# Hybrid Quantum-Classical Policy Gradient for Adaptive Control of Cyber-Physical Systems: A Comparative Study of VQC vs. MLP

arXiv: https://arxiv.org/abs/2510.06010 · HTML: https://mlsanity.com/paper/2510.06010/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Quantum reinforcement learning, one of 15 directions in Deep reinforcement learning methods.
- Builds on 4 of its 9 references that are in the map.
- First posted on arXiv 7 Oct 2025.

## Placed in

- Deep reinforcement learning methods / [Quantum reinforcement learning](https://mlsanity.com/deeprl/quantum-reinforcement-learning/)

## Builds on (most cited first, 4 of 4)

- [A Survey on Quantum Reinforcement Learning](https://mlsanity.com/paper/2211.03464/) (2022)
- [Quantum reinforcement learning in continuous action space](https://mlsanity.com/paper/2012.10711/) (2020)
- [Fidelity-based Probabilistic Q-learning for Control of Quantum Systems](https://mlsanity.com/paper/1806.03145/) (2018)
- [An Introduction to Quantum Reinforcement Learning (QRL)](https://mlsanity.com/paper/2409.05846/) (2024)

## Abstract (arXiv)

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.