorporating fixed (CZ) or trainable (IsingZZ) entangling gates. Entangled circuits consistently outperform separable counterparts with comparable parameter counts and, in low-capacity regimes, match or exceed classical multilayer perceptron baselines. Representation similarity analysis further shows that entangled circuits learn structurally distinct features, consistent with improved modelling of interacting state variables. These findings establish entanglement as a function resource for representation learning in competitive reinforcement learning.

Peiyong Wang, Kieran Hymas, James Quach

Technology, CSIRO Clayton, Research Way, Clayton, VIC 3168, Australia.

Quantum RL Quantum Machine Learning Representation Learning for RL Quantum Neural Networks Multi-Agent Reinforcement Learning Hybrid Quantum-Classical ML

Mar 10, 2026

Learning from Radio using Variational Quantum RF Sensing

In modern wireless networks, radio channels serve a dual role. Whilst their primary function is to carry bits of information from a transmitter to a receiver, the intrinsic sensitivity of transmitted signals to the physical structure of the environment makes the channel a powerful source of knowledge about the world. In this paper, we consider an agent that learns about its environment using a quantum sensing probe, optimised using a quantum circuit, which interacts with the radio-frequency (RF) electromagnetic field. We use data obtained from a ray-tracer to train the quantum circuit and learning model and we provide extensive experiments under realistic conditions on a localisation task. We show that using quantum sensors to learn from radio signals can enable intelligent systems that require no channel measurements at deployment, remain sensitive to weak and obstructed RF signals, and can learn about the world despite operating with strictly less information than classical baselines.

Ivana Nikoloska

Signal Processing Systems Group, Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, 5612 AP, The Netherlands

Wireless Localization Remote Sensing Quantum Machine Learning

Mar 10, 2026

A Hybrid Quantum Circuit Born Machine Framework for Financial Volatility Forecasting: Quantum-Assisted Training and Classical Inference

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.

Yixiong Chen

Quantitative Finance Quantum Machine Learning Hybrid Quantum-Classical ML Quantum Circuit Born Machines Financial Time Series

Mar 10, 2026

Noise Models Impacts and Mitigation Strategies in Photonic Quantum Machine Learning

Photonic Quantum Machine Learning (PQML) is an emerging method to implement scalable, energy-efficient quantum information processing by combining photonic quantum computing technologies with machine learning techniques. The features of photonic technologies offer several benefits: room-temperature operation; fast (low delay) processing of signals; and the possibility of representing computations in high-dimensional (Hilbert) spaces. This makes photonic technologies a good candidate for the near-term development of quantum devices. However, noise is still a major limiting factor for the performance, reliability, and scalability of PQML implementations. This review provides a detailed and systematic analysis of the sources of noise that will affect PQML implementations. We will present an overview of the principal photonic quantum computer designs and summarize the many different types of quantum machine learning algorithms that have been successfully implemented using photonic quantum computer architectures such as variational quantum circuits, quantum neural networks, and quantum support vector machines. We identify and categorize the primary sources of noise within photonic quantum systems and how these sources of noise behave algorithm-specifically with respect to degrading the accuracy of learning, unstable training, and slower convergence than expected. Additionally, we review traditional and advanced techniques for characterizing noise and provide an extensive survey of strategies for mitigating the effects of noise on learning performance. Finally, we discuss recent advances that demonstrate PQML's capability to operate in real-world settings with realistic noise conditions and future obstacles that will challenge the use of PQML as an effective quantum processing platform.

A. M. A. S. D. Alagiyawanna, Asoka Karunananda

Department of Computational Mathematics, University of Moratuwa, Sri Lanka

Quantum Machine Learning Photonic Computing Quantum Error Mitigation

Mar 10, 2026

Mitigating Frequency Learning Bias in Quantum Models via Multi-Stage Residual Learning

Quantum machine learning models based on parameterized circuits can be viewed as Fourier series approximators. However, they often struggle to learn functions with multiple frequency components, particularly high-frequency or non-dominant ones; a phenomenon we term the quantum Fourier parameterization bias. Inspired by recent advances in classical Fourier neural operators (FNOs), we adapt the multi-stage residual learning idea to the quantum domain, iteratively training additional quantum modules on the residuals of previous stages. We evaluate our method on a synthetic benchmark composed of spatially localized frequency components with diverse envelope shapes (Gaussian, Lorentzian, triangular). Systematic experiments show that the number of qubits, the encoding scheme, and residual learning are all crucial for resolving multiple frequencies; residual learning alone can improve test MSE significantly over a single-stage baseline trained for the same total number of epochs. Our work provides a practical framework for enhancing the spectral expressivity of quantum models and offers new insights into their frequency-learning behavior.

Ammar Daskin

Department of Computer Engineering, Istanbul Medeniyet University, Istanbul, Turkiye, 34000

Quantum Machine Learning Quantum Neural Networks Residual Learning

Mar 4, 2026

Fermi-Dirac thermal measurements: A framework for quantum hypothesis testing and semidefinite optimization

Quantum measurements are the means by which we recover messages encoded into quantum states. They are at the forefront of quantum hypothesis testing, wherein the goal is to perform an optimal measurement for arriving at a correct conclusion. Mathematically, a measurement operator is Hermitian with eigenvalues in [0,1]. By noticing that this constraint on each eigenvalue is the same as that imposed on fermions by the Pauli exclusion principle, we interpret every eigenmode of a measurement operator as an independent effective fermionic mode. Under this perspective, various objective functions in quantum hypothesis testing can be viewed as the total expected energy associated with these fermionic occupation numbers. By instead fixing a temperature and minimizing the total expected fermionic free energy, we find that optimal measurements for these modified objective functions are Fermi-Dirac thermal measurements, wherein their eigenvalues are specified by Fermi-Dirac distributions. In the low-temperature limit, their performance closely approximates that of optimal measurements for quantum hypothesis testing, and we show that their parameters can be learned by classical or hybrid quantum-classical optimization algorithms. This leads to a new quantum machine-learning model, termed Fermi-Dirac machines, consisting of parameterized Fermi-Dirac thermal measurements-an alternative to quantum Boltzmann machines based on thermal states. Beyond hypothesis testing, we show how general semidefinite optimization problems can be solved using this approach, leading to a novel paradigm for semidefinite optimization on quantum computers, in which the goal is to implement thermal measurements rather than prepare thermal states. Finally, we propose quantum algorithms for implementing Fermi-Dirac thermal measurements, and we also propose second-order hybrid quantum-classical optimization algorithms.

Nana Liu, Mark M. Wilde

Institute of Natural Sciences, School of Mathematical Sciences, Ministry of Education Key Laboratory in Scientific and Engineering Computing, and Global College, Shanghai Jiao Tong University, Shanghai 200240, China · School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14850, USA

Quantum Machine Learning Semidefinite Programming Hybrid Quantum-Classical ML

Mar 3, 2026

From Reachability to Learnability: Geometric Design Principles for Quantum Neural Networks

Classical deep networks are effective because depth enables adaptive geometric deformation of data representations. In quantum neural networks (QNNs), however, depth or state reachability alone does not guarantee this feature-learning capability. We study this question in the pure-state setting by viewing encoded data as an embedded manifold in

\mathbb{C}P^{2^n-1}

and analysing infinitesimal unitary actions through Lie-algebra directions. We introduce Classical-to-Lie-algebra (CLA) maps and the criterion of almost Complete Local Selectivity (aCLS), which combines directional completeness with data-dependent local selectivity. Within this framework, we show that data-independent trainable unitaries are complete but non-selective, i.e. learnable rigid reorientations, whereas pure data encodings are selective but non-tunable, i.e. fixed deformations. Hence, geometric flexibility requires a non-trivial joint dependence on data and trainable weights. We further show that accessing high-dimensional deformations of many-qubit state manifolds requires parametrised entangling directions; fixed entanglers such as CNOT alone do not provide adaptive geometric control. Numerical examples validate that aCLS-satisfying data re-uploading models outperform non-tunable schemes while requiring only a quarter of the gate operations. Thus, the resulting picture reframes QNN design from state reachability to controllable geometry of hidden quantum representations.

Vishal S. Ngairangbam, Michael Spannowsky

Institute for Particle Physics Phenomenology, Department of Physics Durham University, Durham DH1 3LE, United Kingdom · Institute for Theoretical Physics, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Str. 1, 76131 Karlsruhe, Germany

Quantum Neural Networks Quantum Machine Learning Quantum Feature Maps Quantum Circuit Trainability

Mar 1, 2026

Communication-Efficient Quantum Federated Learning over Large-Scale Wireless Networks

Quantum federated learning (QFL) combines the robust data processing of quantum computing with the privacy-preserving features of federated learning (FL). However, in large-scale wireless networks, optimizing sum-rate is crucial for unlocking the true potential of QFL, facilitating effective model sharing and aggregation as devices compete for limited bandwidth amid dynamic channel conditions and fluctuating power resources. This paper studies a novel sum-rate maximization problem within a muti-channel QFL framework, specifically designed for non-orthogonal multiple access (NOMA)-based large-scale wireless networks. We develop a sum-rate maximization problem by jointly considering quantum device's channel selection and transmit power. Our formulated problem is a non-convex, mixed-integer nonlinear programming (MINLP) challenge that remains non-deterministic polynomial time (NP)-hard even with specified channel selection parameters. The complexity of the problem motivates us to create an effective iterative optimization approach that utilizes the sophisticated quantum approximate optimization algorithm (QAOA) to derive high-quality approximate solutions. Additionally, our study presents the first theoretical exploration of QFL convergence properties under full device participation, rigorously analyzing real-world scenarios with nonconvex loss functions, diverse data distributions, and the effects of quantum shot noise. Extensive simulation results indicate that our multi-channel NOMA-based QFL framework enhances model training and convergence behavior, surpassing conventional algorithms in terms of accuracy and loss. Moreover, our quantum-centric joint optimization approach achieves more than a 100% increase in sum-rate while ensuring rapid convergence, significantly outperforming the state-of-the-arts.

Shaba Shaon, Christopher G. Brinton, Dinh C. Nguyen

ECE Department, The University of Alabama in Huntsville, Huntsville, AL 35899, USA · Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN, 47907, USA

Quantum Federated Learning Wireless Resource Allocation Wireless Communications Quantum Machine Learning

Feb 27, 2026

Scaling Quantum Machine Learning without Tricks: Full-Resolution and Diverse Image Generation

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.

Jonas Jäger, Florian J. Kiwit, Carlos A. Riofrío

BMW Group, Munich, Germany · Department of Computer Science and Institute of Applied Mathematics, University of British Columbia (UBC), Vancouver, Canada · Stewart Blusson Quantum Matter Institute (QMI), Vancouver, Canada +1

Quantum Generative Modeling Image Generation Quantum Machine Learning Variational Quantum Circuits Generative Adversarial Networks

Feb 27, 2026

Comparing Classical and Quantum Variational Classifiers on the XOR Problem

Quantum machine learning applies principles such as superposition and entanglement to data processing and optimization. Variational quantum models operate on qubits in high-dimensional Hilbert spaces and provide an alternative approach to model expressivity. We compare classical models and a variational quantum classifier on the XOR problem. Logistic regression, a one-hidden-layer multilayer perceptron, and a two-qubit variational quantum classifier with circuit depths 1 and 2 are evaluated on synthetic XOR datasets with varying Gaussian noise and sample sizes using accuracy and binary cross-entropy. Performance is determined primarily by model expressivity. Logistic regression and the depth-1 quantum circuit fail to represent XOR reliably, whereas the multilayer perceptron and the depth-2 quantum circuit achieve perfect test accuracy under representative conditions. Robustness analyses across noise levels, dataset sizes, and random seeds confirm that circuit depth is decisive for quantum performance on this task. Despite matching accuracy, the multilayer perceptron achieves lower binary cross-entropy and substantially shorter training time. Hardware execution preserves the global XOR structure but introduces structured deviations in the decision function. Overall, deeper variational quantum classifiers can match classical neural networks in accuracy on low-dimensional XOR benchmarks, but no clear empirical advantage in robustness or efficiency is observed in the examined settings.

Miras Seilkhan, Adilbek Taizhanov

Quantum Machine Learning Variational Quantum Circuits Binary Classification

Feb 27, 2026

Hybrid Quantum Temporal Convolutional Networks

Quantum machine learning models for sequential data face scalability challenges with complex multivariate signals. We introduce the Hybrid Quantum Temporal Convolutional Network (HQTCN), which combines classical temporal windowing with a quantum convolutional neural network core. By applying a shared quantum circuit across temporal windows, HQTCN captures long-range dependencies while achieving significant parameter reduction. Evaluated on synthetic NARMA sequences and high-dimensional EEG time-series, HQTCN performs competitively with classical baselines on univariate data and outperforms all baselines on multivariate tasks. The model demonstrates particular strength under data-limited conditions, maintaining high performance with substantially fewer parameters than conventional approaches. These results establish HQTCN as a parameter-efficient approach for multivariate time-series analysis.

Junghoon Justin Park, Maria Pak, Sebin Lee +4

Seoul National University Seoul, Korea · Wells Fargo New York, USA · Brookhaven National Laboratory New York, USA

Quantum Machine Learning Hybrid Quantum-Classical ML Quantum Convolutional Neural Networks

Feb 26, 2026

Quantum Deep Learning: A Comprehensive Review

Quantum deep learning (QDL) explores the use of both quantum and quantum-inspired resources to determine when deep learning's core capabilities, such as expressivity, generalization, and scalability, can be enhanced based on specific resource constraints. Distinct from broader quantum machine learning, QDL emphasizes compositional depth at the pipeline level and the integration of quantum or quantum-inspired components within end-to-end workflows. This review provides an operational definition of QDL and introduces a taxonomy comprising four primary paradigms: hybrid quantum-classical models, quantum deep neural networks, quantum algorithms for deep learning primitives, and quantum-inspired classical algorithms. Theoretical principles are connected to advanced architectures, software toolchains, and experimental demonstrations across superconducting, trapped-ion, photonic, semiconductor spin, and neutral-atom systems, as well as quantum annealers. Claims of quantum advantage are critically assessed by distinguishing provable complexity-theoretic separations from empirical observations. The analysis characterizes trade-offs between model expressivity, trainability, and classical simulability, while systematically detailing the bottlenecks imposed by optimization landscapes, input-output access models, and hardware constraints. Applications are surveyed in domains encompassing image classification, natural language processing, scientific discovery, quantum data processing, and quantum optimal control, underscoring fair benchmarking against optimized classical counterparts and a comprehensive assessment of resource requirements. This review serves as a tutorial entry point for graduate students while guiding readers to specialized literature. It concludes with a verification-aware roadmap to transition QDL from near-term demonstrations to scalable and fault-tolerant implementations.

Yanjun Ji, Zhao-Yun Chen, Marco Roth +10

Institute for Quantum Computing Analytics (PGI-12), Forschungszentrum Jülich, 52425 Jülich, Germany · Institute of Artificial Intelligence, Hefei Comprehensive National Science Center, Hefei, Anhui, 230088, P. R. China · Fraunhofer Institute for Manufacturing Engineering and Automation (IPA), Nobelstrasse 12, Stuttgart 70569, Germany +18

Quantum Machine Learning Quantum Neural Networks Hybrid Quantum-Classical ML Quantum-Inspired ML

Feb 26, 2026

Long Range Frequency Tuning for QML

Angle-encoded variational quantum circuits admit a truncated Fourier series representation of their output, but approximating functions with maximum frequency

ω_{\max}

using fixed unary encoding requires

\mathcal{O}(ω_{\max})

encoding gates. Trainable-frequency (TF) circuits promise a reduction by learning the data-encoding prefactors alongside the ansatz parameters, adapting the accessible frequency spectrum to the target during training. We identify a practical barrier that prevents this promise from being realized: the prefactor gradient is suppressed by the spectral gap between the circuit's accessible frequencies and the target spectrum, independently of the ansatz parameters, confining gradient-driven prefactor movement to a narrow neighborhood of initialization. We propose ternary grid initialization -- setting prefactors to

\{1, 3, 9, \ldots, 3^{k-1}\}

-- which ensures every target frequency within

[-ω_{\max}, ω_{\max}]

lies within

\tfrac{1}{2}

unit of the accessible spectrum at initialization, so that the spectral-gap bound no longer constrains the target-driven gradient to be small. This is a necessary condition for reliable convergence, whose sufficiency we establish empirically. On a synthetic benchmark with target frequencies shifted well beyond the standard initialization range, ternary initialization achieves median

R^2 = 0.997

versus

0.18

for unary initialization, with

100\%

of runs achieving

R^2 > 0.95

against

0\%

. CMA-ES with

20\times

the evaluation budget reaches only

25\%

success, confirming the limitation is a property of the optimization landscape rather than of gradient-based optimization specifically. Real-world validation on two benchmark datasets demonstrates consistent advantages over both fixed and trainable unary baselines.

Michael Poppel, Markus Baumann, Sebastian Wölckert +2

LMU Munich & Aqarios GmbH, Munich, Germany · LMU Munich, Munich, Germany

Quantum Machine Learning Variational Quantum Circuits Quantum Circuit Trainability Quantum Circuit Optimization

Feb 24, 2026

Deep Sequence Modeling with Quantum Dynamics: Language as a Wave Function

We introduce a sequence modeling framework in which the latent state is a complex-valued wave function evolving on a finite-dimensional Hilbert space under a learned, time-dependent Hamiltonian. Unlike standard recurrent architectures that rely on gating mechanisms to suppress competing hypotheses, our framework utilizes quantum interference: the Hamiltonian steers the phases of complex amplitudes so that conflicting interpretations cancel while compatible ones reinforce. The dynamics are strictly unitary, ensuring that the state norm is preserved exactly at every time step via a Cayley (Crank--Nicolson) discretization. Token probabilities are extracted using the Born rule, a quadratic measurement operator that couples magnitudes and relative phases. Our primary theoretical contribution is a separation theorem characterizing the representational advantage of this readout: we define a family of disambiguation tasks that a complex unitary model of dimension

N

solves exactly, but which requires a state dimension of

Ω(N^2)

for any real-valued orthogonal model equipped with a standard affine-softmax readout. This quadratic gap arises because the Born rule implicitly lifts the

N

-dimensional state into the space of rank-one Hermitian matrices, accessing pairwise phase correlations that are inaccessible to linear projections. Finally, we derive a continuity equation for the latent probability mass, yielding conserved pairwise currents that serve as a built-in diagnostic for tracing information flow between dimensions.

Ahmed Nebli, Hadi Saadatdoorabi, Kevin Yam

cAI Technology GmbH

Sequence Modeling Quantum-Inspired ML Language Modeling Quantum Machine Learning Quantum Neural Networks

Feb 22, 2026

Kaiwu-PyTorch-Plugin: Bridging Deep Learning and Photonic Quantum Computing for Energy-Based Models and Active Sample Selection

This paper introduces the Kaiwu-PyTorch-Plugin (KPP) to bridge Deep Learning and Photonic Quantum Computing across multiple dimensions. KPP integrates the Coherent Ising Machine into the PyTorch ecosystem, addressing classical inefficiencies in Energy-Based Models. The framework facilitates quantum integration in three key aspects: accelerating Boltzmann sampling, optimizing training data via Active Sampling, and constructing hybrid architectures like QBM-VAE and Q-Diffusion. Empirical results on single-cell and OpenWebText datasets demonstrate KPPs ability to achieve SOTA performance, validating a comprehensive quantum-classical paradigm.

Hongdong Zhu, Qi Gao, Yin Ma +6

Beijing QBoson Quantum Technology Co., Ltd. · Chinese Academy of Sciences

Hybrid Quantum-Classical ML Quantum Machine Learning Quantum Generative Modeling Energy-Based Models

Feb 20, 2026

Auto Quantum Machine Learning for Multisource Classification

With fault-tolerant quantum computing on the horizon, there is growing interest in applying quantum computational methods to data-intensive scientific fields like remote sensing. Quantum machine learning (QML) has already demonstrated potential for such demanding tasks. One area of particular focus is quantum data fusion -- a complex data analysis problem that has attracted significant recent attention. In this work, we introduce an automated QML (AQML) approach for addressing data fusion challenges. We evaluate how AQML-generated quantum circuits perform compared to classical multilayer perceptrons (MLPs) and manually designed QML models when processing multisource inputs. Furthermore, we apply our method to change detection using the multispectral ONERA dataset, achieving improved accuracy over previously reported QML-based change detection results.

Tomasz Rybotycki, Sebastian Dziura, Piotr Gawron

Center of Excellence in Artificial Intelligence, AGH University, al. Mickiewicza 30, 30-059 Cracow, Poland · Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, ul. Bartycka 18, 00-716 Warsaw, Poland · Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland

Quantum Machine Learning Classification Remote Sensing Change Detection

Feb 20, 2026

Theory and interpretability of Quantum Extreme Learning Machines: a Pauli-transfer matrix approach

Quantum reservoir computers (QRCs) have emerged as a promising approach to quantum machine learning, since they utilize the natural dynamics of quantum systems for data processing and are simple to train. Here, we consider

n

-qubit quantum extreme learning machines (QELMs) with initial-state encoding and continuous-time reservoir dynamics. We apply the Pauli transfer matrix (PTM) formalism to theoretically analyze the influence of encoding, reservoir dynamics, and measurement operations (including temporal multiplexing) on the QELM performance. This formalism reveals the complete set of (nonlinear) features generated by the encoding, and shows how the subsequent quantum channels linearly transform these Pauli features before they are probed by the chosen measurement operators. Optimizing such a QELM can therefore be cast as a decoding problem in which one shapes the channel-induced transformations such that task-relevant features become available to the regressor, effectively reversing the information scrambling of a unitary. Operator spreading under unitary evolution determines decodability of Pauli features, which underlies the nonlinear processing capacity of the reservoir. When paired with certain observables, structured Hamiltonians can reduce model expressivity, as reflected in a low readout rank. We trace this effect to Hamiltonian symmetries and derive asymptotic rank estimates for symmetry-resolved observable families. The PTM formalism yields a nonlinear vector (auto-)regression model as an interpretable classical representation of a QELM. As a specific application, we focus on forecasting nonlinear dynamical systems and show that a QELM trained on such trajectories learns a surrogate-approximation to the underlying flow map.

Markus Gross, Hans-Martin Rieser

Institute for AI Safety and Security, German Aerospace Center (DLR), Sankt Augustin and Ulm, Germany

Quantum Machine Learning Quantum Reservoir Computing

Feb 20, 2026

Quantum Maximum Likelihood Prediction via Hilbert Space Embeddings

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.

Sreejith Sreekumar, Nir Weinberger

Information Geometry Quantum Machine Learning

Feb 18, 2026

Structured Unitary Tensor Network Representations for Circuit-Efficient Quantum Data Encoding

Encoding classical data into quantum states is a central bottleneck in quantum machine learning: many widely used encodings are circuit-inefficient, requiring deep circuits and substantial quantum resources, which limits scalability on quantum hardware. In this work, we propose tensor network-based quantum data encoding (TNQE), a circuit-efficient framework built on structured unitary tensor network (TN) representations. TNQE first represents each classical input via a TN decomposition and then compiles the resulting tensor cores into an encoding circuit through two complementary core-to-circuit strategies. To make this compilation trainable while respecting the unitary nature of quantum operations, we introduce a unitary-aware constraint that parameterizes TN cores as learnable block unitaries, enabling them to be directly optimized and directly encoded as quantum operators. The proposed TNQE framework enables explicit control over circuit depth and qubit resources, allowing the construction of shallow, resource-efficient circuits. Across a range of benchmarks, TNQE achieves encoding circuits as shallow as

0.04\times

the depth of amplitude encoding, while naturally scaling to high-resolution images (

256 \times 256

) and demonstrating practical feasibility on real quantum hardware.

Guang Lin, Toshihisa Tanaka, Qibin Zhao

RIKEN Center for Advanced Intelligence Project · Tokyo University of Agriculture and Technology

Quantum Data Encoding Quantum Machine Learning Tensor Networks Quantum Circuit Compilation

Feb 18, 2026

DistributedEstimator: Distributed Training of Quantum Neural Networks via Circuit Cutting

Circuit cutting decomposes a large quantum circuit into smaller subcircuits executed independently; expectation values are recovered by classically combining subcircuit outcomes. Prior work characterises cutting overhead via subcircuit counts and sampling complexity, but its end-to-end impact on iterative, estimator-driven training pipelines remains under-measured from a systems perspective. We propose DistributedEstimator, a cut-aware estimator execution pipeline that treats circuit cutting as a staged distributed workload, instrumenting each query across four phases: partitioning, subexperiment generation, parallel execution, and classical reconstruction. Using logged runtime traces and learning outcomes on two binary classification workloads (Iris and MNIST), we quantify cutting overheads, scaling limits, and sensitivity to injected stragglers, and assess whether accuracy and robustness are preserved under matched training budgets. Reconstruction dominates per-query time -- a median of 53% and 95th percentile of 58% at three cuts -- bounding achievable speed-up under parallelism. Despite this, test accuracy is fully preserved on Iris and maintained without systematic degradation on MNIST across all cut configurations. Robustness under Gaussian noise and FGSM perturbations is similarly preserved, with several configurations matching or improving on the uncut baseline. Exponential growth of subexperiment counts (

{O}(9^c)

for CNOT-based decomposition) is a fundamental barrier limiting practical experimentation to small qubit counts. These results establish that practical scaling for learning workloads requires reducing and overlapping reconstruction, scheduling policies for barrier-dominated critical paths, and computationally efficient reconstruction strategies for larger qubit counts.

Prabhjot Singh, Adel N. Toosi, Rajkumar Buyya

Quantum Cloud Computing and Distributed Systems (qCLOUDS) Lab, School of Computing and Information Systems, The University of Melbourne, Melbourne, VIC, 3010, Australia

Quantum Machine Learning Distributed Training Quantum Neural Networks

Feb 16, 2026

Distributed Quantum Gaussian Processes for Multi-Agent Systems

Gaussian Processes (GPs) are a powerful tool for probabilistic modeling, but their performance is often constrained in complex, large-scale real-world domains due to the limited expressivity of classical kernels. Quantum computing offers the potential to overcome this limitation by embedding data into exponentially large Hilbert spaces, capturing complex correlations that remain inaccessible to classical computing approaches. In this paper, we propose a Distributed Quantum Gaussian Process (DQGP) method in a multi-agent setting to enhance modeling capabilities and scalability. To address the challenging non-Euclidean optimization problem, we develop a Distributed consensus Riemannian Alternating Direction Method of Multipliers (DR-ADMM) algorithm that aggregates local agent models into a global model. We evaluate the efficacy of our method through numerical experiments conducted on a quantum simulator in classical hardware. We use real-world, non-stationary elevation datasets of NASA's Shuttle Radar Topography Mission and synthetic datasets generated by Quantum Gaussian Processes. Beyond modeling advantages, our framework highlights potential computational speedups that quantum hardware may provide, particularly in Gaussian processes and distributed optimization.

Meet Gandhi, George P. Kontoudis

Colorado School of Mines, Golden, USA

Gaussian Processes Quantum Machine Learning Multi-Agent Systems Distributed Optimization

Feb 16, 2026

The Signal Horizon: Local Blindness and the Contraction of Pauli-Weight Spectra in Noisy Quantum Encodings

The performance of quantum classifiers is typically analyzed through global state distinguishability or the trainability of variational models. This study investigates how much class information remains accessible under locality-constrained measurements in the presence of noise. The authors formulate binary quantum classification as constrained quantum state discrimination and introduce a locality-restricted distinguishability measure quantifying the maximum bias achievable by observables acting on at most

k

subsystems. For

n

-qubit systems subject to independent depolarizing noise, the locally accessible signal is governed by a Pauli-weight-dependent contraction mechanism. This motivates a computable predictor, the

k

-local Pauli-accessible amplitude

A_{k}(p)

, which lower bounds the optimal

k

-local classification advantage. Numerical experiments on four-qubit encodings demonstrate quantitative agreement between empirical accuracy and the prediction across noise levels. The research identifies an operational breakdown threshold where

k

-local classifiers become indistinguishable from random guessing despite persistent global distinguishability.

Ait Haddou Marwan

Independent Researcher

Quantum Machine Learning Noise Robustness

Feb 4, 2026

Instance-optimal high-precision shadow tomography with few-copy measurements: A metrological approach

We study the sample complexity of shadow tomography in the high-precision regime under realistic measurement constraints. Given an unknown

d

-dimensional quantum state

ρ

and a known set of observables

\{O_i\}_{i=1}^m

, the goal is to estimate expectation values

\{\mathrm{tr}(O_iρ)\}_{i=1}^m

to accuracy

ε

in

L_p

-norm, using possibly adaptive measurements that act on

O(\mathrm{polylog}(d))

number of copies of

ρ

at a time. We focus on the regime where

ε

is below an instance-dependent threshold. Our main contribution is an instance-optimal characterization of the sample complexity as

\tildeΘ(Γ_p/ε^2)

, where

Γ_p

is a function of

\{O_i\}_{i=1}^m

defined via an optimization formula involving the inverse Fisher information matrix. Previously, tight bounds were known only in special cases, e.g. Pauli shadow tomography with

L_\infty

-norm error. Concretely, we first analyze a simpler oblivious variant where the goal is to estimate an observable of the form

\sum_{i=1}^m α_i O_i

with

\|α\|_q = 1

(where

q

is dual to

p

) revealed after the measurement. For single-copy measurements, we obtain a sample complexity of

Θ(Γ^{\mathrm{ob}}_p/ε^2)

. We then show

\tildeΘ(Γ_p/ε^2)

is necessary and sufficient for the original problem, with the lower bound applying to unbiased, bounded estimators. Our upper bounds rely on a two-step algorithm combining coarse tomography with local estimation. Notably,

Γ^{\mathrm{ob}}_\infty = Γ_\infty

. In both cases, allowing

c

-copy measurements improves the sample complexity by at most

Ω(1/c)

. Our results establish a quantitative correspondence between quantum learning and metrology, unifying asymptotic metrological limits with finite-sample learning guarantees.

Senrui Chen, Weiyuan Gong, Sisi Zhou

IQIM, California Institute of Technology · SEAS, Harvard University · Perimeter Institute

Sample Complexity Quantum Machine Learning

Jan 18, 2026

Semidefinite Programming for Quantum Channel Learning

The problem of reconstructing a quantum channel from a sample of classical data is considered. When the total fidelity can be represented as a ratio of two quadratic forms (e.g., in the case of mapping a mixed state to a pure state, projective operators, unitary learning, and others), Semidefinite Programming (SDP) can be applied to solve the fidelity optimization problem with respect to the Choi matrix. A remarkable feature of SDP is that the optimization is convex, which allows the problem to be efficiently solved by a variety of numerical algorithms. We have tested several commercially available SDP solvers, all of which allowed for the reconstruction of quantum channels of different forms. A notable feature is that the Kraus rank of the obtained quantum channel typically comprises less than a few percent of its maximal possible value. This suggests that a relatively small Kraus rank quantum channel is typically sufficient to describe experimentally observed classical data. The theory was also applied to the problem of reconstructing projective operators from data. Finally, we discuss a classical computational model based on quantum channel transformation, performed and calculated on a classical computer, possibly hardware-optimized.

Mikhail Gennadievich Belov, Victor Victorovich Dubov, Vadim Konstantinovich Ivanov +3

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, GSP-1, Moscow, Vorob’evy Gory, 119991, Russia and Autretech Group, Skolkovo Innovation Center, Nobel Street, Building 7, Moscow, 121205, Russia · Peter the Great St. Petersburg Polytechnic University, 195251, Russia · Ioffe Institute, Politekhnicheskaya 26, St Petersburg, 194021, Russia

Semidefinite Programming Quantum Machine Learning