Offline Channel-Independent QAOA Angles for RIS Power Aggregation: Unit-Circle Phase Dictionaries and Infinite-Size Spin-Glass Limits

Abstract

Reconfigurable intelligent surfaces (RIS) maximize received power by setting per-element phases. Discrete-phase optimization is NP-hard in the worst case, while the quantum approximate optimization algorithm (QAOA) applied to RIS faces limited phase alphabets, either per-problem angle optimization or uncharacterized training cost exposed to barren plateaus, and no scalable performance benchmark. We introduce a $2^M$-phase $\theta$ dictionary for optimizing power $\Vert \mathbf{A}{e}^{j\theta }{\Vert }^2$ having $K\times N$ channel matrix $\mathbf{A}$ and QAOA angle offline optimization with instance and size-independent infinite-size limit of the mixed-$q$ Gaussian ensemble of Basso et al. Our design bounds the spin-Hamiltonian interaction order to at most quartic for any $M$, and the deployed order-2 reduction lies below the even-$q\ge 4$ regime in which constant-level QAOA limitations are proved. We perform analytical, state-vector, matrix-product-state and Pauli-path-simulation numerical studies for $N=K\le 100$ and QAOA depth $p=9$, verifying offline angle transfer to Rayleigh, Rician/line-of-sight, cascaded double-fading and spatially-correlated RIS channels at $N\in \{5,12\}$. We observe performance reaching a near-optimal multi-start single-flip local-search reference for $N\le 16$ under order-2 modeling with $2^5=32$-phase dictionary while the order-4 model shows a performance ceiling below the classical reference. The approach suggests a route to near-optimal large-$N$ performance on future fault-tolerant (FTQ) quantum computers, which enable the higher-depth QAOA circuits.

11 pages, 8 figures