Error Propagation Theory for Variational Non-Markovian Open Quantum Dynamics

• URL: http://arxiv.org/abs/2608.22404v1
• Date: Sun, 23 Aug 2026 13:17:46 GMT
• Title: Error Propagation Theory for Variational Non-Markovian Open Quantum Dynamics
• Abstract summary: Even minute errors in the time evolution can translate into substantial deviations in physical observables.<n>We develop a theoretical framework that characterizes error propagation in variational non-Markovian dynamics.<n>Our analysis uncovers an intrinsic error-backflow mechanism driven by long-lived environmental memory.
• Score: 10.049898018843265
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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