We show that deep neural networks, including transformers and RNNs, pretrained as usual on next-token prediction, intrinsically discover and represent beliefs over 'quantum' and 'post-quantum' low-dimensional generative models of their training data -- as if performing iterative Bayesian updates over the latent state of this world model during inference as they observe more context. Notably, neural nets easily find these representation whereas there is no finite classical circuit that would do the job. The corresponding geometric relationships among neural activations induced by different input sequences are found to be largely independent of neural-network architecture. Each point in this geometry corresponds to a history-induced probability density over all possible futures, and the relative displacement of these points reflects the difference in mechanism and magnitude for how these distinct pasts affect the future.
We show that deep neural networks, including transformers and RNNs, pretrained as usual on next-token prediction, intrinsically discover and represent beliefs over 'quantum' and 'post-quantum' low-dimensional generative models of their training data -- as if performing iterative Bayesian updates over the latent state of this world model during inference as they observe more context. Notably, neural nets easily find these representation whereas there is no finite classical circuit that would do the job. The corresponding geometric relationships among neural activations induced by different input sequences are found to be largely independent of neural-network architecture. Each point in this geometry corresponds to a history-induced probability density over all possible futures, and the relative displacement of these points reflects the difference in mechanism and magnitude for how these distinct pasts affect the future.
Exploiting the utility of near-term quantum devices is a long-standing challenge whereas hybrid quantum machine learning emerges as a promising candidate. Here we propose a quantum-enhanced deep generative algorithm based on programmable quantum circuit-induced quantum latent codes. To validate the effectiveness of the algorithm, we conduct optical ghost imaging experiments, collecting dataset under varying physical sampling rates. Leveraging a physically enhanced loss function and a pretrained neural network, the quantum algorithm exhibits superior reconstruction performance compared to conventional algorithms. We observe the learnable quantum latent space enhances the out-of-distribution generalization capability of the pretrained model. In the context of computer vision problems, numerical results indicate that quantum latent space can increase the generation diversity of the pretrained model. Furthermore, the algorithm outperforms classical counterparts, particularly in image inpainting and colorization, by a significant margin. Our study demonstrates the utility of hybrid quantum-classical algorithms in enhancing generalization capability, highlighting the potential of near-term quantum devices in large-scale generative artificial intelligence. Quantum circuits can generate hard distributions. Exploiting this known fact, the authors train a mixture of parametric quantum circuits and classical neural networks and show that the addition of the quantum part can enhance the expressive power of the model for generative AI.
This paper explores the potential of utilizing quantum probabilistic models to enhance the efficiency and expressiveness of deep neural networks. Traditional deep learning architectures often struggle with high-dimensional data, necessitating computationally intensive operations. We propose a novel algorithm that integrates quantum probability models into the core computation process of neural networks. This integration leverages the inherent advantages of quantum mechanics, particularly superposition and entanglement, to improve representation learning and parameter estimation. The core mechanism involves mapping the neural network's activation functions and gradient computations into quantum states, allowing for parallel processing and potentially accelerating training and inference. We analyze the theoretical and practical implications of this approach, demonstrating its potential to overcome limitations associated with classical neural networks in specific scenarios. The research emphasizes the benefits of quantum-enhanced representations and efficient parameter estimation.
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.
Quantum Neural Networks (QNNs) represent a novel computational paradigm that merges the principles of quantum computing with the architecture of artificial neural networks. Through the quantum phenomena of superposition, entanglement, and interference, QNNs enable parallel computation in high-dimensional Hilbert spaces, offering the potential to surpass the representational limits of classical models. This review provides a comprehensive overview of the theoretical foundations and architectures of QNNs, including Quantum Perceptrons, Variational Quantum Circuits (VQCs), Quantum Convolutional Neural Networks (QCNNs), and Quantum Recurrent Neural Networks (QRNNs). Furthermore, it discusses hybrid quantum–classical training mechanisms and key challenges such as barren plateaus, decoherence, and sampling complexity. The review also highlights recent applications of QNNs in medical diagnostics, materials science, and financial forecasting, demonstrating their potential to accelerate computation and improve predictive accuracy. Finally, future research directions are discussed in relation to computational efficiency, model interpretability, and integration with next-generation quantum hardware.
Deep neural networks are a powerful tool for characterizing quantum states. Existing networks are typically trained with experimental data gathered from the quantum state that needs to be characterized. But is it possible to train a neural network offline, on a different set of states? Here we introduce a network that can be trained with classically simulated data from a fiducial set of states and measurements, and can later be used to characterize quantum states that share structural similarities with the fiducial states. With little guidance of quantum physics, the network builds its own data-driven representation of a quantum state, and then uses it to predict the outcome statistics of quantum measurements that have not been performed yet. The state representations produced by the network can also be used for tasks beyond the prediction of outcome statistics, including clustering of quantum states and identification of different phases of matter.
This paper proposes a novel approach to Bayesian inference leveraging the capabilities of Quantum Neural Networks (QNNs). Traditional Bayesian inference methods suffer from significant computational complexity, particularly when dealing with large datasets and intricate models. This research addresses this limitation by formulating Bayesian inference as a training problem for a QNN. The core idea involves harnessing the inherent parallelism of QNNs to perform efficient probability calculations, thereby accelerating the inference process. We explore the theoretical framework and outline the key components of this model, emphasizing the synergy between quantum machine learning and Bayesian inference principles. The presented approach offers a potentially transformative pathway towards scalable and efficient Bayesian reasoning, particularly in domains where classical methods are struggling to keep pace with increasing data volumes and model complexity. This work lays the groundwork for future research and development in this burgeoning field.