# Quantum Boltzmann Machines for Sample-Efficient Reinforcement Learning

arXiv: https://arxiv.org/abs/2511.04856 · HTML: https://mlsanity.com/paper/2511.04856/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Quantum reinforcement learning, one of 15 directions in Deep reinforcement learning methods.
- Builds on 18 of its 49 references that are in the map.
- First posted on arXiv 6 Nov 2025.

## Placed in

- Deep reinforcement learning methods / [Quantum reinforcement learning](https://mlsanity.com/deeprl/quantum-reinforcement-learning/)

## Builds on (most cited first, 18 of 18)

- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [QT-Opt: Scalable Deep Reinforcement Learning for Vision-Based Robotic Manipulation](https://mlsanity.com/paper/1806.10293/) (2018)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [Continuous Deep Q-Learning with Model-based Acceleration](https://mlsanity.com/paper/1603.00748/) (2016)
- [Parametrized quantum policies for reinforcement learning](https://mlsanity.com/paper/2103.05577/) (2021)
- [A Survey on Quantum Reinforcement Learning](https://mlsanity.com/paper/2211.03464/) (2022)
- [CAQL: Continuous Action Q-Learning](https://mlsanity.com/paper/1909.12397/) (2019)
- [Reinforcement Learning Using Quantum Boltzmann Machines](https://mlsanity.com/paper/1612.05695/) (2016)
- [On the Sample Complexity of Quantum Boltzmann Machine Learning](https://mlsanity.com/paper/2306.14969/) (2023)
- [Q-Learning for Continuous Actions with Cross-Entropy Guided Policies](https://mlsanity.com/paper/1903.10605/) (2019)
- [Training and Classification using a Restricted Boltzmann Machine on the D-Wave 2000Q](https://mlsanity.com/paper/2005.03247/) (2020)
- [Optimizing Objective Functions from Trained ReLU Neural Networks via Sampling](https://mlsanity.com/paper/2205.14189/) (2022)
- [Gaussian-binary Restricted Boltzmann Machines on Modeling Natural Image Statistics](https://mlsanity.com/paper/1401.5900/) (2014)
- [Expressive equivalence of classical and quantum restricted Boltzmann machines](https://mlsanity.com/paper/2502.17562/) (2025)
- [Free energy-based reinforcement learning using a quantum processor](https://mlsanity.com/paper/1706.00074/) (2017)
- [On Quantum Circuits for Discrete Graphical Models](https://mlsanity.com/paper/2206.00398/) (2022)
- [Using Quantum Solved Deep Boltzmann Machines to Increase the Data Efficiency of RL Agents](https://mlsanity.com/paper/2408.17240/) (2024)

## Abstract (arXiv)

We introduce theoretically grounded Continuous Semi-Quantum Boltzmann Machines (CSQBMs) that supports continuous-action reinforcement learning. By combining exponential-family priors over visible units with quantum Boltzmann distributions over hidden units, CSQBMs yield a hybrid quantum-classical model that reduces qubit requirements while retaining strong expressiveness. Crucially, gradients with respect to continuous variables can be computed analytically, enabling direct integration into Actor-Critic algorithms. Building on this, we propose a continuous Q-learning framework that replaces global maximization by efficient sampling from the CSQBM distribution, thereby overcoming instability issues in continuous control.