Quantum Hitting Time according to a given distribution
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.
Cite
@article{arxiv.2302.08871,
title = {Quantum Hitting Time according to a given distribution},
author = {P. Boito and G. M. Del Corso},
journal= {arXiv preprint arXiv:2302.08871},
year = {2024}
}