Error Propagation Theory for Variational Non-Markovian Open Quantum Dynamics

Abstract:Variational approaches based on neural quantum states and physics-informed neural networks provide powerful paradigms for simulating non-Markovian open quantum dynamics. However, extending these methods into the strongly non-Markovian regime reveals a critical bottleneck: even minute errors in the time evolution can translate into substantial deviations in physical observables. The fundamental origin of this stringent precision requirement, as well as how non-Markovianity governs it, remains an open question. Here, we develop a theoretical framework that systematically characterizes error propagation in variational non-Markovian dynamics. By combining analytical derivations with numerical verification, we present the first quantitative description of variational error evolution over time. Our analysis uncovers an intrinsic error-backflow mechanism driven by long-lived environmental memory. This mechanism establishes a fundamental precision barrier and provides concrete guidance for designing robust variational algorithms for strongly non-Markovian quantum systems.

arXiv:2608.22404 [quant-ph]

(or arXiv:2608.22404v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.22404 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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