Hybrid Quantum Algorithm for Simulating Real-Time Thermal Correlation Functions

Abstract

We present a hybrid Path Integral Monte Carlo (hPIMC) algorithm to calculate real-time quantum thermal correlation functions for condensed phase 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. Our method does not rely on variational quantum algorithms and offers an alternative path for near-term quantum algorithm design. We show that by using a quantum computer to compute short-time matrix elements of the quantum propagator, our hybrid algorithm achieves an asymptotic quantum speed-up over its classical counterpart. We employ the recently developed Probabilistic Imaginary-Time Evolution (PITE) algorithm to simulate imaginary-time evolution accurately, and we introduce a novel low-depth circuit that simulates evolution under the kinetic energy operator using an approximate Discrete Variable Representation (DVR). We investigate the accuracy of combining PITE with the approximate DVR by computing the position-position thermal correlation function of a proton transfer reaction on a classical computer. We estimate the circuit depth and CNOT gate count to compute short-time matrix elements for a 1D system with our method to be on the order of 10⁵ with a space overhead of 30 qubits.