AI 中文总结
本文对比经典、量子及量子启发方法在抽样框架最优分层任务中的表现，发现经典遗传算法在测试规模下仍是首选，量子设备未达经典GPU的效果，QUBO解与基准存在差距。
AI 中文摘要
最优分层是将各层聚合成少量最终层，以最小化满足目标精度约束所需的总样本量。该组合目标被重新表述为组内离散度的替代指标，可转化为二次无约束二元优化（QUBO）问题。本文对该替代指标的四种求解器开展对比案例研究，所有求解器均在swissmunicipalities数据集提供的相同20层框架下，受异构免费层级约束运行，四种求解器分别为：D-Wave构建的QUBO（此处通过模拟退火求解，无法使用QPU访问）、基于门的量子处理器（IBM Quantum，运行量子近似优化算法QAOA）、光子熵量子计算设备（QCi Dirac-3）、作为对照的经典GPU伊辛机（Fixstars Amplify AE）。求解器在硬件、计算预算、迭代次数以及IBM求解器的编码方式上存在差异，因此本次对比为案例研究而非受控实验。以包含129个样本单元的遗传算法基准为参照，最知名的QUBO解（目标值501.0）经Bethel-Chromy评估后对应样本量为160，存在约24%的差距，该差距源于找到的最优解而非经认证的全局最优解；IBM和Dirac-3的结果差距更大，分别为262和286；IBM的结果与稀疏量子晶格上的SWAP路由退化一致，但无法排除其他影响因素，而Dirac-3虽实现了真正的优化，却仍不及免费GPU在数秒内得到的结果。本文结论为，在本次测试的规模下，经典遗传算法仍是最优分层的首选方法，这反映出两点：一是离散度替代指标无法编码为低次多项式，与真实的Bethel-Chromy目标存在差距；二是IBM和Dirac-3的运行存在求解器及平台特定的限制，且这些发现未确立任何结果的全局最优性。
英文摘要
Optimal stratification aggregates strata into a small number of final strata to minimise total sample size required to meet target precision constraints. This combinatorial objective, reformulated as a within-cluster dispersion surrogate, can be expressed as a quadratic unconstrained binary optimisation (QUBO) problem. This paper reports a comparative case study of four solvers for that surrogate, run under heterogeneous free-tier constraints on an identical twenty-stratum frame from the swissmunicipalities dataset: a D-Wave-formulated QUBO, solved here by simulated annealing (QPU access unavailable); a gate-based quantum processor (IBM Quantum, running QAOA); a photonic entropy-quantum-computing device (QCi Dirac-3); and a classical GPU-based Ising machine as control (Fixstars Amplify AE). Solvers differ in hardware, computational budget, iteration count, and, for IBM, the encoding itself, so the comparison is a case study rather than a controlled experiment. Against a genetic-algorithm benchmark of 129 sample units, the best-known QUBO solution (objective 501.0) maps, after Bethel-Chromy evaluation, to a sample size of 160, a gap of roughly 24%, tied to the best solution found rather than a certified optimum. IBM and Dirac-3 fall further short, at 262 and 286; the IBM result is consistent with SWAP-routing degradation on a sparse qubit lattice, though not isolated from other causes, while Dirac-3, despite genuine optimisation, settles short of what a free GPU reaches in seconds. The paper concludes that a classical genetic algorithm remains, at the scale tested, the method of choice for optimal stratification, reflecting (a) limits of the dispersion surrogate versus the true Bethel-Chromy objective, not encodable as a low-degree polynomial, and (b) solver- and platform-specific limits in the IBM and Dirac-3 runs. These findings do not establish global optimality for either result.
Comments6 figures, 28 pages
