Creating Non-Equilibrium States with Quantum Generative Models

Abstract

Quantum denoising diffusion models (QDDMs) have recently been proposed as generative models for quantum-state distributions, with existing approaches primarily designed for pure or nearly pure-state ensembles. In this work, we develop design strategies to extend QDDMs to complex mixed-state distributions. The main modification to the denoising architecture introduces a Haar-random auxiliary qubit and replaces post-measurement extraction with a partial trace over the auxiliary qubits, naturally enabling mixed-state generation. We investigate different auxiliary-state constructions and two forward diffusion processes based on depolarizing noise and scrambling circuits. The proposed framework is benchmarked on single-qubit distributions and mixed-state ensembles arising from open quantum-system dynamics, including thermal and non-equilibrium steady-state distributions, extending the evaluation to physically motivated ensembles. Across the benchmarks considered, the partial-trace approach generally achieves better reconstruction for single-qubit mixed-state distributions and accurately reproduces the considered steady-state distributions, while post-measurement approach remains advantageous for pure-state ensembles. We further find that the choice of auxiliary states strongly influences the geometry of the generated distributions, whereas no systematic advantage is observed between depolarizing and scrambling diffusion. Finally, we demonstrate the feasibility of implementing the proposed framework on a real quantum processor through an adaptation for IBM Quantum hardware.