# Reinforcement Learning Using Quantum Boltzmann Machines

arXiv: https://arxiv.org/abs/1612.05695 · HTML: https://mlsanity.com/paper/1612.05695/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Dec 2016.

## Built on by (most cited first, 20 of 20)

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- [A Survey on Quantum Reinforcement Learning](https://mlsanity.com/paper/2211.03464/) (2022)
- [Recent Advances for Quantum Neural Networks in Generative Learning](https://mlsanity.com/paper/2206.03066/) (2022)
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- [Quantum Generative Diffusion Model: A Fully Quantum-Mechanical Model for Generating Quantum State Ensemble](https://mlsanity.com/paper/2401.07039/) (2024)
- [Towards Multi-Agent Reinforcement Learning using Quantum Boltzmann Machines](https://mlsanity.com/paper/2109.10900/) (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)
- [Quantum Artificial Intelligence: A Brief Survey](https://mlsanity.com/paper/2408.10726/) (2024)
- [Assessment of image generation by quantum annealer](https://mlsanity.com/paper/2103.08373/) (2021)
- [Quantum Machine Learning For Classical Data](https://mlsanity.com/paper/2105.03684/) (2021)
- [Using Quantum Solved Deep Boltzmann Machines to Increase the Data Efficiency of RL Agents](https://mlsanity.com/paper/2408.17240/) (2024)
- [Quantum deep reinforcement learning for humanoid robot navigation task](https://mlsanity.com/paper/2509.11388/) (2025)
- [Quantum Boltzmann Machines for Sample-Efficient Reinforcement Learning](https://mlsanity.com/paper/2511.04856/) (2025)
- [Variational Quantum Conditional Boltzmann Machines for Time-Series Forecasting: Architectures, Symmetric Hyperparameter Evaluation, and a Nonlinear Benchmark](https://mlsanity.com/paper/2607.24065/) (2026)
- [Improved Quantum Algorithms for Reinforcement Learning Under a Generative Model](https://mlsanity.com/paper/2608.02826/) (2026)

## Abstract (arXiv)

We investigate whether quantum annealers with select chip layouts can outperform classical computers in reinforcement learning tasks. We associate a transverse field Ising spin Hamiltonian with a layout of qubits similar to that of a deep Boltzmann machine (DBM) and use simulated quantum annealing (SQA) to numerically simulate quantum sampling from this system. We design a reinforcement learning algorithm in which the set of visible nodes representing the states and actions of an optimal policy are the first and last layers of the deep network. In absence of a transverse field, our simulations show that DBMs are trained more effectively than restricted Boltzmann machines (RBM) with the same number of nodes. We then develop a framework for training the network as a quantum Boltzmann machine (QBM) in the presence of a significant transverse field for reinforcement learning. This method also outperforms the reinforcement learning method that uses RBMs.