Simulation of open quantum systems on universal quantum computers

TL;DR

This paper introduces a scalable method for simulating open quantum systems on quantum computers, enabling the study of dissipative dynamics and steady states without auxiliary qubits, advancing practical quantum advantage demonstrations.

Contribution

The authors propose a novel approach using an adjoint density matrix to simulate non-unitary open quantum system dynamics efficiently on quantum computers.

Findings

Effective sampling of the adjoint density matrix without auxiliary qubits.

Ability to analyze long-time properties like steady states and thermal equilibrium.

Successful application to dissipative XY and disordered Heisenberg models.

Abstract

The rapid development of quantum computers has enabled demonstrations of quantum advantages on various tasks. However, real quantum systems are always dissipative due to their inevitable interaction with the environment, and the resulting non-unitary dynamics make quantum simulation challenging with only unitary quantum gates. In this work, we present an innovative and scalable method to simulate open quantum systems using quantum computers. We define an adjoint density matrix as a counterpart of the true density matrix, which reduces to a mixed-unitary quantum channel and thus can be effectively sampled using quantum computers. This method has several benefits, including no need for auxiliary qubits and noteworthy scalability. Moreover, some long-time properties like steady states and the thermal equilibrium can also be investigated as the adjoint density matrix and the true dissipated one converge to the same state. Finally, we present deployments of this theory in the dissipative quantum $XY$ model for the evolution of correlation and entropy with short-time dynamics and the disordered Heisenberg model for many-body localization with long-time dynamics. This work promotes the study of real-world many-body dynamics with quantum computers, highlighting the potential to demonstrate practical quantum advantages.