CnNOT gates for implementing random quantum walks*

Quantum walks have been investigated for traversing graphs with certain oracles. This is important for building quantum routers on future quantum computers. Buliding quantum walk circuits benefit from the exponential increase in speed when compared to classical random walks. Here we invesitgated CnNOT based implementation of quantum walks along different length cycles and 2-D hypercycle. We decomposed the circuits into a set of series and parallel combinations of elementary CNOT and single qubit gates and simulated them theoretically taking into consideration the deterministic functioning of the gates. In addition, we ran a Python code simulating the same circuits on an IBM-Q supercomputer implemented with superconducting qubits. Based on the outputs, we highlight the physical constraints behind the real backend results and give numerical approximations for the errors for higher qubit number systems.