Quantum Generative Modeling

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Overview

Quantum generative modeling studies how to create samples from learned distributions, including images, molecules, signals, and quantum states. Its main approaches include quantum circuit Born machines and generative adversarial networks, diffusion and flow-matching models, and quantum annealing, often combined with classical neural networks. These methods are explored for sampling complex distributions, preparing quantum states, and generating data for tasks with limited training examples. A central open question is whether they offer reliable benefits over well-matched classical models, given challenges in trainability, noise, hardware scale, and fair evaluation.

Latest papers

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54 papers8 papers in the last four weeks, up 14% on the four weeks before. 0.0% of all new papers.

May 2, 2026

From Characterization To Construction: Generative Quantum Circuit Synthesis from Gate Set Tomography Data

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

King Yiu Yu, Aritra Sarkar, Erbing Hua +3

1Quantum and Computer Engineering, Delft University of Technology, The Netherlands · 2QuTech, Delft University of Technology, The Netherlands · 3Kavli Institute of Nanoscience Delft, Delft University of Technology, The Netherlands

Quantum Circuit CompilationQuantum Generative ModelingQuantum Machine LearningQuantum Circuit Synthesis
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Apr 13, 2026

HHL with a Coherent Fourier Oracle: A Proof-of-Concept Quantum Architecture for Joint Melody-Harmony Generation

Quantum algorithms with a proven theoretical speedup over classical computation are rare. Among the most prominent is the Harrow-Hassidim-Lloyd (HHL) algorithm for solving sparse linear systems. Here, HHL is applied to encode melodic preference: the system matrix encodes Narmour implication-realisation and Krumhansl-Kessler tonal stability, so its solution vector is a music-cognition-weighted note-pair distribution. The key constraint of HHL is that reading its output classically cancels the quantum speedup; the solution must be consumed coherently. This motivates a coherent Fourier harmonic oracle: a unitary that applies chord-transition weights directly to the HHL amplitude vector, so that a single measurement jointly selects both melody notes and a two-chord progression. A two-note/two-chord (2/2) block is used to contain the exponential growth of the joint state space that would otherwise make classical simulation of larger blocks infeasible. For demonstrations of longer passages, blocks are chained classically - each block's collapsed output conditions the next -- as a temporary workaround until fault-tolerant hardware permits larger monolithic circuits. A four-block chain produces 8 notes over 8 chords with grammatically valid transitions at every block boundary. Independent rule-based harmony validation confirms that 97% of generated chord progressions are rated strong or acceptable. The primary motivation is that HHL carries a proven exponential speedup over classical linear solvers; this work demonstrates that a coherent HHL+oracle pipeline - the prerequisite for that speedup to be realised in a musical setting - is mechanically achievable. Audio realisations of representative outputs are made available for listening online.

Alexis Kirke

Music GenerationSymbolic Music GenerationQuantum Generative Modeling
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Apr 13, 2026

Minimizing classical resources in variational measurement-based quantum computation for generative modeling

Measurement-based quantum computation (MBQC) is a framework for quantum information processing in which a computational task is carried out through one-qubit measurements on a highly entangled resource state. Due to the indeterminacy of the outcomes of a quantum measurement, the random outcomes of these operations, if not corrected, yield a variational quantum channel family. Traditionally, this randomness is corrected through classical processing in order to ensure deterministic unitary computations. Recently, variational measurement-based quantum computation (VMBQC) has been introduced to exploit this measurement-induced randomness to gain an advantage in generative modeling. A limitation of this approach is that the corresponding channel model has twice as many parameters compared to the unitary model, scaling as N×DN \times D, where NN is the number of logical qubits (width) and DD is the depth of the VMBQC model. This can often make optimization more difficult and may lead to poorly trainable models. In this paper, we present a restricted VMBQC model that extends the unitary setting to a channel-based one using only a single additional trainable parameter. We show, both numerically and algebraically, that this minimal extension is sufficient to generate probability distributions that cannot be learned by the corresponding unitary model.

Arunava Majumder, Hendrik Poulsen Nautrup, Hans J. Briegel

University of Innsbruck, Department of Theoretical Physics, Technikerstraße 21a, A-6020 Innsbruck, Austria.

Quantum Generative Modeling
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Apr 1, 2026

Learning and Generating Mixed States Prepared by Shallow Channel Circuits

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

Fangjun Hu, Christian Kokail, Milan Kornjača +5

QuEra Computing Inc. · School of Engineering and Applied Sciences, Harvard University · JILA and Department of Physics, CU Boulder

Quantum Generative ModelingQuantum State PreparationQuantum Machine LearningQuantum Many-Body Physics
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Apr 1, 2026

Multi-Mode Quantum Annealing for Generative Representation Learning with Boltzmann Priors

Energy-based models provide a natural bridge between statistical physics and machine learning by representing data through structured energy landscapes. Boltzmann machines are a particularly compelling class of such models for capturing complex interactions among latent variables, but their use in modern generative learning has been limited by the classical intractability of sampling from general (non-restricted) Boltzmann distributions. Here we develop a quantum-annealing-based framework that enables variational autoencoders with general Boltzmann priors. The framework employs three complementary annealing modes tailored to different stages of learning and deployment: diabatic quantum annealing provides unbiased Boltzmann samples for efficient training, slower annealing concentrates samples near low-energy configurations of the learned prior for unconditional generation, and conditional annealing with external fields steers the learned energy landscape toward attribute-specific regions for conditional generation and semantic editing. Using up to 2000 qubits on a D-Wave Advantage2 processor, we demonstrate stable training and high-quality generation on MNIST, Fashion-MNIST, and CelebA, achieving faster convergence and lower reconstruction loss than a Gaussian-prior VAE with the same encoder-decoder architecture. Beyond generation, the learned energy function provides out-of-distribution detection signals that add discriminative power beyond reconstruction loss. We demonstrate that these scores separate in-distribution samples from held-out digit classes in one-class MNIST experiments and improve the detection of market regime shifts in financial data. These results establish quantum annealing as a practical and controllable physical mechanism for energy-based representation learning and generative modeling beyond the reach of tractable classical approaches.

Gilhan Kim, Daniel K. Park

Department of Statistics and Data Science, Yonsei University, Seoul 03722, Republic of Korea · Department of Applied Statistics, Yonsei University, Seoul 03722, Republic of Korea · Department of Quantum Information, Yonsei University, Seoul 03722, Republic of Korea

Quantum Generative ModelingVariational AutoencodersConditional Generative ModelingQuantum Annealing
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Mar 27, 2026

MolPaQ: Modular Quantum-Classical Patch Learning for Interpretable Molecular Generation

Molecular generative models must jointly ensure validity, diversity, and property control, yet existing approaches typically trade off among these objectives. We present MOLPAQ, a modular quantum-classical generator that assembles molecules from quantum-generated latent patches. A \b{eta}-VAE pretrained on QM9 learns a chemically aligned latent manifold; a reduced conditioner maps molecular descriptors into this space; and a parameter-efficient quantum patch generator produces entangled node embeddings that a valence-aware aggregator reconstructs into valid molecular graphs. Adversarial fine-tuning with a latent critic and chemistry-shaped reward yields 100% RDKit validity, 99.75% novelty, and 0.905 diversity. Beyond aggregate metrics, the pretrained quantum generator, steered by the conditioner, improves mean QED by approx. 2.3% and increases aromatic motif incidence by approx. 10-12% relative to a parameter-matched classical generator, highlighting its role as a compact topology-shaping operator.

Syed Rameez Naqvi, Lu Peng

Department of Computer Science, Tulane University, New Orleans, LA, USA.

Molecular Graph GenerationQuantum Generative ModelingConditional Generative ModelingHybrid Quantum-Classical MLMolecular Optimization
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Mar 25, 2026

SpinGQE: A Generative Quantum Eigensolver for Spin Hamiltonians

The ground state search problem is central to quantum computing, with applications spanning quantum chemistry, condensed matter physics, and optimization. The Variational Quantum Eigensolver (VQE) has shown promise for small systems but faces significant limitations. These include barren plateaus, restricted ansatz expressivity, and reliance on domain-specific structure. We present SpinGQE, an extension of the Generative Quantum Eigensolver (GQE) framework to spin Hamiltonians. Our approach reframes circuit design as a generative modeling task. We employ a transformer-based decoder to learn distributions over quantum circuits that produce low-energy states. Training is guided by a weighted mean-squared error loss between model logits and circuit energies evaluated at each gate subsequence. We validate our method on the four-qubit Heisenberg model, demonstrating successfulconvergencetonear-groundstates. Throughsystematichyperparameterexploration, we identify optimal configurations: smaller model architectures (12 layers, 8 attention heads), longer sequence lengths (12 gates), and carefully chosen operator pools yield the most reliable convergence. Our results show that generative approaches can effectively navigate complex energy landscapes without relying on problem-specific symmetries or structure. This provides a scalable alternative to traditional variational methods for general quantum systems. An open-source implementation is available at https://github.com/Mindbeam-AI/SpinGQE.

Alexander Holden, Moinul Hossain Rahat, Nii Osae Osae Dade

Mindbeam AI† · Department of Computer and Data Sciences, Case Western Reserve University

Quantum Circuit SynthesisVariational Quantum AlgorithmsQuantum Generative ModelingQuantum Many-Body Physics
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Mar 25, 2026

Transcending Classical Neural Network Boundaries: A Quantum-Classical Synergistic Paradigm for Seismic Data Processing

In recent years, a number of neural-network (NN) methods have exhibited good performance in seismic data processing, such as denoising, interpolation, and frequency-band extension. However, these methods rely on stacked perceptrons and standard activation functions, which imposes a bottleneck on the representational capacity of deep-learning models, making it difficult to capture the complex and non-stationary dynamics of seismic wavefields. Different from the classical perceptron-stacked NNs which are fundamentally confined to real-valued Euclidean spaces, the quantum NNs leverage the exponential state space of quantum mechanics to map the features into high-dimensional Hilbert spaces, transcending the representational boundary of classical NNs. Based on this insight, we propose a quantum-classical synergistic generative adversarial network (QC-GAN) for seismic data processing, serving as the first application of quantum NNs in seismic exploration. In QC-GAN, a quantum pathway is used to exploit the high-order feature correlations, while the convolutional pathway specializes in extracting the waveform structures of seismic wavefields. Furthermore, we design a QC feature complementarity loss to enforce the feature orthogonality in the proposed QC-GAN. This novel loss function can ensure that the two pathways encode non-overlapping information to enrich the capacity of feature representation. On the whole, by synergistically integrating the quantum and convolutional pathways, the proposed QC-GAN breaks the representational bottleneck inherent in classical GAN. Experimental results on denoising and interpolation tasks demonstrate that QC-GAN preserves wavefield continuity and amplitude-phase information under complex noise conditions.

Zhengyi Yuan, Xintong Dong, Xinyang Wang +2

College of Instrumentation and Electrical Engineering, Jilin University, Changchun 130026, China.

Quantum Neural NetworksHybrid Quantum-Classical MLQuantum Generative ModelingSeismology
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Mar 23, 2026

Latent Style-based Quantum Wasserstein GAN for Drug Design

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

Julien Baglio, Yacine Haddad, Richard Polifka

Center for Quantum Computing and Quantum Coherence (QC2), Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland · QuantumBasel, Schorenweg 44b, CH-4144 Arlesheim, Switzerland · Laboratory for High Energy Physics (LHEP), Physics Institute, Faculty of Sciences, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland +1

Molecular GenerationQuantum Generative ModelingQuantum Machine Learning
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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 ModelingImage GenerationQuantum Machine LearningQuantum State Preparation
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Mar 17, 2026

Generative AI for Quantum Circuits and Quantum Code: A Technical Review and Taxonomy

We review thirteen generative systems and five supporting datasets for quantum circuit and quantum code generation, identified through a structured scoping review of Hugging Face, arXiv, and provenance tracing (January-February 2026). We organize the field along two axes: artifact type (Qiskit code, OpenQASM programs, circuit graphs); crossed with training regime (supervised fine-tuning, verifier-in-the-loop RL, diffusion/graph generation, agentic optimization); and systematically apply a three-layer evaluation framework covering syntactic validity, semantic correctness, and hardware executability. The central finding is that while all reviewed systems address syntax and most address semantics to some degree, none reports end-to-end evaluation on quantum hardware (Layer 3b), leaving a significant gap between generated circuits and practical deployment. Scope note: quantum code refers throughout to quantum program artifacts (QASM, Qiskit); we do not cover generation of quantum error-correcting codes (QEC).

Juhani Merilehto

University of Vaasa & University of Turku

Quantum Circuit SynthesisQuantum Generative ModelingGenerative AI Evaluation
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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-ZZ 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 MachinesQuantum Machine LearningQuantum Generative ModelingVariational Quantum CircuitsBarren Plateaus
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Mar 6, 2026

Score Reversal Is Not Free for Quantum Diffusion Models

Classical reverse diffusion is generated by changing the drift at fixed noise. We show that the quantum version of this principle obeys an exact law with a sharp phase boundary. For Gaussian pure-loss dynamics, the canonical model of continuous-variable decoherence, we prove that the unrestricted instantaneous reverse optimum exhibits a noiseless-to-noisy transition: below a critical squeezing-to-thermal ratio, reversal can be noiseless; above it, complete positivity forces irreducible reverse noise whose minimum cost we determine in closed form. The optimal reverse diffusion is uniquely covariance-aligned and simultaneously minimizes the geometric, metrological, and thermodynamic price of reversal. For multimode trajectories, the exact cost is additive in a canonical set of mode-resolved data, and a globally continuous protocol attains this optimum on every mixed-state interval. If a pure nonclassical endpoint is included, the same pointwise law holds for every t>0t>0, but the optimum diverges as 2/t2/t: exact Gaussian reversal of a pure quantum state is dynamically unattainable. These results establish the exact Gaussian benchmark against which any broader theory of quantum reverse diffusion must be measured.

Ammar Fayad

Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

Quantum Generative Modeling
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Mar 6, 2026

Toward Generative Quantum Utility via Correlation-Complexity Map

We study a practical question in generative quantum machine learning: given a classical dataset, can we determine, before training, whether it is well suited to a quantum generative model? We focus on a class of quantum circuits known as instantaneous quantum polynomial-time (IQP) circuits, whose output distributions are widely believed to be difficult to sample from using classical methods. These circuits are used to build our quantum generative models. We introduce a Correlation-Complexity Map, a simple diagnostic built from two quantities computed from data samples. The first measures how closely the dataset's spectral correlation patterns resemble those naturally produced by IQP circuits, while the second quantifies how much of the dataset's structural correlation cannot be captured by simple pairwise models. In other words, we can estimate beforehand how well a dataset can be approximated by our model family and also how complex its correlations are, indicating possible failures of classical models. Applying this framework, we identify turbulence data as a promising target for quantum generative modeling. Guided by this analysis, we use a latent-parameter adaptation scheme that reuses a compact IQP circuit over a temporal sequence by learning and interpolating a low-dimensional latent trajectory, and observe competitive performance against classical baselines in a low-data, low-parameter regime. These results suggest that dataset-level diagnostics can help prioritize problems where quantum generative models are most likely to be useful, with improvements in data and parameter efficiency.

Chen-Yu Liu, Leonardo Placidi, Eric Brunner +1

Quantinuum, Partnership House, London, UK · Quantinuum, Otemachi Financial City Grand Cube, Tokyo, Japan

Quantum Generative Modeling
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Mar 6, 2026

Implementation of Quantum Implicit Neural Representation in Deterministic and Probabilistic Autoencoders for Image Reconstruction/Generation Tasks

We propose a quantum implicit neural representation (QINR)-based autoencoder (AE) and variational autoencoder (VAE) for image reconstruction and generation tasks. Our purpose is to demonstrate that the QINR in VAEs and AEs can transform information from the latent space into highly rich, periodic, and high-frequency features. Additionally, we aim to show that the QINR-VAE can be more stable than various quantum generative adversarial network (QGAN) models in image generation because it can address the low diversity problem. Our quantum-classical hybrid models consist of a classical convolutional neural network (CNN) encoder and a quantum-based QINR decoder. We train the QINR-AE/VAE with binary cross-entropy with logits (BCEWithLogits) as the reconstruction loss. For the QINR-VAE, we additionally employ Kullback-Leibler divergence for latent regularization with beta/capacity scheduling to prevent posterior collapse. We introduce learnable angle-scaling in data reuploading to address optimization challenges. We test our models on the MNIST, E-MNIST, and Fashion MNIST datasets to reconstruct and generate images. Our results demonstrate that the QINR structure in VAE can produce a wider variety of images with a small amount of data than various generative models that have been studied. We observe that the generated/reconstructed images from the QINR-VAE/AE are clear with sharp boundaries and details. Overall, we find that the addition of QINR-based quantum layers into the AE/VAE frameworks shows improved performance of reconstruction/generation under the constrained experimental setting relative to the specific baselines.

Saadet Müzehher Eren

Department of Physics, Izmir Institute of Technology, Gülbahçe, Urla, 35430, Izmir, Turkey.

Variational AutoencodersQuantum Generative ModelingAutoencodersImage GenerationImage ReconstructionQuantum Neural Networks
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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 ModelingImage GenerationQuantum Machine LearningVariational Quantum CircuitsGenerative Adversarial Networks
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Feb 25, 2026

Learning Quantum Data Distribution via Chaotic Quantum Diffusion Model

Generative models for quantum data pose significant challenges but hold immense potential in fields such as chemoinformatics and quantum physics. Quantum denoising diffusion probabilistic models (QuDDPMs) enable efficient learning of quantum data distributions by progressively scrambling and denoising quantum states. However, existing implementations typically rely on circuit-based random unitary dynamics, which can be costly to implement and sensitive to control imperfections, particularly on analog quantum hardware. We propose the chaotic quantum diffusion model, a framework that generates projected ensembles via chaotic Hamiltonian time evolution, providing a flexible and hardware-compatible diffusion mechanism. Requiring only global, time-independent control, our approach substantially reduces implementation overhead across diverse analog quantum platforms while achieving accuracy comparable to QuDDPMs. This method improves trainability and robustness, broadening the applicability of quantum generative modeling.

Quoc Hoan Tran, Koki Chinzei, Yasuhiro Endo +1

Quantum Laboratory, Fujitsu Research, Fujitsu Limited, Kawasaki, Kanagawa 211-8588, Japan

Quantum Generative ModelingDiffusion Models
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Feb 24, 2026

Stochastic Neural Networks for Quantum Devices

This work presents a formulation to express and optimize stochastic neural networks as quantum circuits in gate-based quantum computing. Motivated by a classical perceptron, stochastic artificial neurons are introduced and combined into a quantum neural network. The Kiefer-Wolfowitz algorithm in combination with simulated annealing is used for training the network weights. Several topologies and models are presented, including shallow fully connected networks, Hopfield Networks, Restricted Boltzmann Machines, Autoencoders and convolutional neural networks. We also demonstrate the combination of our optimized neural networks as an oracle for the Grover algorithm to realize a quantum generative AI model.

Bodo Rosenhahn, Tobias J. Osborne, Christoph Hirche

Institute for Information Processing (tnt/L3S), Leibniz Universität Hannover, Germany · Institute for Theoretical Physics (ITP/L3S), Leibniz Universität Hannover, Germany

Quantum Neural NetworksHybrid Quantum-Classical MLQuantum Generative Modeling
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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 MLQuantum Machine LearningQuantum Generative ModelingEnergy-Based Models
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Feb 19, 2026

Quantum Scrambling Born Machine

Quantum generative modeling, where the Born rule naturally defines probability distributions through measurement of parameterized quantum states, is a promising near-term application of quantum computing. We propose a Quantum Scrambling Born Machine in which a fixed entangling unitary -- acting as a scrambling reservoir -- provides multi-qubit entanglement, while only single-qubit rotations are optimized. We consider three entangling unitaries -- a Haar random unitary and two physically realizable approximations, a finite-depth brickwork random circuit and analog time evolution under nearest-neighbor spin-chain Hamiltonians -- and show that, for the benchmark distributions and system sizes considered, once the entangler produces near-Haar-typical entanglement the model learns the target distribution with weak sensitivity to the scrambler's microscopic origin. Finally, promoting the Hamiltonian couplings to trainable parameters casts the generative task as a variational Hamiltonian problem, with performance competitive with representative classical generative models at matched parameter count.

Marcin Płodzień

Qilimanjaro Quantum Tech, Carrer de Veneçuela 74, 08019 Barcelona, Spain

Quantum Circuit Born MachinesQuantum Generative ModelingVariational Quantum Circuits
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Feb 17, 2026

Molecular Design beyond Training Data with Novel Extended Objective Functionals of Generative AI Models Driven by Quantum Annealing Computer

Deep generative modeling to stochastically design small molecules is an emerging technology for accelerating drug discovery and development. However, one major issue in molecular generative models is their lower frequency of drug-like compounds. To resolve this problem, we developed a novel framework for optimization of deep generative models integrated with a D-Wave quantum annealing computer, where our Neural Hash Function (NHF) presented herein is used both as the regularization and binarization schemes simultaneously, of which the latter is for transformation between continuous and discrete signals of the classical and quantum neural networks, respectively, in the error evaluation (i.e., objective) function. The compounds generated via the quantum-annealing generative models exhibited higher quality in both validity and drug-likeness than those generated via the fully-classical models, and was further indicated to exceed even the training data in terms of drug-likeness features, without any restraints and conditions to deliberately induce such an optimization. These results indicated an advantage of quantum annealing to aim at a stochastic generator integrated with our novel neural network architectures, for the extended performance of feature space sampling and extraction of characteristic features in drug design.

Hayato Kunugi, Mohsen Rahmani, Yosuke Iyama +8

Inovation to Implementation Laboratories, Central Pharmaceutical Research Institute, Japan Tobacco Inc., 1-1 Murasaki-cho, Takatsuki, 569-1125, Japan. · D-Wave Systems Inc., 3033 Beta Ave, Burnaby, V5G 4M9, Canada.

Molecular GenerationQuantum Generative ModelingDrug DiscoveryMolecular OptimizationHybrid Quantum-Classical MLQuantum Annealing
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Feb 16, 2026

From Classical to Quantum: Extending Prometheus for Unsupervised Discovery of Phase Transitions in Three Dimensions and Quantum Systems

We extend the Prometheus framework for unsupervised phase transition discovery from two-dimensional classical systems to three-dimensional classical systems and quantum many-body systems. Building upon preliminary observations from a 2D Ising model student abstract [Yee et al., 2026], we address two fundamental questions: (1) Does the framework scale to higher dimensions where exact solutions are unavailable? (2) Can it generalize to quantum phase transitions driven by quantum fluctuations rather than thermal fluctuations? For the 3D Ising model on lattices up to L=32L{=}32, we achieve critical temperature detection within 0.01% of literature values (\Tc/J=4.511±0.005\Tc/J = 4.511 \pm 0.005) and extract critical exponents with ≥70%{\geq}70\% accuracy, with statistical analysis correctly identifying the 3D Ising universality class (p=0.72p = 0.72). For quantum systems, we develop quantum-aware VAE (Q-VAE) architectures operating on complex-valued wavefunctions with fidelity-based loss functions, achieving 2% accuracy in quantum critical point detection for the transverse field Ising model. For the disordered TFIM, we perform a consistency check of activated dynamical scaling ln⁡ξ∼∣h−\hc∣−ψ\ln ξ\sim |h - \hc|^{-ψ}, extracting tunneling exponent ψ=0.48±0.08ψ= 0.48 \pm 0.08 consistent with theoretical predictions (ψ=0.5ψ= 0.5, Δχ2=12.3Δχ^2 = 12.3, p<0.001p < 0.001). This demonstrates that unsupervised learning can identify qualitatively different types of critical behavior, serving as a consistency check on known IRFP physics.

Brandon Yee, Wilson Collins, Pairie Koh +1

Physics Lab, Yee Collins Research Group

Phase TransitionsQuantum Many-Body PhysicsUnsupervised LearningQuantum Generative Modeling
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Aug 17, 2025

Quantum Flow Matching

The flow matching has rapidly become a dominant paradigm in classical generative modeling, offering an efficient way to interpolate between two complex distributions. We extend this idea to the quantum realm and introduce the Quantum Flow Matching (QFM), a quantum-circuit realization that offers efficient interpolation between two density matrices. QFM offers systematic preparation of density matrices and generation of samples for accurately estimating observables, and can be realized on quantum computers without the need for costly circuit redesigns. We validate its versatility on a set of applications: (i) generating target states with prescribed magnetization and entanglement entropy, (ii) estimating nonequilibrium free-energy differences to test the quantum Jarzynski equality, and (iii) expediting the study on superdiffusion. These results position QFM as a unifying and promising framework for generative modeling across quantum systems.

Zidong Cui, Pan Zhang, Ying Tang

Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China · Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China · School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS, Hangzhou 310024, China +3

Flow MatchingQuantum Generative ModelingQuantum Machine LearningGenerative ModelingQuantum State Preparation
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May 28, 2025

Physics-inspired Generative AI models via real hardware-based noisy quantum diffusion

Quantum Diffusion Models (QDMs) are an emerging paradigm in Generative AI that aims to use quantum properties to improve the performances of their classical counterparts. However, existing algorithms are not easily scalable due to the limitations of near-term quantum devices. Following our previous work on QDMs, here we propose and implement two physics-inspired protocols. In the first, we use the formalism of quantum stochastic walks, showing that a specific interplay of quantum and classical dynamics in the forward process produces statistically more robust models generating sets of MNIST images with lower Fréchet Inception Distance (FID) than using totally classical dynamics. In the second approach, we realize an algorithm to generate images by exploiting the intrinsic noise of real IBM quantum hardware with only four qubits. Our work could be a starting point to pave the way for new scenarios for large-scale algorithms in quantum Generative AI, where quantum noise is neither mitigated nor corrected, but instead exploited as a useful resource.

Marco Parigi, Stefano Martina, Francesco Aldo Venturelli +1

Department of Physics and Astronomy, University of Florence, Via Sansone 1, Sesto Fiorentino, 50019, Florence, Italy. · LENS - European Laboratory for Non-Linear Spectroscopy, University of Florence, Via Nello Carrara 1, Sesto Fiorentino, 50019, Florence, Italy. · Department of Engineering, Pompeu Fabra, T`anger 122-140, Barcelona, 08018, Barcelona, Spain.

Quantum Generative ModelingDiffusion-Based Image GenerationDiffusion Models
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