# A hybrid quantum-classical approach for inference on restricted Boltzmann machines

arXiv: https://arxiv.org/abs/2304.12418 · HTML: https://mlsanity.com/paper/2304.12418/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 38 references that are in the map.
- First posted on arXiv 31 Mar 2023.

## Builds on (most cited first, 16 of 16)

- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Assessing Generative Models via Precision and Recall](https://mlsanity.com/paper/1806.00035/) (2018)
- [Pros and Cons of GAN Evaluation Measures: New Developments](https://mlsanity.com/paper/2103.09396/) (2021)
- [Application of Quantum Annealing to Training of Deep Neural Networks](https://mlsanity.com/paper/1510.06356/) (2015)
- [Learning and Inference on Generative Adversarial Quantum Circuits](https://mlsanity.com/paper/1808.03425/) (2018)
- [Reinforcement Learning Using Quantum Boltzmann Machines](https://mlsanity.com/paper/1612.05695/) (2016)
- [Training and Classification using a Restricted Boltzmann Machine on the D-Wave 2000Q](https://mlsanity.com/paper/2005.03247/) (2020)
- [A Path Towards Quantum Advantage in Training Deep Generative Models with Quantum Annealers](https://mlsanity.com/paper/1912.02119/) (2019)
- [Restricted Boltzmann Machines for galaxy morphology classification with a quantum annealer](https://mlsanity.com/paper/1911.06259/) (2019)
- [A Hybrid Quantum enabled RBM Advantage: Convolutional Autoencoders For Quantum Image Compression and Generative Learning](https://mlsanity.com/paper/2001.11946/) (2020)
- [Comparison of D-Wave Quantum Annealing and Classical Simulated Annealing for Local Minima Determination](https://mlsanity.com/paper/1911.03338/) (2019)
- [Training a quantum annealing based restricted Boltzmann machine on cybersecurity data](https://mlsanity.com/paper/2011.13996/) (2020)
- [On the challenges of using D-Wave computers to sample Boltzmann Random Variables](https://mlsanity.com/paper/2111.15295/) (2021)
- [Towards Sampling from Nondirected Probabilistic Graphical models using a D-Wave Quantum Annealer](https://mlsanity.com/paper/1905.00159/) (2019)
- [Generative and discriminative training of Boltzmann machine through Quantum annealing](https://mlsanity.com/paper/2002.00792/) (2020)
- [Efficient Evaluation of the Partition Function of RBMs with Annealed Importance Sampling](https://mlsanity.com/paper/2007.11926/) (2020)

## Built on by (most cited first, 3 of 3)

- [Generalization Bounds in Hybrid Quantum-Classical Machine Learning Models](https://mlsanity.com/paper/2504.08456/) (2025)
- [Comparison of D-Wave Quantum Annealing and Gibbs Monte Carlo for Sampling from a Probability Distribution of a Restricted Boltzmann Machine](https://mlsanity.com/paper/2508.10228/) (2025)
- [Investigation of D-Wave quantum annealing for training Restricted Boltzmann Machines and mitigating catastrophic forgetting](https://mlsanity.com/paper/2508.15697/) (2025)

## Abstract (arXiv)

Boltzmann machine is a powerful machine learning model with many real-world applications, for example by constructing deep belief networks. Statistical inference on a Boltzmann machine can be carried out by sampling from its posterior distribution. However, uniform sampling from such a model is not trivial due to an extremely multi-modal distribution. Quantum computers have the promise of solving some non-trivial problems in an efficient manner. We explored the application of a D-Wave quantum annealer to generate samples from a restricted Boltzmann machine. The samples are further improved by Markov chains in a hybrid quantum-classical setup. We demonstrated that quantum annealer samples can improve the performance of Gibbs sampling compared to random initialization. The hybrid setup is considerably more efficient than a pure classical sampling. We also investigated the impact of annealing parameters (temperature) to improve the quality of samples. By increasing the amount of classical processing (Gibbs updates) the benefit of quantum annealing vanishes, which may be justified by the limited performance of today's quantum computers compared to classical.