基于给定分布的量子击中时间
Quantum Hitting Time according to a given distribution
AI总结：
本研究聚焦离散时间Szegedy量子行走的量子击中时间，既以线性代数语言详细证明了时间可逆行走的二次加速特性，又通过理论与数值实验探索用一般分布替代平稳分布定义量子击中时间的方案。
摘要：
本研究聚焦于离散时间Szegedy量子行走的量子击中时间概念，并将其与经典对应概念进行对比。在适当假设下，已知量子击中时间的量级为经典击中时间的平方根：这种二次加速是量子方法计算优势的一个显著例证。\n 本文的研究目的有两方面。一方面，我们以线性代数领域研究者熟悉的语言，详细证明了Szegedy框架下时间可逆行走的二次加速特性。此外，我们通过理论推导与数值实验，探索了在量子击中时间的定义中使用一般分布替代平稳分布的可行性。
英文摘要：
In this work we focus on the notion of quantum hitting time for discrete-time Szegedy quantum walks, compared to its classical counterpart. Under suitable hypotheses, quantum hitting time is known to be of the order of the square root of classical hitting time: this quadratic speedup is a remarkable example of the computational advantages associated with quantum approaches. Our purpose here is twofold. On one hand, we provide a detailed proof of quadratic speedup for time-reversible walks within the Szegedy framework, in a language that should be familiar to the linear algebra community. Moreover, we explore the use of a general distribution in place of the stationary distribution in the definition of quantum hitting time, through theoretical considerations and numerical experiments.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
