Hybrid and hardware-oriented approaches for quantum diffusion models

Classical diffusion models have achieved remarkable results in terms of sample quality and variability. The quantum counterpart of these models is still to be explored thoroughly and offers a promising research direction in the field of quantum generative models. In this work, we introduce two versions of a quantum diffusion model, using parameterized quantum circuits to sample from quantum state distributions, while performing training via classical simulations. The first model is a quantum-hardware-oriented design, based on denoising diffusion probabilistic models, for which we demonstrate an implementation on real quantum hardware. The second model is a hybrid approach, based on denoising diffusion implicit models, that uses a classical neural network to enhance the expressive power. We show that the second version produces samples of higher quality and variability, but requires additional classical-quantum encoding and decoding overhead, underscoring a trade-off between expressive power and hardware efficiency. We demonstrate our method on MNIST images encoded as quantum states, as sample quality is easier to visualize and objective metrics are more widely available. While our results do not surpass classical diffusion models in the generation of classical samples, this study suggests the viability of using quantum diffusion models for learning quantum state distributions.