Accelerated Quantum Monte Carlo with Probabilistic Computers

TL;DR

This paper demonstrates significant acceleration of Quantum Monte Carlo algorithms using specialized digital and analog processors, potentially enabling faster simulations of quantum models with performance close to quantum annealers.

Contribution

It introduces a novel hardware approach that accelerates QMC simulations by up to six orders of magnitude, providing a benchmark and roadmap for future quantum and classical computing integrations.

Findings

Achieved 2-3 orders of magnitude acceleration with digital processors.

Further 2-3 orders of magnitude acceleration with analog processors.

Analog hardware performance within a factor of 10 of quantum annealers.

Abstract

Quantum Monte Carlo (QMC) techniques are widely used in a variety of scientific problems and much work has been dedicated to developing optimized algorithms that can accelerate QMC on standard processors (CPU). With the advent of various special purpose devices and domain specific hardware, it has become increasingly important to establish clear benchmarks of what improvements these technologies offer compared to existing technologies. In this paper, we demonstrate 2 to 3 orders of magnitude acceleration of a standard QMC algorithm using a specially designed digital processor, and a further 2 to 3 orders of magnitude by mapping it to a clockless analog processor. Our demonstration provides a roadmap for 5 to 6 orders of magnitude acceleration for a transverse field Ising model (TFIM) and could possibly be extended to other QMC models as well. The clockless analog hardware can be viewed as the classical counterpart of the quantum annealer and provides performance within a factor of $<10$ of the latter. The convergence time for the clockless analog hardware scales with the number of qubits as $\sim N$, improving the $\sim N^2$ scaling for CPU implementations, but appears worse than that reported for quantum annealers by D-Wave.