Generic Method for Integrating Lindblad Master Equations

TL;DR

This paper introduces a generic, efficient method for solving Lindblad master equations in open quantum systems by expanding the Lindbladian exponential into a truncated Taylor series, improving computational efficiency and compatibility with tensor networks.

Contribution

The paper presents a novel approach to integrate Lindblad equations using a truncated Taylor series, enhancing numerical efficiency and enabling seamless tensor network integration.

Findings

Method improves memory and computation efficiency for large systems

Validated with examples of damped Rabi oscillations and Heisenberg chain

Outperforms existing techniques in benchmark tests

Abstract

The time evolution of Markovian open quantum systems is governed by Lindblad master equations, whose solution can be formally written as the Lindbladian exponential acting on the initial density matrix. By expanding this Lindbladian exponential into the Taylor series, we propose a generic method for integrating Lindblad master equations. In this method, the series is truncated, retaining a finite number of terms, and the iterative actions of Lindbladian on the density matrix follow the corresponding master equation. Our method offers significant improvements in numerical efficiencies both in memory cost and computation time, especially for systems with many degrees of freedom. Moreover, our proposed method can be integrated seamlessly with tensor networks. Two illustrative examples, a two-level system exhibiting damped Rabi oscillations and a driven dissipative Heisenberg chain, are used to demonstrate the validity of our method. The superiority of our method is benchmarked with detailed performance tests.