# A Survey on Quantum Reinforcement Learning

arXiv: https://arxiv.org/abs/2211.03464 · HTML: https://mlsanity.com/paper/2211.03464/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 148 references that are in the map.
- First posted on arXiv 7 Nov 2022.

## Builds on (most cited first, 30 of 51)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [Reinforcement Learning with Deep Energy-Based Policies](https://mlsanity.com/paper/1702.08165/) (2017)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [A Brief Survey of Deep Reinforcement Learning](https://mlsanity.com/paper/1708.05866/) (2017)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Variational Quantum Circuits for Deep Reinforcement Learning](https://mlsanity.com/paper/1907.00397/) (2019)
- [Absence of Barren Plateaus in Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2011.02966/) (2020)
- [Breaking the Sample Size Barrier in Model-Based Reinforcement Learning with a Generative Model](https://mlsanity.com/paper/2005.12900/) (2020)
- [Parametrized quantum policies for reinforcement learning](https://mlsanity.com/paper/2103.05577/) (2021)
- [Quantum-enhanced machine learning](https://mlsanity.com/paper/1610.08251/) (2016)
- [Reinforcement Learning with Quantum Variational Circuits](https://mlsanity.com/paper/2008.07524/) (2020)
- [Continuous-variable quantum neural networks](https://mlsanity.com/paper/1806.06871/) (2018)
- [An end-to-end trainable hybrid classical-quantum classifier](https://mlsanity.com/paper/2102.02416/) (2021)
- [Variational Quantum Reinforcement Learning via Evolutionary Optimization](https://mlsanity.com/paper/2109.00540/) (2021)
- [Learning to Optimize Variational Quantum Circuits to Solve Combinatorial Problems](https://mlsanity.com/paper/1911.11071/) (2019)
- [The power of block-encoded matrix powers: improved regression techniques via faster Hamiltonian simulation](https://mlsanity.com/paper/1804.01973/) (2018)
- [Quantum Multi-Agent Reinforcement Learning via Variational Quantum Circuit Design](https://mlsanity.com/paper/2203.10443/) (2022)
- [Quantum Algorithms for Reinforcement Learning with a Generative Model](https://mlsanity.com/paper/2112.08451/) (2021)
- [Introduction to Quantum Reinforcement Learning: Theory and PennyLane-based Implementation](https://mlsanity.com/paper/2108.06849/) (2021)
- [Quantum Multi-Agent Meta Reinforcement Learning](https://mlsanity.com/paper/2208.11510/) (2022)
- [Quantum exploration algorithms for multi-armed bandits](https://mlsanity.com/paper/2007.07049/) (2020)
- [Quantum Policy Iteration via Amplitude Estimation and Grover Search -- Towards Quantum Advantage for Reinforcement Learning](https://mlsanity.com/paper/2206.04741/) (2022)
- [Reinforcement Learning Using Quantum Boltzmann Machines](https://mlsanity.com/paper/1612.05695/) (2016)
- [Deep Reinforcement Learning with Quantum-inspired Experience Replay](https://mlsanity.com/paper/2101.02034/) (2021)

## Built on by (most cited first, 30 of 53)

- [Quantum Deep Hedging](https://mlsanity.com/paper/2303.16585/) (2023)
- [Quantum Policy Gradient Algorithm with Optimized Action Decoding](https://mlsanity.com/paper/2212.06663/) (2022)
- [Asynchronous training of quantum reinforcement learning](https://mlsanity.com/paper/2301.05096/) (2023)
- [Explaining Quantum Circuits with Shapley Values: Towards Explainable Quantum Machine Learning](https://mlsanity.com/paper/2301.09138/) (2023)
- [Quantum policy gradient algorithms](https://mlsanity.com/paper/2212.09328/) (2022)
- [Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applications](https://mlsanity.com/paper/2307.00908/) (2023)
- [Quantum Machine Learning Architecture Search via Deep Reinforcement Learning](https://mlsanity.com/paper/2407.20147/) (2024)
- [Quantum Bayesian Optimization](https://mlsanity.com/paper/2310.05373/) (2023)
- [VQC-Based Reinforcement Learning with Data Re-uploading: Performance and Trainability](https://mlsanity.com/paper/2401.11555/) (2024)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Benchmarking Quantum Reinforcement Learning](https://mlsanity.com/paper/2501.15893/) (2025)
- [Provably Efficient Exploration in Quantum Reinforcement Learning with Logarithmic Worst-Case Regret](https://mlsanity.com/paper/2302.10796/) (2023)
- [Evolutionary Optimization for Designing Variational Quantum Circuits with High Model Capacity](https://mlsanity.com/paper/2412.12484/) (2024)
- [A Study on Optimization Techniques for Variational Quantum Circuits in Reinforcement Learning](https://mlsanity.com/paper/2405.12354/) (2024)
- [An Introduction to Quantum Reinforcement Learning (QRL)](https://mlsanity.com/paper/2409.05846/) (2024)
- [Learning to Program Quantum Measurements for Machine Learning](https://mlsanity.com/paper/2505.13525/) (2025)
- [Quantum Natural Policy Gradients: Towards Sample-Efficient Reinforcement Learning](https://mlsanity.com/paper/2304.13571/) (2023)
- [Quantum computing and artificial intelligence: status and perspectives](https://mlsanity.com/paper/2505.23860/) (2025)
- [Quantum Reinforcement Learning by Adaptive Non-local Observables](https://mlsanity.com/paper/2507.19629/) (2025)
- [Quantum-enhanced Computer Vision: Going Beyond Classical Algorithms](https://mlsanity.com/paper/2510.07317/) (2025)
- [Model-based Offline Quantum Reinforcement Learning](https://mlsanity.com/paper/2404.10017/) (2024)
- [Guided-SPSA: Simultaneous Perturbation Stochastic Approximation assisted by the Parameter Shift Rule](https://mlsanity.com/paper/2404.15751/) (2024)
- [Robustness and Generalization in Quantum Reinforcement Learning via Lipschitz Regularization](https://mlsanity.com/paper/2410.21117/) (2024)
- [Fourier Analysis of Variational Quantum Circuits for Supervised Learning](https://mlsanity.com/paper/2411.03450/) (2024)
- [Quantum Lipschitz Bandits](https://mlsanity.com/paper/2504.02251/) (2025)
- [Quantum Long Short-term Memory with Differentiable Architecture Search](https://mlsanity.com/paper/2508.14955/) (2025)
- [BCQQ: Batch-Constraint Quantum Q-Learning with Cyclic Data Re-uploading](https://mlsanity.com/paper/2305.00905/) (2023)
- [Quantum Artificial Intelligence: A Brief Survey](https://mlsanity.com/paper/2408.10726/) (2024)
- [Quantum deep Q learning with distributed prioritized experience replay](https://mlsanity.com/paper/2304.09648/) (2023)
- [Comprehensive Library of Variational LSE Solvers](https://mlsanity.com/paper/2404.09916/) (2024)

## Abstract (arXiv)

Quantum reinforcement learning is an emerging field at the intersection of quantum computing and machine learning. While we intend to provide a broad overview of the literature on quantum reinforcement learning - our interpretation of this term will be clarified below - we put particular emphasis on recent developments. With a focus on already available noisy intermediate-scale quantum devices, these include variational quantum circuits acting as function approximators in an otherwise classical reinforcement learning setting. In addition, we survey quantum reinforcement learning algorithms based on future fault-tolerant hardware, some of which come with a provable quantum advantage. We provide both a birds-eye-view of the field, as well as summaries and reviews for selected parts of the literature.