Three approaches for representing Lindblad dynamics by a matrix-vector notation

TL;DR

This paper reviews three methods to represent Lindblad dynamics in matrix-vector form, improving numerical implementation for open quantum systems, demonstrated on a driven two-level system with spontaneous emission.

Contribution

It introduces and compares three approaches for matrix-vector representation of Lindblad dynamics, enhancing computational efficiency in quantum system simulations.

Findings

All three methods successfully represent Lindblad dynamics in matrix-vector form.

The approaches are demonstrated on a driven two-level system with spontaneous emission.

The methods improve numerical implementation of open quantum system simulations.

Abstract

Markovian dynamics of open quantum systems are described by the L-GKS equation, known also as the Lindblad equation. The equation is expressed by means of left and right matrix multiplications. This formulation hampers numerical implementations. Representing the dynamics by a matrix-vector notation overcomes this problem. We review three approaches to obtain such a representation. The methods are demonstrated for a driven two-level system subject to spontaneous emission.