Faster Quantum Monte Carlo Simulation by Random Compilation
Abstract
Quantum Monte Carlo (QMC) algorithms are among the most powerful classical methods for simulating quantum systems, yet their accuracy is often limited by the systematic errors in the approximations used, such as Trotterization. Here we introduce randomly compiled quantum Monte Carlo (RC-QMC) as a general framework that suppresses these systematic errors by averaging over a family of approximations rather than relying on a single fixed one. This strategy is grounded in the concept of randomized compiling from quantum computing, which suppresses errors by sampling over quantum gates, at essentially no additional computational cost. Consequently, our framework achieves a computational advantage over standard QMC methods when estimating a target state to a desired level of accuracy. We illustrate this advantage on two key Monte Carlo algorithms: (1) path integral quantum Monte Carlo for estimating thermal states, and (2) the quantum trajectories method for simulating open system dynamics. In aggregate, these results represent a cross-fertilization of quantum and classical algorithms, are readily generalizable to other QMC methods, and suggest wider applications in classical simulation.
Related
- A Compilation Framework for Quantum Simulation of Non-unitary Dynamics
- Bidirectional Path Integral Monte Carlo Simulation of Quantum Circuits
- Fast and accurate rare-event simulation by Markov chain Monte Carlo for general quantum codes
- Numerical simulation of D-Wave's quantum advantage experiment with time-dependent variational Monte Carlo
- Classical simulation of amplitude-damped bucket-brigade quantum random access memories via predictable branch evolution
BibTeX
@misc{martyn2026faster,
title = {{Faster Quantum Monte Carlo Simulation by Random Compilation}},
author = {John M. Martyn and Joshua Lin and Neill C. Warrington and Isaac L. Chuang and Andrew J. Daley},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10486},
eprint = {2609.10486},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10486},
}
RIS
TY - UNPB
TI - Faster Quantum Monte Carlo Simulation by Random Compilation
AU - John M. Martyn
AU - Joshua Lin
AU - Neill C. Warrington
AU - Isaac L. Chuang
AU - Andrew J. Daley
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10486
UR - https://arxiv.org/abs/2609.10486
AB - Quantum Monte Carlo (QMC) algorithms are among the most powerful classical methods for simulating quantum systems, yet their accuracy is often limited by the systematic errors in the approximations used, such as Trotterization. Here we introduce randomly compiled quantum Monte Carlo (RC-QMC) as a general framework that suppresses these systematic errors by averaging over a family of approximations rather than relying on a single fixed one. This strategy is grounded in the concept of randomized compiling from quantum computing, which suppresses errors by sampling over quantum gates, at essentially no additional computational cost. Consequently, our framework achieves a computational advantage over standard QMC methods when estimating a target state to a desired level of accuracy. We illustrate this advantage on two key Monte Carlo algorithms: (1) path integral quantum Monte Carlo for estimating thermal states, and (2) the quantum trajectories method for simulating open system dynamics. In aggregate, these results represent a cross-fertilization of quantum and classical algorithms, are readily generalizable to other QMC methods, and suggest wider applications in classical simulation.
ER -