# Quantum reinforcement learning in continuous action space

arXiv: https://arxiv.org/abs/2012.10711 · HTML: https://mlsanity.com/paper/2012.10711/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2020.

## Built on by (most cited first, 29 of 29)

- [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)
- [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)
- [Variational Quantum Soft Actor-Critic](https://mlsanity.com/paper/2112.11921/) (2021)
- [Policy Gradients using Variational Quantum Circuits](https://mlsanity.com/paper/2203.10591/) (2022)
- [Quantum policy gradient algorithms](https://mlsanity.com/paper/2212.09328/) (2022)
- [Reservoir Computing via Quantum Recurrent Neural Networks](https://mlsanity.com/paper/2211.02612/) (2022)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Warm-Start Variational Quantum Policy Iteration](https://mlsanity.com/paper/2404.10546/) (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)
- [Photonic Quantum Policy Learning in OpenAI Gym](https://mlsanity.com/paper/2108.12926/) (2021)
- [Quantum framework for Reinforcement Learning: Integrating Markov decision process, quantum arithmetic, and trajectory search](https://mlsanity.com/paper/2412.18208/) (2024)
- [Auxiliary Task-based Deep Reinforcement Learning for Quantum Control](https://mlsanity.com/paper/2302.14312/) (2023)
- [Quantum deep Q learning with distributed prioritized experience replay](https://mlsanity.com/paper/2304.09648/) (2023)
- [Quantum-Enhanced Hybrid Reinforcement Learning Framework for Dynamic Path Planning in Autonomous Systems](https://mlsanity.com/paper/2504.20660/) (2025)
- [Quantum Reinforcement Learning-Guided Diffusion Model for Image Synthesis via Hybrid Quantum-Classical Generative Model Architectures](https://mlsanity.com/paper/2509.14163/) (2025)
- [Dissecting Quantum Reinforcement Learning: A Systematic Evaluation of Key Components](https://mlsanity.com/paper/2511.17112/) (2025)
- [GPA: Grover Policy Agent for Generating Optimal Quantum Sensor Circuits](https://mlsanity.com/paper/2502.13755/) (2025)
- [Scalable Quantum Reinforcement Learning on NISQ Devices with Dynamic-Circuit Qubit Reuse and Grover Optimization](https://mlsanity.com/paper/2509.16002/) (2025)
- [CutReg: A loss regularizer for enhancing the scalability of QML via adaptive circuit cutting](https://mlsanity.com/paper/2506.14858/) (2025)
- [HCQA: Hybrid Classical-Quantum Agent for Generating Optimal Quantum Sensor Circuits](https://mlsanity.com/paper/2508.21246/) (2025)
- [Hybrid Quantum-Classical Policy Gradient for Adaptive Control of Cyber-Physical Systems: A Comparative Study of VQC vs. MLP](https://mlsanity.com/paper/2510.06010/) (2025)
- [Lyapunov-Aware Quantum-Inspired Reinforcement Learning for Continuous-Time Vehicle Control: A Feasibility Study](https://mlsanity.com/paper/2510.18852/) (2025)
- [Quantum-Embedded Dynamic Security Control using Hybrid Deep Reinforcement Learning](https://mlsanity.com/paper/2512.04095/) (2025)
- [Quantum-Accelerated Deep Reinforcement Learning for Frequency Regulation Enhancement](https://mlsanity.com/paper/2512.04439/) (2025)
- [Quantum entanglement provides a competitive advantage in adversarial games](https://mlsanity.com/paper/2603.10289/) (2026)
- [Entanglement as a Structural Complexity Axis: A PAC-Bayesian View of Generalization in Quantum Policies and Value Functions](https://mlsanity.com/paper/2607.06230/) (2026)

## Abstract (arXiv)

Quantum reinforcement learning (QRL) is a promising paradigm for near-term quantum devices. While existing QRL methods have shown success in discrete action spaces, extending these techniques to continuous domains is challenging due to the curse of dimensionality introduced by discretization. To overcome this limitation, we introduce a quantum Deep Deterministic Policy Gradient (DDPG) algorithm that efficiently addresses both classical and quantum sequential decision problems in continuous action spaces. Moreover, our approach facilitates single-shot quantum state generation: a one-time optimization produces a model that outputs the control sequence required to drive a fixed initial state to any desired target state. In contrast, conventional quantum control methods demand separate optimization for each target state. We demonstrate the effectiveness of our method through simulations and discuss its potential applications in quantum control.