AI 中文总结
研究中亚灌溉调度这一紧密耦合组合问题，通过线性化根区水平衡将其转化为QUBO问题，基于乌兹别克斯坦花拉子模棉花区观测数据构建实例，对四个层次进行基准测试及缩放研究，提供了物理基础、数据完整且可重现的编码。
AI 中文摘要
在水资源稀缺的中亚地区，旋转灌溉调度是一个紧密耦合的组合问题：土壤湿度记忆将每个灌溉决策与一个区域内的所有后续日期联系起来，田间邻接在重叠窗口日将各区域耦合，刚性渠道旋转对水输送进行时间量化。我们通过将根区水平衡线性化，将其表述为二次无约束二进制优化（QUBO）问题，因此二次作物压力目标产生的物理耦合作为无高阶项的二体伊辛相互作用；只有水预算约束需要人为的全对全惩罚，我们用一个比一般规定紧一个数量级的实例自适应权重边界来证明这一点。每个实例都是根据乌兹别克斯坦花拉子模一个棉花区的观测数据构建的：美国国家航空航天局（NASA）POWER气象数据、粮农组织（FAO）-56彭曼 - 蒙特斯蒸散量、SoilGrids 2.0水力学数据、实测毛细通量以及记录的渠道旋转窗口，这些数据以量子比特数减少的形式输入。我们对四个层次进行了基准测试——精确求解器、匹配预算启发式算法、理想态矢量量子近似优化算法（QAOA）以及噪声模型加IBM Heron执行——并对多达584个变量的土壤实例进行了缩放研究。精确的分支定界法在数秒内通过150个变量证明了最优性，并且通过缩放预算修复了固定评估预算下启发式算法的退化，因此在与部署相关的规模上没有出现经典的可扩展性障碍，我们也未声称有量子优势；我们为量子实用时代提供了一个具有物理基础、数据完整、可重现的社会关键调度问题的编码。
英文摘要
Rotational irrigation scheduling in water-scarce Central Asia is a densely coupled combinatorial problem: soil-moisture memory links each irrigation decision to all later days within a zone, field adjacency couples zones on overlapping window days, and rigid canal rotations quantize water delivery in time. We formulate it as a Quadratic Unconstrained Binary Optimization (QUBO) by linearizing the root-zone water balance, so the quadratic crop-stress objective generates the physical couplings as 2-local Ising interactions with no higher-order terms; only the water-budget constraint requires an artificial all-to-all penalty, which we certify with an instance-adaptive weight bound an order of magnitude tighter than generic prescriptions. Every instance is built from observed data for a cotton district in Khorezm, Uzbekistan: NASA POWER meteorology, FAO-56 Penman--Monteith evapotranspiration, SoilGrids~2.0 hydraulics, measured capillary fluxes, and documented canal-rotation windows that enter as qubit-count reductions. We benchmark four tiers -- exact solvers, matched-budget heuristics, ideal-statevector quantum approximate optimization algorithm (QAOA), and noise-model plus IBM Heron execution -- and add a scaling study on soil instances up to 584 variables. Exact branch-and-bound proves optimality in seconds through 150 variables, and heuristic degradation at fixed evaluation budget is repaired by scaling the budget, so no classical scalability wall appears at deployment-relevant sizes, and none is claimed. On hardware, the informative signal is optimum-sampling enrichment over uniform sampling. We claim no quantum advantage; we deliver a physically grounded, data-complete, reproducible encoding of a societally critical scheduling problem for the quantum-utility era.
Comments14 pages, 4 figures, 3 tables
