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This research establishes a rigorous reverse-time denoising theory for continuously measured quantum systems, drawing a direct parallel to the score functions used in classical generative diffusion models. By deriving exact reverse-time dynamics from forward stochastic Schrödinger equations, the work provides a principled framework for generating complex ensembles of quantum states from simpler distributions using learned feedback Hamiltonians. This advancement bridges theoretical quantum mechanics with practical generative modeling techniques, potentially enabling new methods for quantum state preparation and simulation.
Generating quantum ensembles via reverse-time quantum diffusions
arXiv:2606.03848v2 Announce Type: replace Abstract: We establish a reverse-time denoising theory for quantum diffusions of continuously measured quantum systems. Starting from the stochastic Schr\"odinger 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.
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.
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)
arXiv:2606.03848 [quant-ph]
(or arXiv:2606.03848v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2606.03848 Focus to learn more arXiv-issued DOI via DataCite
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