精确搜索多集合交集的量子算法
Exact quantum algorithm for searching of multiple sets intersection
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中文总结 AI 辅助
本文基于Long的相位匹配方法，提出并证明了一种能精确搜索多个集合交集的量子算法，并给出相应量子电路，通过数值模拟验证了理论结果。
中文摘要 AI 辅助
当目标集合的全局预言机可用时，Grover算法在非结构化搜索中实现了二次加速。然而，其成功概率通常低于100%。为解决这一问题，Long通过引入相位匹配条件提出了Grover搜索算法的改进版本，该版本能以理论零失败率搜索目标集合。尽管如此，在许多应用中，目标集合由多个约束集合的交集决定。现有大多数基于Grover的方法仅限于两个集合的交集，且并非总能成功搜索目标集合。在本工作中，基于Long的方法，我们提出了一种精确搜索多个集合交集的算法。我们推导并证明了用于精确搜索交集的相位匹配条件。此外，我们给出了实现精确交集搜索的量子电路。最后，我们通过数值模拟支持了我们的理论结果。
英文摘要
Grover's algorithm achieves a quadratic speedup for unstructured search when a global oracle for the target set is available. However, its success probability is generally below $100\%$. To overcome this issue, Long presented a modified version of Grover's search algorithm by introducing a phase-matching condition, which can search for the target set with zero theoretical failure rate. Nevertheless, in many applications, the target set is determined by the intersection of multiple constrained sets. Most existing Grover-based methods are limited to the intersection of only two sets and are not always successful in searching for the target set. In this work, based on Long's method, we propose an algorithm for exactly searching the intersection of multiple sets. We derive and prove a phase-matching condition for searching the intersection exactly. Furthermore, we present a quantum circuit that implements exact intersection search. Finally, we support our theoretical results with numerical simulations.
发表机构
- School of Mathematical Sciences, Hangzhou Dianzi University（杭州电子科技大学数学科学学院）
- School of Computer and Computing Science, Hangzhou City University（杭州城市大学计算机与计算科学学院）
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