Search-base algorithms have widespread applications in different scenarios. Grover's quantum search algorithms and its generalization, amplitude amplification, provide a quadratic speedup over classical search algorithms for unstructured search. We consider the problem of searching with prior knowledge. More preciously, search for the solution among N items with a prior probability distribution. This letter proposes a new generalization of Grover's search algorithm which performs better than the standard Grover algorithm in average under this setting. We prove that our new algorithm achieves the optimal expected success probability of finding the solution if the number of queries is fixed.

中文翻译：

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具有先验知识的量子搜索

基于搜索的算法在不同的场景中有着广泛的应用。Grover 的量子搜索算法及其泛化，振幅放大，为非结构化搜索提供了经典搜索算法的二次加速。我们考虑使用先验知识进行搜索的问题。更重要的是，在具有先验概率分布的 N 项中搜索解决方案。这封信提出了 Grover 搜索算法的新泛化，该算法在此设置下的平均性能优于标准 Grover 算法。我们证明了我们的新算法在查询数量固定的情况下实现了找到解决方案的最佳预期成功概率。