Year: 2008
Type: article
Abstract: We define the hitting (or absorbing) time for the case of continuous quantum walks by measuring the walk at random times, according to a Poisson process with measurement rate $\ensuremath{\lambda}$. From this definition we derive an explicit formula for the hitting time, and explore its dependence on the measurement rate. As the measurement rate goes to either 0 or infinity the hitting time diverges; the first divergence reflects the weakness of the measurement, while the second limit results from the quantum zeno effect. Continuous-time quantum walks, like discrete-time quantum walks but unlike classical random walks, can have infinite hitting times. We present several conditions for existence of infinite hitting times, and discuss the connection between infinite hitting times and graph symmetry.
Source: Physical Review A
Authors: Martin Varbanov, Hari Krovi, Todd A. Brun
Institution: University of Southern California
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1977392168