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Chinese Physics Letters

Quantum Search Algorithm Based on Multi-Phase

李坦, 鲍皖苏, 林文铅, 张侯, 付向群

Published Jan 1, 2014• 1 citation
OpenAlex

Abstract

当目标项目的部分超过 1/4 时，格罗弗量搜索算法的成功概率快速减少，在阶段起一个重要作用的地方。因此，我们使用多重阶段补充对方。我们获得三个有用性质和成功概率的一条重要定理并且为阶段的一个任意的数字设计最佳的阶段的一个系统的答案。把结果基于这些，我们最后建议概率其成功就随阶段的数字的增加升起与的一个多相的量搜索算法当目标项目的部分在更低的限制上时，一次单个重复，和它趋于是 100% 。

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当目标项目的部分超过 1/4 时，格罗弗量搜索算法的成功概率快速减少，在阶段起一个重要作用的地方。因此，我们使用多重阶段补充对方。我们获得三个有用性质和成功概率的一条重要定理并且为阶段的一个任意的数字设计最佳的阶段的一个系统的答案。把结果基于这些，我们最后建议概率其成功就随阶段的数字的增加升起与的一个多相的量搜索算法当目标项目的部分在更低的限制上时，一次单个重复，和它趋于是 100% 。
The success probability of the Grover quantum search algorithm decreases quickly when the fraction of target items exceeds 1/4, where the phase plays a significant role. Therefore, we use multiple phases to complement each other. We obtain three useful properties and an important theorem of the success probability and design a systematic solution of the optimal phases for an arbitrary number of phases. Based on these results, we finally propose a multi-phase quantum search algorithm whose success probability rises with the increase of the number of phases with just a single iteration, and it tends to be 100% when the fraction of target items is over a lower limit.
Grover's search algorithm has attracted great attention due to its quadratic speedup over classical algorithms in unsorted database search problems. However, Grover's algorithm is inefficient in multi-target search problems, except in the case of 1/4 of the data in the database satisfying the search conditions. Long presented a modified version of Grover's search algorithm by introducing a phase-matching condition that can search for the target state with a zero theoretical failure rate. In this work, we present an optimized exact multi-target search algorithm based on the modified Grover's algorithm by transforming the canonical diffusion operator to a more efficient diffusion operator, which can solve the multi-target search problem with a 100% success rate while requiring fewer gate counts and shallower circuit depth. After that, the optimized multi-target algorithm for four different items, including 2-qubit with 2 targets, 5-qubit with 2 targets, 5-qubit with 4 targets, and 6-qubit with 3 targets, are implemented on MindSpore framework. The experimental results show that, compared with Grover's algorithm and the modified Grover's algorithm, the proposed algorithm can reduce the quantum gate count by at least 21.1% and the depth of the quantum circuit by at least 11.4% and maintain a 100% success probability. Our code are available at https://github.com/mindsporelab/models/tree/master/research/arxiv_papers/GROVER-OP. Thanks for the support provided by MindSpore Community.