基于QAOA的M-QAM MIMO最大似然检测：ML速率离线角度设计与关联无限尺寸自旋玻璃模型
M-QAM MIMO Maximum-Likelihood Detection with QAOA: ML-Rate Offline Angle Design and Correlated Infinite-Size Spin-Glass Models
AI总结：
该研究针对M-QAM MIMO的ML检测问题，提出关联无限尺寸自旋玻璃框架，首次将ML速率用于QAOA角度设计，在高QAM阶数、多天线场景下实现了优于精确ML的BER性能，为FTQ电路近最优解码提供了方向。
AI中文摘要：
量子近似优化算法（QAOA）针对多输入多输出（MIMO）系统中NP难的最大似然（ML）检测问题。现有M进制正交幅度调制（M-QAM）检测器通过期望伊辛能量设计角度，方式包括在线逐实例、热启动或斜坡式，而单次训练设计仅适用于B/QPSK或块局部场景，导致M-QAM缺乏尺寸可扩展的基准。其无限尺寸自旋玻璃理论假设无序独立，这与B/QPSK的保留协方差匹配，但不匹配M-QAM的关联耦合与场。我们开发了关联无限尺寸多物种自旋玻璃框架，其协方差匹配评估器使该能量成为具有尺寸可扩展基准的离线目标。此外，首次将ML速率（采样ML序列的指数速率）用于MIMO检测中的QAOA角度设计。能量评估器无q参数，成本为O(p·4^p)，而ML速率将角度从固定q_ref量子比特参考转移。测试覆盖4096-QAM、128天线、p=30，每符号信噪比（SNR）0-45 dB。模拟中，ML速率遵循幂律r0·p^(-α)，采样设计对应更大指数，其在5×5 16-QAM（0-20 dB）和3×3 64-QAM（8-28 dB）上跟踪精确ML，且比特误码率（BER）优势随SNR扩大至两个数量级。该方法为更深层无噪声容错量子（FTQ）电路上的近最优解码指明方向。
英文摘要：
The quantum approximate optimization algorithm (QAOA) targets NP-hard maximum-likelihood (ML) detection in multiple-input multiple-output (MIMO) systems. Existing $M$-ary quadrature amplitude modulation (M-QAM) detectors design angles by expected Ising energy: online per instance, warm-started, or ramped, while train-once designs remain B/QPSK-only or block-local, leaving M-QAM without a size-scalable benchmark. Their infinite-size spin-glass theory assumes independent disorder, matching the retained covariances at B/QPSK but not M-QAM's correlated couplings and fields. We develop a correlated infinite-size multi-species spin-glass framework whose covariance-matched evaluators make that energy an offline objective with a size-scalable benchmark. In addition, the ML rate, the exponential rate of sampling the ML string, is for the first time exploited for QAOA angle design in MIMO detection. The energy evaluator is $q$-free at $O(p\,4^p)$ cost while the ML rate transfers angles from a fixed $q_{\rm ref}$-qubit reference. Tests reach 4096-QAM, 128 antennas, $p=30$ and per-symbol SNR 0-45 dB. In simulations, ML rates fall as a power law $r_0\,p^{-α}$, with larger exponents for the sampling design, which tracks exact ML at $5\times5$ 16-QAM (0-20 dB) and $3\times3$ 64-QAM (8-28 dB) while its bit-error rate (BER) advantage widens with SNR to two orders of magnitude. The approach points toward near-optimum decoding on deeper noiseless fault-tolerant quantum (FTQ) circuits.
