Generating quantum ensembles via reverse-time quantum diffusions
Abstract
We establish a reverse-time denoising theory for quantum diffusions of continuously measured quantum systems. Starting from the stochastic Schrödinger equation of a forward noising dynamics, we derive the exact reverse-time dynamics for quantum trajectories, whose law coincides with the time-reversal of the original process. We prove that the denoising dynamics is a physically admissible quantum diffusion, with the same measurement-induced noise but a state-dependent feedback Hamiltonian, a direct analogue of the "score function" of generative classical diffusion models. This provides a principled framework for converting samples of a simple distribution into those of a more complex ensemble of quantum states. We show how the denoising dynamics can be directly learnt from forward trajectory data, and how to exploit purification to initialise the denoising process.
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BibTeX
@misc{bompais2026generating,
title = {{Generating quantum ensembles via reverse-time quantum diffusions}},
author = {Maël Bompais and Mădălin Guţă and Juan P. Garrahan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.03848},
eprint = {2606.03848},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.03848},
}
RIS
TY - UNPB
TI - Generating quantum ensembles via reverse-time quantum diffusions
AU - Maël Bompais
AU - Mădălin Guţă
AU - Juan P. Garrahan
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2606.03848
UR - https://arxiv.org/abs/2606.03848
AB - We establish a reverse-time denoising theory for quantum diffusions of continuously measured quantum systems. Starting from the stochastic Schrödinger equation of a forward noising dynamics, we derive the exact reverse-time dynamics for quantum trajectories, whose law coincides with the time-reversal of the original process. We prove that the denoising dynamics is a physically admissible quantum diffusion, with the same measurement-induced noise but a state-dependent feedback Hamiltonian, a direct analogue of the "score function" of generative classical diffusion models. This provides a principled framework for converting samples of a simple distribution into those of a more complex ensemble of quantum states. We show how the denoising dynamics can be directly learnt from forward trajectory data, and how to exploit purification to initialise the denoising process.
ER -