# On the challenges of using D-Wave computers to sample Boltzmann Random Variables

arXiv: https://arxiv.org/abs/2111.15295 · HTML: https://mlsanity.com/paper/2111.15295/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 13 references that are in the map.
- First posted on arXiv 30 Nov 2021.

## Builds on (most cited first, 5 of 5)

- [Application of Quantum Annealing to Training of Deep Neural Networks](https://mlsanity.com/paper/1510.06356/) (2015)
- [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)
- [High-quality Thermal Gibbs Sampling with Quantum Annealing Hardware](https://mlsanity.com/paper/2109.01690/) (2021)
- [Towards Multi-Agent Reinforcement Learning using Quantum Boltzmann Machines](https://mlsanity.com/paper/2109.10900/) (2021)

## Built on by (most cited first, 4 of 4)

- [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)
- [Using Quantum Solved Deep Boltzmann Machines to Increase the Data Efficiency of RL Agents](https://mlsanity.com/paper/2408.17240/) (2024)
- [Quantum Adiabatic Generation of Human-Like Passwords](https://mlsanity.com/paper/2506.08917/) (2025)

## Abstract (arXiv)

Sampling random variables following a Boltzmann distribution is an NP-hard problem involved in various applications such as training of textitBoltzmann machines, a specific kind of neural network. Several attempts have been made to use a D-Wave quantum computer to sample such a distribution, as this could lead to significant speedup in these applications. Yet, at present, several challenges remain to efficiently perform such sampling. We detail the various obstacles and explain the remaining difficulties in solving the sampling problem on a D-wave machine.