Understanding Quantum Tunneling through Quantum Monte Carlo Simulations

TL;DR

This paper demonstrates that quantum Monte Carlo simulations can accurately predict tunneling rates in quantum annealing, showing a quadratic speedup with open boundary conditions and providing insights through an instanton framework.

Contribution

It reveals the scaling behavior of QMC tunneling rates and introduces a method to predict quantum annealer performance using QMC simulations with improved efficiency.

Findings

QMC tunneling rate scales as $O( ext{Δ}^2)$, matching incoherent tunneling.

Open boundary conditions in QMC lead to a quadratic speedup.

QMC can effectively predict quantum annealer performance.

Abstract

The tunneling between the two ground states of an Ising ferromagnet is a typical example of many-body tunneling processes between two local minima, as they occur during quantum annealing. Performing quantum Monte Carlo (QMC) simulations we find that the QMC tunneling rate displays the same scaling with system size, as the rate of incoherent tunneling. The scaling in both cases is $O(\Delta^2)$, where $\Delta$ is the tunneling splitting. An important consequence is that QMC simulations can be used to predict the performance of a quantum annealer for tunneling through a barrier. Furthermore, by using open instead of periodic boundary conditions in imaginary time, equivalent to a projector QMC algorithm, we obtain a quadratic speedup for QMC, and achieve linear scaling in $\Delta$. We provide a physical understanding of these results and their range of applicability based on an instanton picture.