Quantum Hitting Time according to a given distribution

• URL: http://arxiv.org/abs/2302.08871v1
• Date: Fri, 17 Feb 2023 13:41:23 GMT
• Title: Quantum Hitting Time according to a given distribution
• Authors: P. Boito, G. M. Del Corso
• Abstract summary: We focus on the notion of quantum hitting time for discrete-time Szegedy quantum walks, compared to its classical counterpart. We provide a detailed proof of quadratic speedup for time-reversible walks within the Szegedy framework. We explore the use of a general distribution in place of the stationary distribution in the definition of quantum hitting time.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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