AI 中文总结
该研究提出Rand-SEMI-QAOA方法，基于压缩量子寄存器的有限预算深度一MaxCut集成，在特定MaxCut实例上取得0.9421的近似比，结果有限尺寸且资源明确，未确立量子优势。
AI 中文摘要
我们提出了Rand-SEMI-QAOA，一种基于(3,1)-QRAC松弛的有限预算QRAO-QAOA MaxCut集成方法。该方法从已实现的伽罗瓦稳定器相互无偏基（MUB）系统的乘积-X族中无放回均匀采样标签。每个选定的态-混合器对针对松弛的QRAO能量独立优化，随后通过确定性泡利符号解码进行评估。对已实现的非计算MUB目录的穷尽扫描显示，在20个经过验证的族均值单元中，乘积-X族有18个排名第一，且在r=5、6、7的所有测试单元中均排名第一。针对n∈{18,20,22}的2400个随机连通3-正则MaxCut实例组成的完整队列，带上限的匹配基数调度在单QAOA层下达到图均值解码最佳集近似比0.9421，而K=r²调度达到0.9319。这些统计数据基于公开的冻结选择池，未估计选择种子的变异性。精确规范恒等式表明，乘积族标签在r维符号规范群下生成QRAO哈密顿量的轨道。对于常见角度和松弛能量，确定性综合征分析证明分支退相，而各向异性高斯代理在β=b/r尺度上控制相干标签平均响应。该理论未对独立优化的解码最大值排序。结果是有限尺寸且资源明确的，未确立量子优势。
英文摘要
We introduce Rand-SEMI-QAOA, a finite-budget QRAO--QAOA ensemble for MaxCut based on a $(3,1)$-QRAC relaxation. The method samples labels uniformly without replacement from the product-$X$ family of an implemented Galois stabilizer mutually unbiased basis (MUB) system. Each selected state--mixer pair is optimized independently for relaxed QRAO energy and then evaluated by deterministic Pauli-sign decoding. Exhaustive scans of the implemented noncomputational MUB catalog place the product-$X$ family first in 18 of 20 validated family-mean cells and in every tested cell for $r=5,6,7$. On a complete cohort of $2{,}400$ random connected 3-regular MaxCut instances with $n\in\{18,20,22\}$, the capped matched-cardinality schedule attains a graph-mean decoded best-of-set approximation ratio of $0.9421$ with one QAOA layer, while the $K=r^2$ schedule attains $0.9319$. These statistics are conditional on the disclosed frozen selector pools and do not estimate variability over selector seeds. An exact gauge identity shows that product-family labels generate the orbit of the QRAO Hamiltonian under an $r$-dimensional sign-gauge group. For common angles and relaxed energy, deterministic syndrome analysis proves branchwise dephasing, while an anisotropic Gaussian surrogate controls the coherent label-averaged response on the scale $β=b/r$. The theory does not order independently optimized decoded maxima. The results are finite-size and resource-explicit and do not establish quantum advantage.
Comments27 pages, 4 figures
