AI 中文总结
本研究针对伊辛图模型的量子稀有事件估计难题，结合循环信念传播与Chow-Liu算法制备态，构建结构预言机，经二十节点供应链模型验证，量子估计器误差低于经典蒙特卡罗基线。
AI 中文摘要
量子振幅估计可降低稀有事件概率估计的采样成本，但将其应用于关联伊辛图模型时，受限于目标分布制备及实用事件预言机构建的难度。本研究探索两种近似策略以缓解这些挑战：引入结合循环信念传播与Chow-Liu算法的无样本态制备方法，将得到的树近似编译为线性门数与深度的量子电路，并在涵盖不同拓扑、耦合强度及耦合符号的图族中评估其精度；还构建了采用可逆布尔门评估阈值规则的结构预言机。以二十节点供应链中断模型为案例研究，将最大似然振幅估计与四个经典蒙特卡罗基线对比：在本研究全程采用的固定深度方案下，量子估计器与经典方法具有相同的渐近误差标度，但以常数因子实现更低的估计误差；当将振幅编码查询替代原始采样次数作为资源度量时，该误差缩减幅度减小。本研究将统计误差与近似态制备及预言机构建导致的确定性误差分离，并明确实现超越常数因子改进的要求。
英文摘要
Quantum amplitude estimation can reduce the sampling cost of rare-event probability estimation, but applying it to correlated Ising graphical models is limited by the difficulty of preparing the target distribution and building a practical event oracle. This work explores two approximate strategies for mitigating these challenges. We introduce a sample-free state-preparation method combining loopy belief propagation with the Chow--Liu algorithm. The resulting tree approximation is compiled into a quantum circuit with linear gate count and depth, and its accuracy is evaluated across graph families spanning different topologies, coupling strengths, and coupling signs. We also construct a structural oracle that evaluates threshold rules with reversible Boolean gates. Using a twenty-node supply-chain disruption model as a case study, we compare maximum likelihood amplitude estimation against four classical Monte Carlo baselines. Under the fixed-depth schedule used throughout this work, the quantum estimator has the same asymptotic error scaling as the classical methods but achieves lower estimation error by a constant factor. This reduction narrows when amplitude-encoding queries replace raw shots as the resource metric. We separate statistical error from the deterministic errors caused by approximate state preparation and oracle construction, and identify the requirements for achieving an improvement beyond a constant factor.
