Improved Efficiency of Open Quantum System Simulations Using Matrix Products States in the Interaction Picture

TL;DR

This paper introduces an interaction picture approach with matrix product states that significantly reduces computational costs in simulating open quantum systems, especially under high-temperature and strong-coupling conditions.

Contribution

The authors develop a novel interaction picture method that lowers computational costs and accelerates simulations of open quantum systems using matrix product states.

Findings

Accelerates simulations by 1-2 orders of magnitude over existing methods.

Achieves up to 3 orders of magnitude speedup in high-temperature, strong-coupling regimes.

Effective in modeling open quantum systems with highly excited baths.

Abstract

Modeling open quantum systems -- quantum systems coupled to a bath -- is of value in condensed matter theory, cavity quantum electrodynamics, nanosciences and biophysics. The real-time simulation of open quantum systems was advanced significantly by the recent development of chain mapping techniques and the use of matrix product states that exploit the intrinsic entanglement structure in open quantum systems. The computational cost of simulating open quantum systems, however, remains high when the bath is excited to high-lying quantum states. We develop an approach to reduce the computational costs in such cases. The interaction representation for the open quantum system is used to distribute excitations among the bath degrees of freedom so that the occupation of each bath oscillator is ensured to be low. The interaction picture also causes the matrix dimensions to be much smaller in a matrix product state of a chain-mapped open quantum system than in the Schr\"odinger picture. Using the interaction representation accelerates the calculations by 1-2 orders of magnitude over existing matrix-product-state method. In the regime of strong system-bath coupling and high temperatures, the speedup can be as large as 3 orders of magnitude. The approach developed here is especially promising to simulate the dynamics of open quantum systems in the high-temperature and strong-coupling regimes.