Hybrid quantum variational algorithm for simulating open quantum systems with near-term devices

TL;DR

This paper introduces a hybrid quantum-classical variational algorithm designed to simulate open quantum system dynamics on near-term quantum devices, leveraging the TDVP method and demonstrating good agreement with analytical results.

Contribution

It develops a novel HQC algorithm using variational optimization and the Lindblad formalism for simulating open quantum systems on NISQ devices.

Findings

The algorithm accurately simulates open system dynamics.

It extends TDVP to density matrices using Frobenius norm minimization.

Results agree well with analytical solutions.

Abstract

Hybrid quantum-classical (HQC) algorithms make it possible to use near-term quantum devices supported by classical computational resources by useful control schemes. In this paper, we develop an HQC algorithm using an efficient variational optimization approach to simulate open system dynamics under the Noisy-Intermediate Scale Quantum(NISQ) computer. Using the time-dependent variational principle (TDVP) method and extending it to McLachlan TDVP for density matrix which involves minimization of Frobenius norm of the error, we apply the unitary quantum circuit to obtain the time evolution of the open quantum system in the Lindblad formalism. Finally, we illustrate the use of our methods with detailed examples which are in good agreement with analytical calculations.