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

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 θ dictionary for optimizing power \|mathbf{A} e^jθ\|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-qge4 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 leq 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 Nin\{5,12\}. We observe performance reaching a near-optimal multi-start single-flip local-search reference for Nle16 under order-2 modeling with 2⁵{=}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.