# Quantum-enhanced Markov chain Monte Carlo

arXiv: https://arxiv.org/abs/2203.12497 · HTML: https://mlsanity.com/paper/2203.12497/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 89 references that are in the map.
- First posted on arXiv 23 Mar 2022.

## Builds on (most cited first, 7 of 7)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Ising formulations of many NP problems](https://mlsanity.com/paper/1302.5843/) (2013)
- [Mixing time estimation in reversible Markov chains from a single sample path](https://mlsanity.com/paper/1708.07367/) (2017)
- [Scan Order in Gibbs Sampling: Models in Which it Matters and Bounds on How Much](https://mlsanity.com/paper/1606.03432/) (2016)
- [Rapid Mixing Swendsen-Wang Sampler for Stochastic Partitioned Attractive Models](https://mlsanity.com/paper/1704.02232/) (2017)
- [Optimization of population annealing Monte Carlo for large-scale spin-glass simulations](https://mlsanity.com/paper/1710.09025/) (2017)
- [Szegedy Walk Unitaries for Quantum Maps](https://mlsanity.com/paper/2107.07365/) (2021)

## Built on by (most cited first, 6 of 6)

- [Scalable quantum dynamics compilation via quantum machine learning](https://mlsanity.com/paper/2409.16346/) (2024)
- [Quantum Computing and AI: Perspectives on Advanced Automation in Science and Engineering](https://mlsanity.com/paper/2505.10012/) (2025)
- [Machine-Learning-Assisted Photonic Device Development: A Multiscale Approach from Theory to Characterization](https://mlsanity.com/paper/2506.20056/) (2025)
- [An End-to-End Hybrid Quantum-Classical Sampling Workflow for Discrete Markov Random Fields: A Reproducible Case Study](https://mlsanity.com/paper/2607.09893/) (2026)
- [Practical advantage beyond the quadratic speedup limit with fully-quantum walks](https://mlsanity.com/paper/2607.22818/) (2026)
- [Degeneracy Counting Quantum Algorithm using Decoherence](https://mlsanity.com/paper/2608.14941/) (2026)

## Abstract (arXiv)

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.