Towards Quantum Simulation of Non-Markovian Open Quantum Dynamics: A Universal and Compact Theory

TL;DR

This paper introduces a universal, compact quantum master equation framework, DQME-SQ, enabling efficient digital quantum simulations of non-Markovian open quantum systems across various environments.

Contribution

The paper presents the DQME-SQ theory, a universal and exact approach for simulating non-Markovian dynamics on quantum computers, applicable to Gaussian environments.

Findings

Demonstrated digital quantum simulations of bosonic and fermionic non-Markovian dynamics.

Showed DQME-SQ's representability by quantum circuits and universal applicability.

Enabled exploration of complex open quantum systems with quantum computing.

Abstract

Non-Markovianity, the intricate dependence of an open quantum system on its temporal evolution history, holds tremendous implications across various scientific disciplines. However, accurately characterizing the complex non-Markovian effects has posed a formidable challenge for numerical simulations. While quantum computing technologies show promise, a universal theory enabling practical quantum algorithm implementation has been elusive. We address this gap by introducing the dissipaton-embedded quantum master equation in second quantization (DQME-SQ). This exact and compact theory offers two key advantages: representability by quantum circuits and universal applicability to any Gaussian environment. We demonstrate these capabilities through digital quantum simulations of non-Markovian dissipative dynamics in both bosonic and fermionic environments. The DQME-SQ framework opens a new horizon for the efficient exploration of complex open quantum systems by leveraging the rapidly advancing quantum computing technologies.