Arbitrary High Order Low-rank Completely Positive and Trace Preserving (CPTP) Schemes for Lindblad Equations with Time-dependent Hamiltonian

TL;DR

This paper introduces a flexible framework for constructing high-order, low-rank numerical schemes for Lindblad equations with time-dependent Hamiltonians, ensuring physical properties like complete positivity and trace preservation.

Contribution

It presents a novel approach using nested Picard iterative integrators to develop arbitrary high-order, low-rank CPTP schemes for Lindblad equations with time-dependent Hamiltonians.

Findings

Schemes are in Kraus form ensuring complete positivity.

Methods are suitable for low-rank density matrices.

Framework allows high-order accuracy for complex quantum dynamics.

Abstract

In this paper, we develop a framework for designing arbitrary high order low-rank schemes for the Lindblad equation with time-dependent Hamiltonians. Our approach is based on nested Picard iterative integrators (NPI) and results in schemes in Kraus form that are completely positive and trace preserving (CPTP). The schemes are amenable to low rank formulations, making them suitable for problems where the matrix rank of the density matrix is small.