Kraus is King: High-order Completely Positive and Trace Preserving (CPTP) Low Rank Method for the Lindblad Master Equation

TL;DR

This paper introduces high-order numerical methods for the Lindblad master equation that leverage low-rank structures, ensuring complete positivity and trace preservation, thus improving efficiency and accuracy in quantum dynamics simulations.

Contribution

The paper presents a novel high-order method that exploits low-rank structures in density matrices while maintaining the physical properties of the Lindblad equation.

Findings

Methods preserve complete positivity and trace

Achieve high-order accuracy in simulations

Efficiently handle low-rank density matrices

Abstract

We design high order accurate methods that exploit low rank structure in the density matrix while respecting the essential structure of the Lindblad equation. Our methods preserves complete positivity and are trace preserving.