论文标题
Grover搜索算法中的成功概率与连贯性之间的互补性
Complementarity between Success Probability and Coherence in Grover Search Algorithm
论文作者
论文摘要
连贯性在Grover搜索算法（GSA）中起着非常重要的作用。在本文中，我们定义了归一化的连贯性n（c），其中c是连贯的测量。根据大N和香农的最大熵原理的限制，获得了GSA的相干性与成功概率之间令人惊讶的互补关系。也就是说，p_s（t）+n（c（t））\ simeq 1，其中c在相干性和相干性的相对熵方面，t是GSA中搜索迭代的数量。此外，该方程式在理想或嘈杂的环境中都保持不变。考虑到Qubits的数量在最近的嘈杂中间尺度量子（NISQ）时代有限，因此对不同类型的噪声进行了一些精确的数值计算实验。结果表明，成功概率与连贯性之间的互补几乎总是保持。这项工作提供了一种新的观点，可以通过操纵其互补连贯性来提高成功概率，反之亦然。它具有在NISQ时代有助于量子算法设计的极大潜力。
Coherence plays a very important role in Grover search algorithm (GSA). In this paper, we define the normalization coherence N(C), where C is a coherence measurement. In virtue of the constraint of large N and Shannon's maximum entropy principle, a surprising complementary relationship between the coherence and the success probability of GSA is obtained. Namely, P_s(t)+N(C(t))\simeq 1, where C is in terms of the relative entropy of coherence and l_1 norm of coherence, t is the number of the search iterations in GSA. Moreover, the equation holds no matter in ideal or noisy environments. Considering the number of qubits is limited in the recent noisy intermediate-scale quantum (NISQ) era, some exact numerical calculation experiments are presented for different database sizes N with different types of noises. The results show that the complementary between the success probability and the coherence almost always hold. This work provides a new perspective to improve the success probability by manipulating its complementary coherence, and vice versa. It has an excellent potential for helping quantum algorithms design in the NISQ era.
