Simulating Open Quantum System Dynamics on NISQ Computers with Generalized Quantum Master Equations

TL;DR

This paper introduces a quantum algorithm leveraging the Generalized Quantum Master Equation to simulate open quantum system dynamics on NISQ computers, overcoming limitations of traditional methods and validated on IBM hardware.

Contribution

It develops a novel quantum algorithm using GQME and Sz.-Nagy dilation to simulate open quantum systems beyond the Lindblad approximation on NISQ devices.

Findings

Reliable results achieved on NISQ IBM computers.

Quantum circuit depth impacts accuracy.

Method extends simulation capabilities for complex open systems.

Abstract

We present a quantum algorithm based on the Generalized Quantum Master Equation (GQME) approach to simulate open quantum system dynamics on noisy intermediate-scale quantum (NISQ) computers. This approach overcomes the limitations of the Lindblad equation, which assumes weak system-bath coupling and Markovity, by providing a rigorous derivation of the equations of motion for any subset of elements of the reduced density matrix. The memory kernel resulting from the effect of the remaining degrees of freedom is used as input to calculate the corresponding non-unitary propagator. We demonstrate how the Sz.-Nagy dilation theorem can be employed to transform the non-unitary propagator into a unitary one in a higher-dimensional Hilbert space, which can then be implemented on quantum circuits of NISQ computers. We validate our quantum algorithm as applied to the spin-boson benchmark model by analyzing the impact of the quantum circuit depth on the accuracy of the results when the subset is limited to the diagonal elements of the reduced density matrix. Our findings demonstrate that our approach yields reliable results on NISQ IBM computers.