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

TL;DR

The paper introduces EH-TEMPO, an efficient algorithm for simulating non-Markovian quantum dynamics by reformulating influence functionals as imaginary time evolutions, achieving high accuracy and significant computational speedups.

Contribution

It presents a novel effective Hamiltonian approach that compresses the influence functional, enabling faster and more scalable simulations of open quantum systems.

Findings

Achieves up to 17.5x speedup on GPU hardware.

Maintains numerically exact accuracy.

Demonstrates superior efficiency over existing methods.

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 against the process tensor TEMPO algorithm using the 7-site Fenna-Matthews-Olson complex model. The results demonstrate that EH-TEMPO achieves numerically exact accuracy with superior efficiency, delivering speedups of up to 17.5x on GPU hardware compared to standard CPU implementations.