Hybrid Quantum Algorithm for Simulating Real-Time Thermal Correlation Functions

TL;DR

This paper introduces a hybrid quantum-classical algorithm for simulating real-time thermal correlation functions in open quantum systems, combining classical path integral techniques with quantum computing for speed-up.

Contribution

It develops a hybrid Path Integral Monte Carlo method utilizing quantum computing for short-time propagator calculations and introduces a low-depth circuit for real-time evolution.

Findings

Achieved quantum speed-up in computing quantum propagators.

Accurately computed thermal correlation functions for a proton transfer.

Demonstrated effectiveness of the hybrid algorithm on open quantum systems.

Abstract

We present a hybrid Path Integral Monte Carlo (hPIMC) algorithm to calculate real-time quantum thermal correlation functions and demonstrate its application to open quantum systems. The hPIMC algorithm leverages the successes of classical PIMC as a computational tool for high-dimensional system studies by exactly simulating dissipation using the Feynman-Vernon influence functional on a classical computer. We achieve a quantum speed-up over the classical algorithm by computing short-time matrix elements of the quantum propagator on a quantum computer. We show that the component of imaginary-time evolution can be performed accurately using the recently developed Probabilistic Imaginary-Time Evolution (PITE) algorithm, and we introduce a novel low-depth circuit for approximate real-time evolution under the kinetic energy operator using a Discrete Variable Representation (DVR). We test the accuracy of the approximation by computing the position-position thermal correlation function of a proton transfer reaction.