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Variational Quantum Reinforcement Learning via Evolutionary Optimization

arXiv 2109.00540 ↗First posted 1 Sep 2021quant-ph cs.AI cs.ETcited by 50

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Abstract (arXiv)

Recent advance in classical reinforcement learning (RL) and quantum computation (QC) points to a promising direction of performing RL on a quantum computer. However, potential applications in quantum RL are limited by the number of qubits available in the modern quantum devices. Here we present two frameworks of deep quantum RL tasks using a gradient-free evolution optimization: First, we apply the amplitude encoding scheme to the Cart-Pole problem; Second, we propose a hybrid framework where the quantum RL agents are equipped with hybrid tensor network-variational quantum circuit (TN-VQC) architecture to handle inputs with dimensions exceeding the number of qubits. This allows us to perform quantum RL on the MiniGrid environment with 147-dimensional inputs. We demonstrate the quantum advantage of parameter saving using the amplitude encoding. The hybrid TN-VQC architecture provides a natural way to perform efficient compression of the input dimension, enabling further quantum RL applications on noisy intermediate-scale quantum devices.

Key facts. Cited by 50 papers in the map (data through 7 Oct 2026). Builds on 47 of its 125 references that are in the map. First posted on arXiv 1 Sep 2021.

Builds on

47 of 125 references.

References · 47

  1. 2016OpenAI Gymcited by 1,684
  2. 2019Mastering Atari, Go, Chess and Shogi by Planning with a Learned Modelcited by 1,327
  3. 2020Variational Quantum Algorithmscited by 687
  4. 2018Supervised learning with quantum enhanced feature spacescited by 654
  5. 2019Parameterized quantum circuits as machine learning modelscited by 330
  6. 2020Agent57: Outperforming the Atari Human Benchmarkcited by 300
  7. 2019Variational Quantum Circuits for Deep Reinforcement Learningcited by 165
  8. 2017Deep Neuroevolution: Genetic Algorithms Are a Competitive Alternative for Training Deep Neural Networks for Reinforcement Learningcited by 148
  9. 2018Quantum generative adversarial networkscited by 128
  10. 2020Quantum Long Short-Term Memorycited by 118
  11. 2019Transfer learning in hybrid classical-quantum neural networkscited by 113
  12. 2017Improving Exploration in Evolution Strategies for Deep Reinforcement Learning via a Population of Novelty-Seeking Agentscited by 107
35 more
  1. 2017Unsupervised Generative Modeling Using Matrix Product Statescited by 87
  2. 2021Federated Quantum Machine Learningcited by 82
  3. 2020Recurrent Quantum Neural Networkscited by 79
  4. 2021Noisy intermediate-scale quantum (NISQ) algorithmscited by 79
  5. 2018Towards Quantum Machine Learning with Tensor Networkscited by 74
  6. 2020Reinforcement Learning with Quantum Variational Circuitscited by 74
  7. 2020Quantum Convolutional Neural Networks for High Energy Physics Data Analysiscited by 64
  8. 2019Tree Tensor Networks for Generative Modelingcited by 63
  9. 2021Quantum Architecture Search via Deep Reinforcement Learningcited by 58
  10. 2020Decentralizing Feature Extraction with Quantum Convolutional Neural Network for Automatic Speech Recognitioncited by 56
  11. 2021Quantum Federated Learning with Quantum Datacited by 53
  12. 2017Learning Relevant Features of Data with Multi-scale Tensor Networkscited by 50
  13. 2021An end-to-end trainable hybrid classical-quantum classifiercited by 49
  14. 2017Active learning machine learns to create new quantum experimentscited by 41
  15. 2017Machine Learning by Unitary Tensor Network of Hierarchical Tree Structurecited by 39
  16. 2018From probabilistic graphical models to generalized tensor networks for supervised learningcited by 31
  17. 2019TensorNetwork for Machine Learningcited by 29
  18. 2018Optimizing Quantum Error Correction Codes with Reinforcement Learningcited by 28
  19. 2018Reinforcement Learning Decoders for Fault-Tolerant Quantum Computationcited by 27
  20. 2020Classification with Quantum Machine Learning: A Surveycited by 23
  21. 2021Introduction to Quantum Reinforcement Learning: Theory and PennyLane-based Implementationcited by 23
  22. 2019Generative Tensor Network Classification Model for Supervised Machine Learningcited by 22
  23. 2021Hybrid Quantum-Classical Graph Convolutional Networkcited by 21
  24. 2021Quantum Self-Supervised Learningcited by 20
  25. 2019Modeling Sequences with Quantum States: A Look Under the Hoodcited by 19
  26. 2018The Expressive Power of Parameterized Quantum Circuitscited by 18
  27. 2020Natural Evolutionary Strategies for Variational Quantum Computationcited by 15
  28. 2019Matrix Product State Based Quantum Classifiercited by 13
  29. 2020Enhanced Adversarial Strategically-Timed Attacks against Deep Reinforcement Learningcited by 13
  30. 2021Variational Quanvolutional Neural Networks with enhanced image encodingcited by 13
  31. 2021Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time-Seriescited by 10
  32. 2015Framework for learning agents in quantum environmentscited by 9
  33. 2019Quantum Unsupervised and Supervised Learning on Superconducting Processorscited by 9
  34. 2021Photonic Quantum Policy Learning in OpenAI Gymcited by 3
  35. 2020Evolving Neural Networks through a Reverse Encoding Treecited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 5; 2023: 9; 2024: 17; 2025: 15; 2026: 2.

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  1. 2022A Survey on Quantum Reinforcement Learningcited by 50
  2. 2022Quantum deep recurrent reinforcement learningcited by 23
  3. 2024Learning to Program Variational Quantum Circuits with Fast Weightscited by 23
  4. 2021Quantum Architecture Search via Continual Reinforcement Learningcited by 22
  5. 2023Asynchronous training of quantum reinforcement learningcited by 20
  6. 2023Tensor networks for quantum machine learningcited by 16
  7. 2022Quantum policy gradient algorithmscited by 15
  8. 2023Federated Quantum Long Short-term Memory (FedQLSTM)cited by 15
  9. 2025Learning to Measure Quantum Neural Networkscited by 15
  10. 2022Quantum Deep Reinforcement Learning for Robot Navigation Taskscited by 14
  11. 2022Reservoir Computing via Quantum Recurrent Neural Networkscited by 14
  12. 2023Efficient quantum recurrent reinforcement learning via quantum reservoir computingcited by 14
38 more
  1. 2024Quantum-Train-Based Distributed Multi-Agent Reinforcement Learningcited by 14
  2. 2023Differentiable Quantum Architecture Search for Quantum Reinforcement Learningcited by 13
  3. 2024Differentiable Quantum Architecture Search in Asynchronous Quantum Reinforcement Learningcited by 13
  4. 2024Quantum Machine Learning Architecture Search via Deep Reinforcement Learningcited by 12
  5. 2024QClusformer: A Quantum Transformer-based Framework for Unsupervised Visual Clusteringcited by 11
  6. 2024Diffusion-Inspired Quantum Noise Mitigation in Parameterized Quantum Circuitscited by 10
  7. 2024Quantum Advantage Actor-Critic for Reinforcement Learningcited by 9
  8. 2024Quantum Gradient Class Activation Map for Model Interpretabilitycited by 9
  9. 2024Evolutionary Optimization for Designing Variational Quantum Circuits with High Model Capacitycited by 9
  10. 2025A Primer on Quantum Machine Learningcited by 9
  11. 2024Hierarchical Quantum Control Gates for Functional MRI Understandingcited by 8
  12. 2023Expressibility-induced Concentration of Quantum Neural Tangent Kernelscited by 7
  13. 2024A Study on Optimization Techniques for Variational Quantum Circuits in Reinforcement Learningcited by 7
  14. 2024An Introduction to Quantum Reinforcement Learning (QRL)cited by 7
  15. 2025Adaptive Non-local Observable on Quantum Neural Networkscited by 7
  16. 2025Differentiable Quantum Architecture Search in Quantum-Enhanced Neural Network Parameter Generationcited by 7
  17. 2025Learning to Program Quantum Measurements for Machine Learningcited by 7
  18. 2025QMoE: A Quantum Mixture of Experts Framework for Scalable Quantum Neural Networkscited by 7
  19. 2023Multi-Agent Quantum Reinforcement Learning using Evolutionary Optimizationcited by 5
  20. 2025Quantum Reinforcement Learning Trading Agent for Sector Rotation in the Taiwan Stock Marketcited by 5
  21. 2025Quantum Reinforcement Learning by Adaptive Non-local Observablescited by 5
  22. 2024Guided-SPSA: Simultaneous Perturbation Stochastic Approximation assisted by the Parameter Shift Rulecited by 4
  23. 2024CHARME: A chain-based reinforcement learning approach for the minor embedding problemcited by 3
  24. 2025Transfer Learning Analysis of Variational Quantum Circuitscited by 3
  25. 2025Introduction to Quantum Machine Learning and Quantum Architecture Searchcited by 3
  26. 2023Quantum deep Q learning with distributed prioritized experience replaycited by 2
  27. 2023Several fitness functions and entanglement gates in quantum kernel generationcited by 2
  28. 2024Optimizing Variational Quantum Circuits Using Metaheuristic Strategies in Reinforcement Learningcited by 2
  29. 2024Quantum Machine Learning: An Interplay Between Quantum Computing and Machine Learningcited by 2
  30. 2025GPA: Grover Policy Agent for Generating Optimal Quantum Sensor Circuitscited by 1
  31. 2025Neural Architecture Search for Quantum Autoencoderscited by 1
  32. 2021QKSA: Quantum Knowledge Seeking Agent -- resource-optimized reinforcement learning using quantum process tomographycited by 0
  33. 2024Architectural Influence on Variational Quantum Circuits in Multi-Agent Reinforcement Learning: Evolutionary Strategies for Optimizationcited by 0
  34. 2025Special-Unitary Parameterization for Trainable Variational Quantum Circuitscited by 0
  35. 2025HCQA: Hybrid Classical-Quantum Agent for Generating Optimal Quantum Sensor Circuitscited by 0
  36. 2025A Hybrid Classical-Quantum Fine Tuned BERT for Text Classificationcited by 0
  37. 2026QLAM: A Quantum Long-Attention Memory Approach to Long-Sequence Token Modelingcited by 0
  38. 2026A Hybrid Quantum-Classical Approach for Melt Pool Prediction in Laser Powder Bed Fusioncited by 0