Unitary Dynamics for Open Quantum Systems with Density-Matrix Purification

TL;DR

This paper introduces a density-matrix purification method that maps non-unitary open quantum system dynamics onto a unitary framework, facilitating simulation on quantum computers and capturing both Markovian and non-Markovian behaviors.

Contribution

The work develops a novel purification approach that extends open quantum system modeling, enabling unitary simulation of complex non-unitary dynamics and deriving interactions from fundamental principles.

Findings

Purification extends beyond complete positivity.

Effectively models Markovian and non-Markovian dynamics.

Demonstrated on quantum simulator with successful mapping.

Abstract

Accurate modeling of quantum systems interacting with environments requires addressing non-unitary dynamics, which significantly complicates computational approaches. In this work, we enhance an open quantum system (OQS) theory using density-matrix purification, enabling a unitary description of dynamics by entangling the system with an environment of equal dimension. We first establish the connection between density-matrix purification and conventional OQS methods. We then demonstrate the standalone applicability of purification theory by deriving system-environment interactions from fundamental design principles. Using model systems, we show that the purification approach extends beyond the complete positivity condition and effectively models both Markovian and non-Markovian dynamics. Finally, we implement density-matrix purification on a quantum simulator, illustrating its capability to map non-unitary OQS dynamics onto a unitary framework suitable for quantum computers.