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arXiv:2405.04247 · Physical Review Research

Quantum-enhanced Markov chain Monte Carlo for systems larger than a quantum computer

Stuart Ferguson, Petros Wallden

Published Mar 3, 2025• 4 citations

Abstract

Quantum computers theoretically promise computational advantages in many tasks, but it is much less clear how such advantages can be maintained when using existing and near-term hardware that has limitations in the number and quality of its qubits. Layden [] proposed a promising application by introducing a quantum-enhanced Markov chain Monte Carlo (QeMCMC) approach to reduce the thermalization time required when sampling from hard probability distributions. In QeMCMC, the size of the required quantum computer scales linearly with the problem, placing limitations on the sizes of systems that can be considered. In this paper we introduce a framework to coarse grain the algorithm in such a way that the quantum computation can be performed using considerably smaller quantum computers and we term the method the coarse grained quantum-enhanced Markov chain Monte Carlo (CGQeMCMC). Example strategies within this framework are put to the test, with the quantum speedup persisting while using only n simulated qubits where n is the number of qubits required in the original QeMCMC—a quadratic reduction in resources. The coarse graining framework has the potential to be practically applicable in the near term as it requires very few qubits to approach classically intractable problem instances; in this case, only six simulated qubits suffice to gain an advantage compared with standard classical approaches when investigating the magnetization of a 36-spin system. Our method can be easily combined with other classical and quantum techniques and is adaptable to various quantum hardware specifications—in particular those with limited connectivity.

DOI: 10.1103/physrevresearch.7.013231

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Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from complicated distributions that are hard to sample from classically, but which seldom arise in applications. Here we introduce a quantum algorithm to sample from distributions that pose a bottleneck in several applications, which we implement on a superconducting quantum processor. The algorithm performs Markov chain Monte Carlo (MCMC), a popular iterative sampling technique, to sample from the Boltzmann distribution of classical Ising models. In each step, the quantum processor explores the model in superposition to propose a random move, which is then accepted or rejected by a classical computer and returned to the quantum processor, ensuring convergence to the desired Boltzmann distribution. We find that this quantum algorithm converges in fewer iterations than common classical MCMC alternatives on relevant problem instances, both in simulations and experiments. It therefore opens a new path for quantum computers to solve useful--not merely difficult--problems in the near term.