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arXiv:2605.03434

Quantum Hierarchical Reinforcement Learning via Variational Quantum Circuits

Yu-Ting Lee, Samuel Yen-Chi Chen, Fu-Chieh Chang

cs.LGquant-phSubmitted May 5, 2026• Announced May 6, 2026• 0 citations
v1 · May 5, 2026v2 · Sep 8, 2026v3 · Sep 19, 2026
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Abstract

Reinforcement learning is one of the most challenging learning paradigms where efficacy and efficiency gains are extremely valuable. Hierarchical reinforcement learning is a variant that leverages temporal abstraction to structure decision-making. While parametrized quantum computations have shown success in non-hierarchical reinforcement learning, whether these advantages adapt to hierarchical decision-making remains a critical open question. In this work, we develop a hybrid hierarchical agent based on the option-critic architecture. This hybrid agent substitutes classical components with variational quantum circuits for feature extractors, option-value functions, termination functions, and intra-option policies. Evaluated on standard benchmarking environments, results show that a hybrid agent utilizing a quantum feature extractor can outperform classical baselines while saving up to 66\% trainable parameters. We also identify an architectural bottleneck that quantum option-value estimation severely degrades performance. Further ablation studies reveal how architectural choices of the quantum circuits affect performance. Our work establishes design principles for parameter-efficient hybrid hierarchical agents.

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Reinforcement learning is one of the most challenging learning paradigms where efficacy and efficiency gains are extremely valuable. Hierarchical reinforcement learning is a variant that leverages temporal abstraction to structure decision-making. While parametrized quantum computations have shown success in non-hierarchical reinforcement learning, whether these advantages adapt to hierarchical decision-making remains a critical open question. In this work, we develop a hybrid hierarchical agent based on the option-critic architecture. This hybrid agent substitutes classical components with variational quantum circuits for feature extractors, option-value functions, termination functions, and intra-option policies. Evaluated on standard benchmarking environments, results show that a hybrid agent utilizing a quantum feature extractor can outperform classical baselines while saving up to 66% trainable parameters. We also identify an architectural bottleneck that quantum option-value estimation severely degrades performance. Further ablation studies reveal how architectural choices of the quantum circuits affect performance. Our work establishes design principles for parameter-efficient hybrid hierarchical agents.
Quantum Reinforcement Learning (QRL) emerged as a branch of reinforcement learning (RL) that uses quantum submodules in the architecture of the algorithm. One branch of QRL focuses on the replacement of neural networks (NN) by variational quantum circuits (VQC) as function approximators. Initial works have shown promising results on classical environments with discrete action spaces, but many of the proposed architectural design choices of the VQC lack a detailed investigation. Hence, in this work we investigate the impact of VQC design choices such as angle embedding, encoding block architecture and postprocessesing on the training capabilities of QRL agents. We show that VQC design greatly influences training performance and heuristically derive enhancements for the analyzed components. Additionally, we show how to design a QRL agent in order to solve classical environments with continuous action spaces and benchmark our agents against classical feed-forward NNs.
In recent years, quantum computing (QC) has been getting a lot of attention from industry and academia. Especially, among various QC research topics, variational quantum circuit (VQC) enables quantum deep reinforcement learning (QRL). Many studies of QRL have shown that the QRL is superior to the classical reinforcement learning (RL) methods under the constraints of the number of training parameters. This paper extends and demonstrates the QRL to quantum multi-agent RL (QMARL). However, the extension of QRL to QMARL is not straightforward due to the challenge of the noise intermediate-scale quantum (NISQ) and the non-stationary properties in classical multi-agent RL (MARL). Therefore, this paper proposes the centralized training and decentralized execution (CTDE) QMARL framework by designing novel VQCs for the framework to cope with these issues. To corroborate the QMARL framework, this paper conducts the QMARL demonstration in a single-hop environment where edge agents offload packets to clouds. The extensive demonstration shows that the proposed QMARL framework enhances 57.7% of total reward than classical frameworks.
Abstract Recent advances in classical reinforcement learning (RL) and quantum computation point to a promising direction for performing RL on a quantum computer. However, potential applications in quantum RL are limited by the number of qubits available in modern quantum devices. Here, we present two frameworks for deep quantum RL tasks using gradient-free evolutionary optimization. First, we apply the amplitude encoding scheme to the Cart-Pole problem, where we demonstrate the quantum advantage of parameter saving using amplitude encoding. Second, we propose a hybrid framework where the quantum RL agents are equipped with a hybrid tensor network-variational quantum circuit (TN-VQC) architecture to handle inputs of dimensions exceeding the number of qubits. This allows us to perform quantum RL in the MiniGrid environment with 147-dimensional inputs. 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.
Hybrid quantum-classical frameworks leverage quantum computing for machine learning; however, variational quantum circuits (VQCs) are limited by local measurements. We introduce an adaptive non-local observable (ANO) paradigm within VQCs for quantum reinforcement learning (QRL), jointly optimizing circuit parameters and multi-qubit measurements. The ANO-VQC architecture serves as the function approximator in Deep Q-Network (DQN) and Asynchronous Advantage Actor-Critic (A3C) algorithms. On multiple benchmark tasks, ANOVQC agents outperform baseline VQCs. Ablation studies reveal that adaptive measurements enhance the function space without increasing circuit depth. Our results demonstrate that adaptive multi-qubit observables can enable practical quantum advantages in reinforcement learning.
In the realm of artificial intelligence, deep rein-forcement learning (RL) agents struggle with generalizability and require substantial computational resources, unlike humans who easily adapt and generalize across tasks. To address these challenges, we introduce Quantum Rainbow, a hybrid algorithm that leverages the neural mechanisms of human decision-making and the efficiency of quantum computing. Quantum Rainbow combines variational quantum circuits with the Rainbow Deep Q-Network (DQN) model to create a novel approach in rein-forcement learning that integrates quantum principles into deep learning paradigms. We evaluate our model using behavioral experiments through the Iowa Gambling Task and 4-Armed Bandit Task. Our investigations reveal a significant relationship between the architecture of quantum circuits and the performance of quantum RL agents. Specifically, using causal discovery methods, we demonstrate the critical role of quantum entanglement in enhancing model performance. These findings not only show promising results but also pave the way for future explorations into optimizing quantum circuit architectures for reinforcement learning applications. This study underscores the potential of quantum-enhanced algorithms to achieve “quantum advantage” by addressing fundamental limitations in conventional deep RL methods.
The emergence of quantum reinforcement learning (QRL) is propelled by advancements in quantum computing (QC) and machine learning (ML), particularly through quantum neural networks (QNN) built on variational quantum circuits (VQC). These advancements have proven successful in addressing sequential decision-making tasks. However, constructing effective QRL models demands significant expertise due to challenges in designing quantum circuit architectures, including data encoding and parameterized circuits, which profoundly influence model performance. In this paper, we propose addressing this challenge with differentiable quantum architecture search (DiffQAS), enabling trainable circuit parameters and structure weights using gradient-based optimization. Furthermore, we enhance training efficiency through asynchronous reinforcement learning (RL) methods facilitating parallel training. Through numerical simulations, we demonstrate that our proposed DiffQAS-QRL approach achieves performance comparable to manually-crafted circuit architectures across considered environments, showcasing stability across diverse scenarios. This methodology offers a pathway for designing QRL models without extensive quantum knowledge, ensuring robust performance and fostering broader application of QRL.