Quantum Diffusion Models

Denoising diffusion probabilistic models have become increasingly important in machine learning, but their quantum counterpart has not been studied yet. In this work, we propose a quantum version of a generative diffusion model. In this algorithm, artificial neural networks are replaced with parameterized quantum circuits, in order to manipulate quantum states directly. We present both a full quantum version and a latent classical-quantum version of the algorithm. In the latent model, the parameterized quantum circuits are trained in a low dimensional representation of data, obtained by employing a pre-trained classical autoencoder. For both models, we show a method for conditioning the output distribution, utilizing ancillary qubits. The models' performance have been evaluated using quantitative metrics complemented by qualitative assessments. For the latent model, we show the implementation of a simplified version on real quantum hardware. The execution on a NISQ device allows to evaluate the performance of the algorithm in the presence of noise.