Abstract
Quantum walks provide a framework for the construction of quantum algorithms. Based on this approach, we consider different walks for testing the commutativity of a finite dimensional algebra. In particular, we consider Szegedy’s and Santos’ quantum walks constructed from complete and torus graphs. Results of numerical experiments are presented, showing that for some choices of the quantum walks we can obtain better detections probabilities than with previous quantum algorithms addressing this problem that were based on Grover’s quantum search. Additionally, we introduce a general notion of quantum detection system that encompasses all the methods considered in this work, among others, and develop the concept of quantum hitting time for this kind of systems as an extension of Szegedy’s seminal ideas.
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