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Improved upper bounds for the hitting times of quantum walks
Physical Review A ( IF 2.9 ) Pub Date : 2021-09-21 , DOI: 10.1103/physreva.104.032215
Yosi Atia , Shantanav Chakraborty

Continuous-time quantum walks have proven to be an extremely useful framework for the design of several quantum algorithms. Often, the running time of quantum algorithms in this framework is characterized by the quantum hitting time: the time required by the quantum walk to find a vertex of interest with a high probability. In this article, we provide improved upper bounds for the quantum hitting time that can be applied to several continuous-time quantum walk (CTQW) based quantum algorithms. In particular, we apply our techniques to the glued-trees problem, improving their hitting time upper bound by a polynomial factor: from O(n5) to O(n2logn). Furthermore, our methods also help to exponentially improve the dependence on precision of the CTQW based algorithm to find a marked node on any ergodic, reversible Markov chain by Chakraborty et al. [Phys. Rev. A 102, 022227 (2020)].

中文翻译:

改进了量子行走命中时间的上限

连续时间量子行走已被证明是设计几种量子算法的非常有用的框架。通常,该框架中量子算法的运行时间以量子命中时间为特征:量子游走以高概率找到感兴趣的顶点所需的时间。在本文中,我们提供了改进的量子命中时间上限,该上限可应用于几种基于连续时间量子行走 (CTQW) 的量子算法。特别是,我们将我们的技术应用于胶合树问题,通过多项式因子提高它们的命中时间上限:(n5)(n2日志n). 此外,我们的方法还有助于以指数方式提高基于 CTQW 的算法对精度的依赖,以在 Chakraborty等人的任何遍历可逆马尔可夫链上找到标记节点[物理。修订版 A 102 , 022227 (2020)]。
更新日期:2021-09-21
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