From quantum-enhanced to quantum-inspired Monte Carlo

TL;DR

This paper analyzes the quantum-enhanced Monte Carlo method, identifying optimal parameters, exploring circuit extensions, and proposing classical simulators to extend its utility as a quantum-inspired algorithm before large-scale quantum hardware is available.

Contribution

It provides a comprehensive analysis of the quantum-enhanced Monte Carlo method, including optimal working points, circuit extensions, and the use of classical simulators to maintain advantages.

Findings

Optimal mixing Hamiltonian strength identified

Tensor-network simulators can maintain scaling advantage

Quantum-inspired Monte Carlo can be effective with classical simulators

Abstract

We perform a comprehensive analysis of the quantum-enhanced Monte Carlo method [Nature, 619, 282-287 (2023)], aimed at identifying the optimal working point of the algorithm. We observe an optimal mixing Hamiltonian strength and analyze the scaling of the total evolution time with the size of the system. We also explore extensions of the circuit, including the use of time-dependent Hamiltonians and reverse digitized annealing. Additionally, we propose that classical, approximate quantum simulators can be used for the proposal step instead of the original real-hardware implementation. We observe that tensor-network simulators, even with unconverged settings, can maintain a scaling advantage over standard classical samplers. This may extend the utility of quantum-enhanced Monte Carlo as a quantum-inspired algorithm, even before the deployment of large-scale quantum hardware.