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We demonstrate an implementation of the hitting time of a discrete timequantum random walk on cubelike graphs using IBM's Qiskit platform. Ourimplementation is based on efficient circuits for the Grover and Shiftoperators. We verify the results about the one-shot hitting time of quantumwalks on a hypercube as proved in[https://link.springer.com/article/10.1007/s00440-004-0423-2]. We extend thestudy to another family of cubelike graphs called the augmented cubes[https://onlinelibrary.wiley.com/doi/abs/10.1002/net.10033]. Based on ournumerical study, we conjecture that for all families of cubelike graphs thereis a linear relationship between the degree of a cubelike graph and its hittingtime which holds asymptotically. That is, for any cubelike graph of degree$\Delta$, the probability of finding the quantum random walk at the target nodeat time $\frac{\pi \Delta}{2}$ approaches 1 as the degree $\Delta$ of thecubelike graph approaches infinity.

Implementation of hitting times of discrete time quantum random walks on Cubelike graphs