# Lyapunov-Aware Quantum-Inspired Reinforcement Learning for Continuous-Time Vehicle Control: A Feasibility Study

arXiv: https://arxiv.org/abs/2510.18852 · HTML: https://mlsanity.com/paper/2510.18852/

## 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 5 of its 9 references that are in the map.
- First posted on arXiv 21 Oct 2025.

## Placed in

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

## Builds on (most cited first, 5 of 5)

- [Universal Quantum Control through Deep Reinforcement Learning](https://mlsanity.com/paper/1803.01857/) (2018)
- [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)
- [Curriculum-based Deep Reinforcement Learning for Quantum Control](https://mlsanity.com/paper/2012.15427/) (2020)
- [PID-Inspired Inductive Biases for Deep Reinforcement Learning in Partially Observable Control Tasks](https://mlsanity.com/paper/2307.05891/) (2023)

## Abstract (arXiv)

This paper presents a novel Lyapunov-Based Quantum Reinforcement Learning (LQRL) framework that integrates quantum policy optimization with Lyapunov stability analysis for continuous-time vehicle control. The proposed approach combines the representational power of variational quantum circuits (VQCs) with a stability-aware policy gradient mechanism to ensure asymptotic convergence and safe decision-making under dynamic environments. The vehicle longitudinal control problem was formulated as a continuous-state reinforcement learning task, where the quantum policy network generates control actions subject to Lyapunov stability constraints. Simulation experiments were conducted in a closed-loop adaptive cruise control scenario using a quantum-inspired policy trained under stability feedback. The results demonstrate that the LQRL framework successfully embeds Lyapunov stability verification into quantum policy learning, enabling interpretable and stability-aware control performance. Although transient overshoot and Lyapunov divergence were observed under aggressive acceleration, the system maintained bounded state evolution, validating the feasibility of integrating safety guarantees within quantum reinforcement learning architectures. The proposed framework provides a foundational step toward provably safe quantum control in autonomous systems and hybrid quantum-classical optimization domains.