论文标题
从字符串检测到正交矢量问题
From String Detection to Orthogonal Vector Problem
论文作者
论文摘要
考虑到Grover的搜索算法（GSA）使用了标准扩散器阶段，我们重新审视了$ 3 $ qubit的独特弦乐检测问题（SDP），并将算法扩展到$ 4 $ QUBITS SDP，并与多个赢家一起。然后，我们研究非均匀分布的非结构化搜索问题，并在量子设置下定义正交矢量问题（OVP）。尽管在原始GSA框架下未达到数值稳定的结果，但我们提供了实施和进一步观察OVP的直觉。我们进一步在修改后的GSA框架下进行特殊案例分析，该框架旨在稳定在任意初始分布下的最终测量。基于分析的结果，我们概括了原始框架和修改都无法正常工作的初始条件。我们还提出了一个短深度电路，而不是利用GSA，该电路可以计算为给定向量的正交对，该向量表示为具有恒定运行时的二进制字符串。
Considering Grover's Search Algorithm (GSA) with the standard diffuser stage applied, we revisit the $3$-qubit unique String Detection Problem (SDP) and extend the algorithm to $4$-qubit SDP with multiple winners. We then investigate unstructured search problems with non-uniform distributions and define the Orthogonal Vector Problem (OVP) under quantum settings. Although no numerically stable results is reached under the original GSA framework, we provide intuition behind our implementation and further observations on OVP. We further perform a special case analysis under the modified GSA framework which aims to stabilize the final measurement under arbitrary initial distribution. Based on the result of the analysis, we generalize the initial condition under which neither the original framework nor the modification works. Instead of utilizing GSA, we also propose a short-depth circuit that can calculate the orthogonal pair for a given vector represented as a binary string with constant runtime.
