# Introduction to Quantum Reinforcement Learning: Theory and PennyLane-based Implementation

arXiv: https://arxiv.org/abs/2108.06849 · HTML: https://mlsanity.com/paper/2108.06849/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 16 references that are in the map.
- First posted on arXiv 16 Aug 2021.

## Builds on (most cited first, 8 of 8)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Variational Quantum Circuits for Deep Reinforcement Learning](https://mlsanity.com/paper/1907.00397/) (2019)
- [Quantum Deep Learning](https://mlsanity.com/paper/1412.3489/) (2014)
- [Quantum Neural Networks: Concepts, Applications, and Challenges](https://mlsanity.com/paper/2108.01468/) (2021)
- [Quantum Scheduling for Millimeter-Wave Observation Satellite Constellation](https://mlsanity.com/paper/2108.00626/) (2021)

## Built on by (most cited first, 23 of 23)

- [A Survey on Quantum Reinforcement Learning](https://mlsanity.com/paper/2211.03464/) (2022)
- [Variational Quantum Reinforcement Learning via Evolutionary Optimization](https://mlsanity.com/paper/2109.00540/) (2021)
- [Quantum Multi-Agent Reinforcement Learning via Variational Quantum Circuit Design](https://mlsanity.com/paper/2203.10443/) (2022)
- [Quantum Architecture Search via Continual Reinforcement Learning](https://mlsanity.com/paper/2112.05779/) (2021)
- [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)
- [Quantum Deep Reinforcement Learning for Robot Navigation Tasks](https://mlsanity.com/paper/2202.12180/) (2022)
- [Variational Quantum Soft Actor-Critic](https://mlsanity.com/paper/2112.11921/) (2021)
- [Quantum Distributed Deep Learning Architectures: Models, Discussions, and Applications](https://mlsanity.com/paper/2202.11200/) (2022)
- [Quantum Advantage Actor-Critic for Reinforcement Learning](https://mlsanity.com/paper/2401.07043/) (2024)
- [Nav-Q: Quantum Deep Reinforcement Learning for Collision-Free Navigation of Self-Driving Cars](https://mlsanity.com/paper/2311.12875/) (2023)
- [A Study on Optimization Techniques for Variational Quantum Circuits in Reinforcement Learning](https://mlsanity.com/paper/2405.12354/) (2024)
- [Compositional optimization of quantum circuits for quantum kernels of support vector machines](https://mlsanity.com/paper/2203.13848/) (2022)
- [Multi-Agent Quantum Reinforcement Learning using Evolutionary Optimization](https://mlsanity.com/paper/2311.05546/) (2023)
- [Quantum framework for Reinforcement Learning: Integrating Markov decision process, quantum arithmetic, and trajectory search](https://mlsanity.com/paper/2412.18208/) (2024)
- [Quantum Computing and Neuromorphic Computing for Safe, Reliable, and explainable Multi-Agent Reinforcement Learning: Optimal Control in Autonomous Robotics](https://mlsanity.com/paper/2408.03884/) (2024)
- [Quantum Hierarchical Reinforcement Learning via Variational Quantum Circuits](https://mlsanity.com/paper/2605.03434/) (2026)
- [Scalable Quantum Reinforcement Learning on NISQ Devices with Dynamic-Circuit Qubit Reuse and Grover Optimization](https://mlsanity.com/paper/2509.16002/) (2025)
- [Quantum feature-map learning with reduced resource overhead](https://mlsanity.com/paper/2510.03389/) (2025)
- [Learning to Coordinate via Quantum Entanglement in Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2602.08965/) (2026)
- [Tutorial on Course-of-Action (COA) Attack Search Methods in Computer Networks](https://mlsanity.com/paper/2205.13763/) (2022)
- [Securing SIM-Assisted Wireless Networks via Quantum Reinforcement Learning](https://mlsanity.com/paper/2602.13238/) (2026)
- [Quantum AS-DeepOnet: Quantum Attentive Stacked DeepONet for Solving 2D Evolution Equations](https://mlsanity.com/paper/2603.02261/) (2026)

## Abstract (arXiv)

The emergence of quantum computing enables for researchers to apply quantum circuit on many existing studies. Utilizing quantum circuit and quantum differential programming, many research are conducted such as textitQuantum Machine Learning (QML). In particular, quantum reinforcement learning is a good field to test the possibility of quantum machine learning, and a lot of research is being done. This work will introduce the concept of quantum reinforcement learning using a variational quantum circuit, and confirm its possibility through implementation and experimentation. We will first present the background knowledge and working principle of quantum reinforcement learning, and then guide the implementation method using the PennyLane library. We will also discuss the power and possibility of quantum reinforcement learning from the experimental results obtained through this work.