Quantum walk is a widely used method in designing quantum algorithms. In this article, we consider the lackadaisical discrete-time quantum walk (DTQW) on strongly regular graphs (SRG). When there is a single marked vertex in a SRG, we prove that lackadaisical DTQW can find the marked vertex with asymptotic success probability 1, with a quadratic speedup compared to classical random walk. This paper deals with any parameter family of SRG and argues that, by adding self-loops with proper weights, the asymptotic success probability can reach 1. The running time and asymptotic success probability matches the result of continuous-time quantum walk, and improves the result of DTQW.

中文翻译：

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基于懒散量子行走的强正则图搜索算法

量子行走是设计量子算法时广泛使用的方法。在本文中，我们考虑强正则图（SRG）上的懒散离散时间量子行走（DTQW）。当 SRG 中存在单个标记顶点时，我们证明了懒散的 DTQW 可以以渐近成功概率 1 找到标记顶点，与经典随机游走相比具有二次加速。本文针对SRG的任意参数族，认为通过添加适当权重的自循环，渐近成功概率可以达到1。运行时间和渐近成功概率与连续时间量子行走的结果相匹配，并提高了DTQW 的结果。