通过量子幅度估计展示二次蒙特卡罗加速：核工程示例
Demonstrating Quadratic Monte Carlo Speedup via Quantum Amplitude Estimation: Nuclear Engineering Examples
浏览论文内容
中文总结 AI 辅助
该研究以核工程为背景，利用基于量子相位估计的量子幅度估计方法，通过具体例子展示了二次加速效果，在玩具问题和U - 238共振积分示例中实现平方误差按O(1/T²)缩放，U - 238示例用14个相位估计量子比特恢复共振积分达约0.03%相对误差。
中文摘要 AI 辅助
我们展示了量子幅度估计（QAE）作为一种在核工程中实现蒙特卡罗型期望值二次加速的途径。使用基于量子相位估计（QPE）的QAE，我们研究了两个例子：离散裂变中子产额期望值和在1/E慢化谱下的U - 238共振积分。玩具问题实现为门级Qiskit电路，共振积分示例通过格罗弗算子的精确特征分解进行模拟以避免状态制备分解瓶颈。在两种情况下，与经典蒙特卡罗缩放O(1/N)相比，平方误差随预言机调用次数T按O(1/T²)缩放。对于U - 238示例，QAE使用m = 14个相位估计量子比特将共振积分恢复到约0.03%的相对误差。
英文摘要
We demonstrate quantum amplitude estimation (QAE) as a route to quadratic speedup for Monte Carlo-type expectation values in nuclear engineering. Using QPE-based QAE, we study two examples: a discrete fission-neutron-yield expectation and a U-238 resonance integral under a $1/E$ slowing-down spectrum. The toy problem is implemented as a gate-level Qiskit circuit, while the resonance-integral example is simulated through an exact eigendecomposition of the Grover operator to avoid state-preparation decomposition bottlenecks. In both cases, the squared error scales as $O(1/T^2)$ with the number of oracle calls $T$, compared with the classical Monte Carlo scaling $O(1/N)$. For the U-238 example, QAE recovers the resonance integral to approximately $0.03%$ relative error with $m=14$ phase-estimation qubits.
