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arXiv · 2302.08871

Quantum Hitting Time according to a given distribution

P. Boito·G. M. Del Corso
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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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P. Boito, G. M. Del Corso. 2023-02-17. Quantum Hitting Time according to a given distribution. https://doi.org/10.1080/03081087.2024.2349197

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