Reading out a parametrized quantum circuit through finite-shot measurements introduces a discrete stochastic component into hybrid quantum-classical neural networks, making gradient-based training inefficient. In this work, we introduce a surrogate-assisted actor-critic method for training hybrid quantum policies that avoids differentiating the quantum circuit during backpropagation. A classical neural surrogate trained on the circuit's input-output pairs from a replay buffer provides a differentiable substitute for actor updates and critic-target computation, while forward interaction and evaluation retain the quantum circuit's measurements. Our experiments on standard MuJoCo continuous-control tasks demonstrate promising policy learning. Notably, on Humanoid, more runs reach high returns than with learned classical baselines. Moreover, the best average return in our ablation comes from a smaller circuit / surrogate, suggesting that strong performance does not depend on a large network. We also derive conditional upstream gradient-error bounds that separate surrogate fitting from the mean-feature relaxation. Together, the results support surrogate-assisted training as an effective and efficient approach to learning hybrid quantum policies.
Quantum computing has a superior advantage in tackling specific problems, such as integer factorization and Simon's problem. For more general tasks in machine learning, by applying variational quantum circuits, more and more quantum algorithms have been proposed recently, especially in supervised learning and unsupervised learning. However, little work has been done in reinforcement learning, arguably more important and challenging. Previous work in quantum reinforcement learning mainly focuses on discrete control tasks where the action space is discrete. In this work, we develop a quantum reinforcement learning algorithm based on soft actor-critic -- one of the state-of-the-art methods for continuous control. Specifically, we use a hybrid quantum-classical policy network consisting of a variational quantum circuit and a classical artificial neural network. Tested in a standard reinforcement learning benchmark, we show that this quantum version of soft actor-critic is comparable with the original soft actor-critic, using much less adjustable parameters. Furthermore, we analyze the effect of different hyper-parameters and policy network architectures, pointing out the importance of architecture design for quantum reinforcement learning.
Training quantum neural networks (QNNs) on near-term hardware remains hampered by two compounding difficulties: the exponential vanishing of gradient variance known as the barren plateau, and the
O(L⋅2n) time and memory cost of differentiating through an
n-qubit,
L-layer circuit. We propose RLQ-Grad, a reinforcement-learning-based optimizer in which a classical policy
πφ (a spectrally-normalized PPO agent) learns to propose parameter updates directly, conditioned on the QNN's current parameters, loss, accuracy, and previous update. Because the surrogate gradient is emitted by a classical network rather than obtained by differentiating through the unitary
U(θ), its variance is not constrained by the barren plateau concentration bound, and its cost scales with the number of trainable parameters rather than the Hilbert-space dimension. We prove these properties formally and verify them on a hardware-efficient ansatz across four supervised benchmarks with up to
n=20 qubits. RLQ-Grad preserves a near-flat gradient-variance curve where backpropagation, parameter-shift, and adjoint differentiation decay by 1 to 2 orders of magnitude. Accounting for the full training pipeline (PPO rollouts, actor-critic updates, and optimizer states), RLQ-Grad needs under 2 MB of memory and runs
2490×,
7876×, and
673× faster per iteration than these three methods at
n=20. It improves top-1 accuracy by up to
+10% over gradient-based baselines on circuits of up to 12 qubits, and matches dedicated barren plateau mitigation methods on CIFAR-10 at 14 to 20 qubits, where evolutionary and gradient-free optimizers collapse to chance.
We explore the use of pure quantum policies, implemented via variational quantum circuits (VQCs), for offline reinforcement learning (RL). In contrast to hybrid models, our policy architecture contains no classical neural layers. Built on the MOOSE framework, we replace the classical policy with a VQC enhanced by trainable input and output weights. The policy is trained entirely offline using synthetic rollouts from a learned surrogate model of a physical cart-pole system. Evaluation in this simulated environment shows that the quantum policy performs on par with the classical baseline in terms of stability, smoothness, and reward accumulation. These results demonstrate that purely quantum models can effectively learn control strategies in model-based offline RL, offering a promising step toward real-world quantum-enhanced decision-making.
Quantum computing offers efficient encapsulation of high-dimensional states. In this work, we propose a novel quantum reinforcement learning approach that combines the Advantage Actor-Critic algorithm with variational quantum circuits by substituting parts of the classical components. This approach addresses reinforcement learning's scalability concerns while maintaining high performance. We empirically test multiple quantum Advantage Actor-Critic configurations with the well known Cart Pole environment to evaluate our approach in control tasks with continuous state spaces. Our results indicate that the hybrid strategy of using either a quantum actor or quantum critic with classical post-processing yields a substantial performance increase compared to pure classical and pure quantum variants with similar parameter counts. They further reveal the limits of current quantum approaches due to the hardware constraints of noisy intermediate-scale quantum computers, suggesting further research to scale hybrid approaches for larger and more complex control tasks.
In recent years, the utility of parameterized quantum circuits as function approximators has been widely studied. In the context of reinforcement learning, this approach has led to variational quantum algorithms such as quantum Q-learning. While these methods show promising empirical results, and can provide provable advantages for artificial problems, it remains unclear whether they can provide a provable quantum advantage over classical approaches for problems of practical relevance. A natural way to investigate this question is through the lens of dequantization: The construction of efficient classical algorithms capable of matching the performance of quantum variational methods. Building on recent kernel-based dequantization results for supervised learning, we take steps towards extending this surrogate-based dequantization program to reinforcement learning. Specifically, we study the simplified setting of reinforcement learning with a uniform generative model in which uniformly random state-action samples are available, which models the regime of sampling from a large experience replay buffer after sufficient exploration. Within this setting, we provide finite sample guarantees for classical kernelized Fitted Q-Iteration, with classical kernels designed to match the inductive bias of particular parameterized quantum circuits. Using these results, we then provide a set of sufficient conditions, on the data-encoding strategy of a parameterized quantum circuit, the corresponding classical kernel, and the problem structure, under which kernelized Fitted Q-Iteration provides a meaningful dequantization of quantum Q-learning, in this simplified setting. Apart from providing rigorous dequantization guarantees when these conditions are met, these results also motivate the use of kernelized fitted Q-iteration as a dequantization heuristic when these sufficient conditions cannot be verified.
Classical reinforcement learning (RL) methods often struggle in complex, high-dimensional environments because of their extensive parameter requirements and challenges posed by stochastic, non-deterministic settings. This study introduces quantum deep reinforcement learning (QDRL) to train humanoid agents efficiently. While previous quantum RL models focused on smaller environments, such as wheeled robots and robotic arms, our work pioneers the application of QDRL to humanoid robotics, specifically in environments with substantial observation and action spaces, such as MuJoCo's Humanoid-v4 and Walker2d-v4. Using parameterized quantum circuits, we explored a hybrid quantum-classical setup to directly navigate high-dimensional state spaces, bypassing traditional mapping and planning. By integrating quantum computing with deep RL, we aim to develop models that can efficiently learn complex navigation tasks in humanoid robots. We evaluated the performance of the Soft Actor-Critic (SAC) in classical RL against its quantum implementation. The results show that the quantum SAC achieves an 8% higher average return (246.40) than the classical SAC (228.36) after 92% fewer steps, highlighting the accelerated learning potential of quantum computing in RL tasks.