Phase-Aware Quantum–Classical Feedback Compression in RIS: Trainability and Performance Limits

Abstract

This paper considers a multi-antenna base station (BS) communicating with a single-antenna user through a reconfigurable intelligent surface (RIS). In large RIS deployments, feeding back the high-dimensional phase vector <inline-formula><tex-math notation="LaTeX">$\boldsymbol{\theta }\in [0,2\pi)^{N}$</tex-math></inline-formula>, where <inline-formula><tex-math notation="LaTeX">$N$</tex-math></inline-formula> is the number of RIS elements, poses a major scalability challenge. Conventional codebook-based compression is limited to fixed linear subspaces. To address this, we propose Phase-Aware Quantum RIS (PAQ-RIS), a hybrid quantum–classical autoencoder that compresses RIS phase profiles using variational quantum circuits. Phase shifts are angle-encoded into quantum states, processed by parameterized quantum circuits, and reconstructed by a classical decoder. Results show that PAQ-RIS improves beamforming accuracy by up to 14.5% over classical autoencoders for an RIS with <inline-formula><tex-math notation="LaTeX">$N=512$</tex-math></inline-formula> elements using <inline-formula><tex-math notation="LaTeX">$q=9$</tex-math></inline-formula> qubits at a feedback compression ratio of approximately 19%. For <inline-formula><tex-math notation="LaTeX">$N=1024$</tex-math></inline-formula>, the framework continues to provide performance gains, achieving beamforming accuracy improvements of up to 11.33%. However, for larger RIS configurations with <inline-formula><tex-math notation="LaTeX">$N=2048$</tex-math></inline-formula> elements, the performance gain decreases, with the best improvement dropping to 4.44% due to barren plateaus and near-Haar-random latent states, establishing the practical scalability limits of quantum-assisted compression.