发表机构
School of Physics, Northwest University; C. N. Yang Institute for Theoretical Physics, Stony Brook University（西北大学物理学院; 石溪大学杨振宁理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出一种交替应用全局和局部Grover算子的量子部分搜索序列，在预言机与全局扩散算子深度相当时，相比GRK算法可降低超过20%的期望电路深度，并给出了精确的成功概率和最优参数。
AI 中文摘要
Grover算法在预言机查询次数方面是最优的。我们可以用精度换取速度，从而产生了量子部分搜索算法。部分搜索算法使用两种Grover算子实现：全局算子和局部算子，其中前者是用于全搜索的标准Grover算子，后者具有作用于搜索子空间的扩散算子。全局-局部-全局序列，也称为Grover-Radhakrishnan-Korepin（GRK）算法，已被证明在预言机查询度量下是最优的。在这项工作中，我们展示了由重复应用固定的全局和局部Grover算子乘积而形成的全局和局部Grover算子的交替序列，可以实现比GRK算法更低的期望电路深度。通过系统分析，我们获得了其精确的成功概率、期望深度和渐近最优参数。我们推导出了由预言机深度与全局扩散算子深度之比表征的边界，该边界将深度最优和预言机最优的部分搜索算法分开。当预言机和全局扩散算子的深度相当时，我们提出的交替部分搜索序列相比GRK算法可以将最小期望电路深度降低超过20%。
英文摘要
Grover's algorithm is optimal in terms of oracle queries. We can trade accuracy for speed, which gives rise to the quantum partial-search algorithm. The partial-search algorithm is implemented using two kinds of Grover operators, global and local, where the former is the standard Grover operator for full search and the latter has a diffusion operator acting on the search subspace. The global-local-global sequence, also known as the Grover-Radhakrishnan-Korepin (GRK) algorithm, has been proved optimal in the oracle-query metric. In this work, we show that the alternating sequence of global and local Grover operators, formed by repeatedly applying a fixed product of global and local Grover operators, can achieve a lower expected circuit depth than the GRK algorithm. Through systematic analysis, we obtain its exact success probability, expected depth, and asymptotically optimal parameters. We derive the boundary, characterized by the ratio between the depths of the oracle and the global diffusion operator, separating the depth-optimal and oracle-optimal partial-search algorithms. When the depths of the oracle and the global diffusion operator are comparable, our proposed alternating partial-search sequence can reduce the minimum expected circuit depth by more than 20\% compared with the GRK algorithm.
Comments20 pages, 7 figures
