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arXiv · 2602.13797

Efficient Simulation of Non-Markovian Path Integrals via Imaginary Time Evolution of an Effective Hamiltonian

Xiaoyu Yang·Limin Liu·Wencheng Zhao·Jiajun Ren·Wei-Hai Fang
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Abstract

Accurately simulating the non-Markovian dynamics of open quantum systems remains a significant challenge. While the recently proposed time-evolving matrix product operator (TEMPO) algorithm based on path integrals successfully circumvents the exponential scaling associated with memory length, its reliance on layer-by-layer tensor contractions and compressions leads to steep scaling with respect to the system Hilbert space dimension. In this work, we introduce the effective Hamiltonian-based TEMPO (EH-TEMPO) algorithm, which reformulates the calculation of the Feynman-Vernon influence functional as an imaginary time evolution governed by an effective Hamiltonian. We demonstrate that this effective Hamiltonian admits a highly compact matrix product operator representation, enabling substantial compression with negligible loss of accuracy. Combining a one-shot global evolution with a backward retrieval approach, EH-TEMPO significantly reduces algorithmic complexity and is naturally suited for GPU acceleration. We benchmark the method by simulating the energy transfer dynamics in the 7-site Fenna-Matthews-Olson complex model and 4-site perylene bisimide model. The results demonstrate that EH-TEMPO achieves numerically exact accuracy with superior efficiency, delivering speedups of up to 17.5$\times$ on GPU hardware compared to standard CPU implementations.

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Xiaoyu Yang, Limin Liu, Wencheng Zhao, Jiajun Ren, Wei-Hai Fang. 2026-06-09. Efficient Simulation of Non-Markovian Path Integrals via Imaginary Time Evolution of an Effective Hamiltonian. https://arxiv.org/abs/2602.13797

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