A single observation can admit several plausible futures, making uncertainty an essential part of world modelling. However, quantum generative models remain underexplored for this task. We introduce Quantum-JEPA, a latent-action JEPA framework that learns distributions of future representations using a conditional quantum Born prior. Circuit measurements generate binary latent actions, which a shared predictor maps to alternative future representations. We train the quantum prior through the quality and diversity of these predictions using a sampled energy objective. Our model learns distinct continuations on constructed multimodal tasks and captures latent-action correlations that support coordinated multi-agent futures. On D3IL, a benchmark of diverse human demonstrations, our trained models generate multiple obstacle-crossing routes from a common starting point without observed motion. On the controlled tasks, our classical and quantum prior implementations improve prediction validity and distributional fidelity over the evaluated variational baselines. Our quantum priors combine competitive predictive quality with a parameter-efficient sampling structure: they avoid an exponentially sized categorical output layer while supporting correlated latent actions. We further validate finite-shot parameter-shift training, including training with readout noise. Unlike most prior work, which focuses on simulation, we also verify the feasibility of inference with trained priors on a real QPU. These results establish a trainable quantum component for JEPA future prediction and a basis for exploring quantum-enhanced world models at larger scales.
A single observation can admit several plausible futures, making uncertainty an essential part of world modelling. However, quantum generative models remain underexplored for this task. We introduce Quantum-JEPA, a latent-action JEPA framework that learns distributions of future representations using a conditional quantum Born prior. Circuit measurements generate binary latent actions, which a shared predictor maps to alternative future representations. We train the quantum prior through the quality and diversity of these predictions using a sampled energy objective. Our model learns distinct continuations on constructed multimodal tasks and captures latent-action correlations that support coordinated multi-agent futures. On D3IL, a benchmark of diverse human demonstrations, our trained models generate multiple obstacle-crossing routes from a common starting point without observed motion. On the controlled tasks, our classical and quantum prior implementations improve prediction validity and distributional fidelity over the evaluated variational baselines. Our quantum priors combine competitive predictive quality with a parameter-efficient sampling structure: they avoid an exponentially sized categorical output layer while supporting correlated latent actions. We further validate finite-shot parameter-shift training, including training with readout noise. Unlike most prior work, which focuses on simulation, we also verify the feasibility of inference with trained priors on a real QPU. These results establish a trainable quantum component for JEPA future prediction and a basis for exploring quantum-enhanced world models at larger scales.
Many applications in quantum simulation, quantum chemistry, and quantum machine learning require not a single quantum state but an ensemble of states characterizing the heterogeneity of a target system. Preparing such ensembles state-by-state is prohibitive in both variational and fault-tolerant settings, thereby motivating a generative modeling approach. We introduce latent-conditioned parameterized quantum circuits (LPQCs), a hybrid quantum-classical framework in which classical neural networks map a latent variable sampled from a prior distribution to the parameters of a parameterized quantum circuit. We prove that LPQCs are universal approximators for probability measures over density operators in the 1-Wasserstein distance, extending classical universal approximation theorems to the quantum-distribution setting. We additionally introduce a multimodal latent prior and a mixture-of-experts circuit architecture, and show empirically that the latent-conditioned parameterization alleviates the barren plateau problem during optimization, a behavior for which we provide rigorous partial guarantees. Numerical experiments validate the framework on a synthetic multi-cluster ensemble of mixed quantum states and on a QM9-derived ensemble of 3-D molecular structures. In these tasks, LPQC outperforms recent quantum generative baselines and matches the generation quality of a classical neural-network baseline, while requiring an output dimension that grows only linearly with the number of qubits rather than exponentially. By leveraging classical expressivity in the latent space, LPQCs offer a tractable route to quantum generative modeling.
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.
Rare events such as financial crashes, climate extremes, and biological anomalies are notoriously difficult to model due to their scarcity and heavy-tailed distributions. Classical deep generative models often struggle to capture these rare occurrences, either collapsing low-probability modes or producing poorly calibrated uncertainty estimates. In this work, we propose the Quantum-Enhanced Generative Model (QEGM), a hybrid classical quantum framework that integrates deep latent-variable models with variational quantum circuits. The framework introduces two key innovations: (i) a hybrid loss function that jointly optimizes reconstruction fidelity and tail-aware likelihood, and (ii) quantum randomness–driven noise injection to enhance sample diversity and mitigate mode collapse. Training proceeds via a hybrid loop where classical parameters are updated through backpropagation while quantum parameters are optimized using parameter-shift gradients. We evaluate QEGM on synthetic Gaussian mixtures and real-world datasets spanning finance, climate, and protein structure. Results demonstrate that QEGM consistently reduces tail KL-divergence by up to 50% compared to state-of-the-art baselines (GAN, VAE, Diffusion), while improving rare-event recall and coverage calibration. These findings highlight the potential as a principled approach for rare-event prediction, offering robustness beyond what is achievable with purely classical methods.
With quantum sensors, simulators and networks emerging, a future of quantum technology may produce quantum states as data---that is, coherently rather than as classical measurement records---thus motivating the study of suitable quantum generalisations of modern machine learning, including the automated, unsupervised extraction of useful representations. Two ingredients are central to the latter: inference, mapping observations to latent representations, and generation, mapping latent states back to synthetic data. Both are related to each other and to joint distributions for training models by the chain-rule of classical probability theory. The fact that quantum states however lack such universal, standard factorisation property thus poses a challenge. Here we develop a conceptual and mathematical framework for unsupervised representation learning from quantum data. Models are joint quantum states over visible and latent systems; state-over-time maps provide a notion of factorisation into a marginal state and inference (generation) channel; models with inference (generation) are ambiguous states---states for which such factorisation obtains---subject to a further consistency condition on extended inference maps as data extension. These stipulations are restrictive: we show that non-trivial models must feature non-linear such maps to the extended space. For three representative state-over-time maps, we completely characterise the ambiguous states, uncovering a hierarchy tied to the positive-partial-transpose (PPT) criterion from entanglement theory. Notably, the Leifer-Spekkens construction supports inference and generation exactly for model classes of PPT states, thus allowing genuinely quantum visible-latent correlations. We also formulate quantum counterparts of exact and approximate inference training, explore weaker notions of data extension and sketch a future research programme.
We propose a novel approach to generative adversarial networks (GANs) in which the standard i.i.d. Gaussian latent prior is replaced or hybridized with a quantum-correlated prior derived from measurements of a 16-qubit entangling circuit. Each latent sample is generated by grouping repeated shots per qubit into a binary fraction, applying the inverse Gaussian CDF to obtain a 16-dimensional Gaussian vector whose joint copula reflects genuine quantum entanglement, and then projecting into the high-dimensional space via a fixed random matrix. By pre-sampling tens of millions of bitstrings, either from a noiseless simulator or from IBM hardware, we build large pools of independent but internally quantum-correlated latents. We integrate this prior into three representative architectures (WGAN, SNGAN, BigGAN) on CIFAR-10, making no changes to the neural network structure or training hyperparameters. The hybrid latent representations incorporating hardware-derived noise consistently lower the FID relative to both the classical baseline and the simulator variant, especially when the quantum component constitutes a substantial fraction of the prior. In addition, we execute on the QPU in parallel to not only save computing time but also further decrease the FID up to 17% in BigGAN. These results indicate that intrinsic quantum randomness and device-specific imperfections can provide a structured inductive bias that enhances GAN performance. Our work demonstrates a practical pipeline for leveraging noisy quantum hardware to enrich deep-generative modeling, opening a new interface between quantum information and machine learning. All code and data are available at https://github.com/Neon8988/GAN_QN.git.
Near-term noisy intermediate-scale quantum circuits can efficiently implement implicit probabilistic models in discrete spaces, supporting distributions that are practically infeasible to sample from using classical means. One of the possible applications of such models, also known as Born machines, is probabilistic inference, which is at the core of Bayesian methods. This paper studies the use of Born machines for the problem of training binary Bayesian neural networks. In the proposed approach, a Born machine is used to model the variational distribution of the binary weights of the neural network, and data from multiple tasks is used to reduce training data requirements on new tasks. The method combines gradientbased meta-learning and variational inference via Born machines, and is shown in a prototypical regression problem to outperform conventional joint learning strategies.