Clock Quantum Monte Carlo: an imaginary-time method for real-time quantum dynamics

TL;DR

This paper introduces a novel quantum Monte Carlo method that leverages the Feynman-Kitaev Clock to simulate real-time quantum dynamics efficiently, incorporating strategies to reduce the sign problem and enable parallel-in-time computation.

Contribution

It combines the Feynman-Kitaev Clock with FCIQMC to create a new approach for simulating quantum dynamics, including sign problem mitigation and parallelization capabilities.

Findings

Demonstrated the method on quantum circuit examples

Developed a technique for sign problem mitigation via time-dependent basis rotations

Enabled parallel-in-time quantum dynamics simulations

Abstract

In quantum information theory, there is an explicit mapping between general unitary dynamics and Hermitian ground state eigenvalue problems known as the Feynman-Kitaev Clock. A prominent family of methods for the study of quantum ground states are quantum Monte Carlo methods, and recently the full configuration interaction quantum Monte Carlo (FCIQMC) method has demonstrated great promise for practical systems. We combine the Feynman-Kitaev Clock with FCIQMC to formulate a new technique for the study of quantum dynamics problems. Numerical examples using quantum circuits are provided as well as a technique to further mitigate the sign problem through time-dependent basis rotations. Moreover, this method allows one to combine the parallelism of Monte Carlo techniques with the locality of time to yield an effective parallel-in-time simulation technique.