# Reinforcement Learning with Quantum Variational Circuits

arXiv: https://arxiv.org/abs/2008.07524 · HTML: https://mlsanity.com/paper/2008.07524/

## Key facts

- Cited by 77 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Aug 2020.

## Built on by (most cited first, 30 of 77)

- [Parametrized quantum policies for reinforcement learning](https://mlsanity.com/paper/2103.05577/) (2021)
- [Federated Quantum Machine Learning](https://mlsanity.com/paper/2103.12010/) (2021)
- [Quantum Architecture Search via Deep Reinforcement Learning](https://mlsanity.com/paper/2104.07715/) (2021)
- [A Survey on Quantum Reinforcement Learning](https://mlsanity.com/paper/2211.03464/) (2022)
- [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)
- [Equivariant quantum circuits for learning on weighted graphs](https://mlsanity.com/paper/2205.06109/) (2022)
- [Quantum machine learning with differential privacy](https://mlsanity.com/paper/2103.06232/) (2021)
- [Quantum deep recurrent reinforcement learning](https://mlsanity.com/paper/2210.14876/) (2022)
- [Learning to Program Variational Quantum Circuits with Fast Weights](https://mlsanity.com/paper/2402.17760/) (2024)
- [Quantum Multi-Agent Meta Reinforcement Learning](https://mlsanity.com/paper/2208.11510/) (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)
- [Hybrid Quantum-Classical Graph Convolutional Network](https://mlsanity.com/paper/2101.06189/) (2021)
- [Quantum Policy Iteration via Amplitude Estimation and Grover Search -- Towards Quantum Advantage for Reinforcement Learning](https://mlsanity.com/paper/2206.04741/) (2022)
- [Quantum Self-Supervised Learning](https://mlsanity.com/paper/2103.14653/) (2021)
- [Asynchronous training of quantum reinforcement learning](https://mlsanity.com/paper/2301.05096/) (2023)
- [Quantum Reinforcement Learning via Policy Iteration](https://mlsanity.com/paper/2203.01889/) (2022)
- [Quantum Deep Reinforcement Learning for Robot Navigation Tasks](https://mlsanity.com/paper/2202.12180/) (2022)
- [Quantum Implicit Neural Representations](https://mlsanity.com/paper/2406.03873/) (2024)
- [Policy Gradients using Variational Quantum Circuits](https://mlsanity.com/paper/2203.10591/) (2022)
- [Quantum policy gradient algorithms](https://mlsanity.com/paper/2212.09328/) (2022)
- [Uncovering Instabilities in Variational-Quantum Deep Q-Networks](https://mlsanity.com/paper/2202.05195/) (2022)
- [Reservoir Computing via Quantum Recurrent Neural Networks](https://mlsanity.com/paper/2211.02612/) (2022)
- [Efficient quantum recurrent reinforcement learning via quantum reservoir computing](https://mlsanity.com/paper/2309.07339/) (2023)
- [Differentiable Quantum Architecture Search in Asynchronous Quantum Reinforcement Learning](https://mlsanity.com/paper/2407.18202/) (2024)
- [Toward Large-Scale Distributed Quantum Long Short-Term Memory with Modular Quantum Computers](https://mlsanity.com/paper/2503.14088/) (2025)
- [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)
- [Exploration of Quantum Neural Architecture by Mixing Quantum Neuron Designs](https://mlsanity.com/paper/2109.03806/) (2021)

## Abstract (arXiv)

The development of quantum computational techniques has advanced greatly in recent years, parallel to the advancements in techniques for deep reinforcement learning. This work explores the potential for quantum computing to facilitate reinforcement learning problems. Quantum computing approaches offer important potential improvements in time and space complexity over traditional algorithms because of its ability to exploit the quantum phenomena of superposition and entanglement. Specifically, we investigate the use of quantum variational circuits, a form of quantum machine learning. We present our techniques for encoding classical data for a quantum variational circuit, we further explore pure and hybrid quantum algorithms for DQN and Double DQN. Our results indicate both hybrid and pure quantum variational circuit have the ability to solve reinforcement learning tasks with a smaller parameter space. These comparison are conducted with two OpenAI Gym environments: CartPole and Blackjack, The success of this work is indicative of a strong future relationship between quantum machine learning and deep reinforcement learning.