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.
Numerical integration with Monte Carlo methods is a central computational task in many scientific and industrial applications, including financial derivative pricing and risk management. Classical Monte Carlo algorithms are computationally demanding: achieving an accuracy $\epsilon$ typically requires a number of funct...
Paolo Recchia, Yu Zhan, Kelvin Koor et al.· 0 citations
Monte Carlo methods are fundamental to finance, system verification, and scientific simulation, but converge slowly: achieving an additive error of є requires O(1/є2) samples. Quantum Amplitude Estimation (QAE) offers a quadratic speedup by encoding the target probabilistic model into a quantum circuit. However, constr...
Seungmin Jeon, Jaeho Choi, J. Jeon et al.· Proceedings of the ACM on Pr...· 0 citations
This work develops a framework for randomized Hamiltonian simulation in which Hamiltonian terms are sampled with arbitrary probabilities and the corresponding short-time evolutions are implemented sequentially, establishing average-error optimization as a practical design principle for randomized Hamiltonian simulation...
The Monte Carlo Projective Quantum Eigensolver (MC-PQE) was recently introduced as an alternative to hybrid algorithms like the variational quantum eigensolver (VQE). By using a quantum Monte Carlo-inspired scheme for energy estimation, MC\nobreakdash-PQE was found to decrease the required measurement cost relative to...
Quantum Monte Carlo (QMC) methods are among the central numerical tools for studying strongly correlated quantum many-body systems, particularly in higher dimensions. As quantum information has introduced new information-theoretic perspectives and diagnostics into many-body physics, QMC methods have accordingly been ex...
Determining whether a quantum evolution can be efficiently simulated classically is central to understanding the boundary between classical and quantum computation. However, polynomial-time simulability is an asymptotic statement, and does not by itself determine whether the (quantum-inspired) classical simulation is a...
Su-Ye-On Chang, Supanut Thanasilp, Zoe Holmes et al.· 0 citations
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