Quantum Simulation of Open Quantum Dynamics via Non-Markovian Quantum State Diffusion

TL;DR

This paper presents a hybrid quantum-classical algorithm for simulating non-Markovian open quantum systems, reducing resource requirements and revealing enhanced dynamic quantum phase transitions due to non-Markovian effects.

Contribution

The authors develop a variational quantum simulation method for non-Markovian dynamics using a complex frequency mode formulation, enabling efficient simulation of dissipative quantum systems.

Findings

Demonstrated simulation of the spin-boson model.

Observed enhanced dynamic quantum phase transitions in TFIM.

Reduced qubit requirements for non-Markovian simulations.

Abstract

Quantum simulation of non-Markovian open quantum dynamics is essential but challenging for standard quantum computers due to their non-Hermitian nature, leading to non-unitary evolution, and the limitations of available quantum resources. Here we introduce a hybrid quantum-classical algorithm designed for simulating dissipative dynamics in system with non-Markovian environment. Our approach includes formulating a non-Markovian Stochastic Schr\"odinger equation with complex frequency modes (cNMSSE) where the non-Markovianity is characterized by the mode excitation. Following this, we utilize variational quantum simulation to capture the non-unitary evolution within the cNMSSE framework, leading to a substantial reduction in qubit requirements. To demonstrate our approach, we investigated the spin-boson model and dynamic quantum phase transitions (DQPT) within transverse field Ising model (TFIM). Significantly, our findings reveal the enhanced DQPT in TFIM due to non-Markovian behavior.