# Training and Classification using a Restricted Boltzmann Machine on the D-Wave 2000Q

arXiv: https://arxiv.org/abs/2005.03247 · HTML: https://mlsanity.com/paper/2005.03247/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 May 2020.

## Built on by (most cited first, 18 of 18)

- [Recent advances for quantum classifiers](https://mlsanity.com/paper/2108.13421/) (2021)
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- [Quantum Machine Learning for Finance](https://mlsanity.com/paper/2109.04298/) (2021)
- [On the challenges of using D-Wave computers to sample Boltzmann Random Variables](https://mlsanity.com/paper/2111.15295/) (2021)
- [A hybrid quantum-classical approach for inference on restricted Boltzmann machines](https://mlsanity.com/paper/2304.12418/) (2023)
- [Probabilistic Sampling of Balanced K-Means using Adiabatic Quantum Computing](https://mlsanity.com/paper/2310.12153/) (2023)
- [Projected Stochastic Gradient Descent with Quantum Annealed Binary Gradients](https://mlsanity.com/paper/2310.15128/) (2023)
- [Quantum Image Denoising: A Framework via Boltzmann Machines, QUBO, and Quantum Annealing](https://mlsanity.com/paper/2307.06542/) (2023)
- [Training Multilayer Perceptrons by Sampling with Quantum Annealers](https://mlsanity.com/paper/2303.12352/) (2023)
- [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)
- [What is Cognitive Computing? An Architecture and State of The Art](https://mlsanity.com/paper/2301.00882/) (2023)
- [Mean-Field Assisted Deep Boltzmann Learning with Probabilistic Computers](https://mlsanity.com/paper/2401.01996/) (2024)
- [Quantum Annealing for Robust Principal Component Analysis](https://mlsanity.com/paper/2501.10431/) (2025)
- [Hyperspectral image segmentation with a machine learning model trained using quantum annealer](https://mlsanity.com/paper/2503.01400/) (2025)
- [Investigation of D-Wave quantum annealing for training Restricted Boltzmann Machines and mitigating catastrophic forgetting](https://mlsanity.com/paper/2508.15697/) (2025)
- [Quantum Boltzmann Machines for Sample-Efficient Reinforcement Learning](https://mlsanity.com/paper/2511.04856/) (2025)

## Abstract (arXiv)

Restricted Boltzmann Machine (RBM) is an energy based, undirected graphical model. It is commonly used for unsupervised and supervised machine learning. Typically, RBM is trained using contrastive divergence (CD). However, training with CD is slow and does not estimate exact gradient of log-likelihood cost function. In this work, the model expectation of gradient learning for RBM has been calculated using a quantum annealer (D-Wave 2000Q), which is much faster than Markov chain Monte Carlo (MCMC) used in CD. Training and classification results are compared with CD. The classification accuracy results indicate similar performance of both methods. Image reconstruction as well as log-likelihood calculations are used to compare the performance of quantum and classical algorithms for RBM training. It is shown that the samples obtained from quantum annealer can be used to train a RBM on a 64-bit `bars and stripes' data set with classification performance similar to a RBM trained with CD. Though training based on CD showed improved learning performance, training using a quantum annealer eliminates computationally expensive MCMC steps of CD.