Structure-preserving numerical schemes for Lindblad equations

TL;DR

This paper introduces a family of high-order, structure-preserving numerical schemes for Lindblad equations that maintain physical properties and improve accuracy, facilitating advanced quantum simulations.

Contribution

The paper develops a simple, high-order deterministic scheme family that preserves physical structure and overcomes issues of traditional methods for Lindblad equations.

Findings

Achieves arbitrary high-order accuracy in theory

Overcomes non-physical issues of traditional schemes

Validated through numerical examples

Abstract

We study a family of structure-preserving deterministic numerical schemes for Lindblad equations. This family of schemes has a simple form and can systemically achieve arbitrary high-order accuracy in theory. Moreover, these schemes can also overcome the non-physical issues that arise from many traditional numerical schemes. Due to their preservation of physical nature, these schemes can be straightforwardly used as backbones for further developing randomized and quantum algorithms in simulating Lindblad equations. In this work, we systematically study this family of structure-preserving deterministic schemes and perform a detailed error analysis, which is validated through numerical examples.