Implementation of quantum hitting times of cubelike graphs on IBM's Qiskit platform

Abstract

In this paper, we give a procedure to construct quantum circuits for implementing discrete-time quantum walks on a family of Cayley graphs called cubelike graphs. We construct these circuits on IBM�s Qiskit platform and demonstrate an implementation of the quantum hitting times on cubelike graphs. Based on our numerical study, we conjecture that for all families of cubelike graphs there is a linear relationship between the degree of a cubelike graph and its hitting time which holds asymptotically. This conjecture, if proved, will generalize the result of hitting times of discrete-time quantum walks on hypercubes to general family of cubelike graphs.