Fixed-Topology UCR State Encoding for High-Dimensional Quantum Reinforcement Learning

Abstract

In the era of noisy intermediate-scale quantum (NISQ) computing, the stable integration of high-dimensional classical states into quantum neural networks is a critical challenge for quantum reinforcement learning. Existing encoding schemes either rely heavily on classical neural networks, which can overshadow the training contributions of the quantum component, or use standard quantum input methods such as amplitude encoding, which suffer from limited trainability, noise sensitivity, and high implementation costs. To address this challenge, this paper repurposes uniformly controlled rotations (UCR) from static state preparation and static data encoding into a state-encoding interface for quantum neural networks, elevating the process of integrating classical states into quantum neural networks to an independent method-ological layer. Across Gymnasium continuous-control tasks, our UCR encoding achieves the best peak return, final return, and evaluation-curve AUC compared to representative angle encoding and amplitude encoding, with the AUC improving by +5.9 to +53.5 return units over angle encoding. While our UCR encoding is not the method with the fewest gates, it eliminates the classical neural networks on which angle encoding relies during dimensionality reduction, provides a fixed, sample-independent topology, and supports explicit resource accounting. On BipedalWalker-v3, UCR encoding reduces the actor parameter count of angle encoding from 1003 to 229 and increases the final return from 220.4 to 264.9, which is higher than the final return of amplitude encoding. A systematic evaluation of gate-level noise shows that the absolute performance advantage of UCR encoding in complex continuous control tasks persists in the low-noise regime, but this advantage window narrows as the input dimension and quantum circuit depth increase. For high-dimensional classical state inputs, UCR encoding achieves a more stable performance–resource trade-off than typical quantum encoding methods. Motivated by the problem of inputting classical states into quantum neural networks, our approach may be further explored in broader machine learning scenarios and higher-dimensional applications.