# Comparison of D-Wave Quantum Annealing and Gibbs Monte Carlo for Sampling from a Probability Distribution of a Restricted Boltzmann Machine

arXiv: https://arxiv.org/abs/2508.10228 · HTML: https://mlsanity.com/paper/2508.10228/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 33 references that are in the map.
- First posted on arXiv 13 Aug 2025.

## Builds on (most cited first, 13 of 13)

- [The Loss Surfaces of Multilayer Networks](https://mlsanity.com/paper/1412.0233/) (2014)
- [Application of Quantum Annealing to Training of Deep Neural Networks](https://mlsanity.com/paper/1510.06356/) (2015)
- [Quantum-Assisted Learning of Hardware-Embedded Probabilistic Graphical Models](https://mlsanity.com/paper/1609.02542/) (2016)
- [Training and Classification using a Restricted Boltzmann Machine on the D-Wave 2000Q](https://mlsanity.com/paper/2005.03247/) (2020)
- [Quantum Annealing Applied to De-Conflicting Optimal Trajectories for Air Traffic Management](https://mlsanity.com/paper/1711.04889/) (2017)
- [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)
- [Benchmarking Quantum Hardware for Training of Fully Visible Boltzmann Machines](https://mlsanity.com/paper/1611.04528/) (2016)
- [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)
- [Towards Sampling from Nondirected Probabilistic Graphical models using a D-Wave Quantum Annealer](https://mlsanity.com/paper/1905.00159/) (2019)
- [A hybrid quantum-classical approach for inference on restricted Boltzmann machines](https://mlsanity.com/paper/2304.12418/) (2023)
- [On the Challenges of Physical Implementations of RBMs](https://mlsanity.com/paper/1312.5258/) (2013)

## Built on by (most cited first, 1 of 1)

- [Investigation of D-Wave quantum annealing for training Restricted Boltzmann Machines and mitigating catastrophic forgetting](https://mlsanity.com/paper/2508.15697/) (2025)

## Abstract (arXiv)

A local-valley (LV) centered approach to assessing the quality of sampling from Restricted Boltzmann Machines (RBMs) was applied to the latest generation of the D-Wave quantum annealer. D-Wave and Gibbs samples from a classically trained RBM were obtained at conditions relevant to the contrastive-divergence-based RBM learning. The samples were compared for the number of the LVs to which they belonged and the energy of the corresponding local minima. No significant (desirable) increase in the number of the LVs has been achieved by decreasing the D-Wave annealing time. At any training epoch, the states sampled by the D-Wave belonged to a somewhat higher number of LVs than in the Gibbs sampling. However, many of those LVs found by the two techniques differed. For high-probability sampled states, the two techniques were (unfavorably) less complementary and more overlapping. Nevertheless, many potentially "important" local minima, i.e., those having intermediate, even if not high, probability values, were found by only one of the two sampling techniques while missed by the other. The two techniques overlapped less at later than earlier training epochs, which is precisely the stage of the training when modest improvements to the sampling quality could make meaningful differences for the RBM trainability. The results of this work may explain the failure of previous investigations to achieve substantial (or any) improvement when using D-Wave-based sampling. However, the results reveal some potential for improvement, e.g., using a combined classical-quantum approach.