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IEEE International Conference on Quantum Computing and Engineering (QCE)

Learning Control with Simulated Variational Quantum Policies in a Surrogate Cart-Pole Environment

Yize Sun, Mohamad Hagog, M. Weber, Daniel M. Hein, Steffen Udluft, Yunpu Ma, Volker Tresp

Published Aug 30, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.1109/qce65121.2025.10459

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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.
This paper investigates the integration of quantum computing into offline reinforcement learning and the deployment of the resulting quantum policy in a real-time control hardware realization of the cart-pole system. Variational Quantum Circuits (VQCs) are used to represent the policy. Classical model-based offline policy search was applied, in which a pure VQC with trainable input-output weights is used as a policy network instead of a classical multilayer perceptron. The goal is to evaluate the potential of deploying quantum architectures in real-world industrial control problems. The experimental results show that the investigated model-based offline policy search is able to generate quantum policies that can balance the hardware cart-pole. A latency analysis reveals that while local simulated execution meets real-time requirements, cloud-based quantum processing remains too slow for closed-loop control.
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.
This paper presents the first algorithm for model-based offline quantum reinforcement learning and demonstrates its functionality on the cart-pole benchmark. The model and the policy to be optimized are each implemented as variational quantum circuits. The model is trained by gradient descent to fit a pre-recorded data set. The policy is optimized with a gradient-free optimization scheme using the return estimate given by the model as the fitness function. This model-based approach allows, in principle, full realization on a quantum computer during the optimization phase and gives hope that a quantum advantage can be achieved as soon as sufficiently powerful quantum computers are available.
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.
The comparative evaluation between classical and quantum reinforcement learning (QRL) paradigms was conducted to investigate their convergence behavior, robustness under observational noise, and computational efficiency in a benchmark control environment. The study employed a multilayer perceptron (MLP) agent as a classical baseline and a parameterized variational quantum circuit (VQC) as a quantum counterpart, both trained on the CartPole-v1 environment over 500 episodes. Empirical results demonstrated that the classical MLP achieved near-optimal policy convergence with a mean return of 498.7 +/- 3.2, maintaining stable equilibrium throughout training. In contrast, the VQC exhibited limited learning capability, with an average return of 14.6 +/- 4.8, primarily constrained by circuit depth and qubit connectivity. Noise robustness analysis further revealed that the MLP policy deteriorated gracefully under Gaussian perturbations, while the VQC displayed higher sensitivity at equivalent noise levels. Despite the lower asymptotic performance, the VQC exhibited significantly lower parameter count and marginally increased training time, highlighting its potential scalability for low-resource quantum processors. The results suggest that while classical neural policies remain dominant in current control benchmarks, quantum-enhanced architectures could offer promising efficiency advantages once hardware noise and expressivity limitations are mitigated.
Quantum Computing aims to streamline machine learning, making it more effective with fewer trainable parameters. This reduction of parameters can speed up the learning process and reduce the use of computational resources. However, in the current phase of quantum computing development, known as the noisy intermediate-scale quantum era (NISQ), learning is difficult due to a limited number of qubits and widespread quantum noise. To overcome these challenges, researchers are focusing on variational quantum circuits (VQCs). VQCs are hybrid algorithms that merge a quantum circuit, which can be adjusted through parameters, with traditional classical optimization techniques. These circuits require only few qubits for effective learning. Recent studies have presented new ways of applying VQCs to reinforcement learning, showing promising results that warrant further exploration. This study investigates the effects of various techniques — data re-uploading, input scaling, output scaling — and introduces exponential learning rate decay in the quantum proximal policy optimization algorithm’s actor-VQC. We assess these methods in the popular Frozen Lake and Cart Pole environments. Our focus is on their ability to reduce the number of parameters in the VQC without losing effectiveness. Our findings indicate that data re-uploading and an exponential learning rate decay significantly enhance hyperparameter stability and overall performance. While input scaling does not improve parameter efficiency, output scaling effectively manages greediness, leading to increased learning speed and robustness.