Generalization of CNOT-based Discrete Circular Quantum Walk: Simulation
  and Effect of Gate Errors
We investigate the counterparts of random walk in universal quantum computing
and their implementation using standard quantum circuits. Quantum walk have
been recently well investigated for traversing graphs with certain oracles. We
focus our study on traversing a 1-D graph, namely a circle, and show how to
implement discrete circular quantum walk in quantum circuits built with
universal CNOT and single quit gates. We review elementary quantum gates and
circuit decomposition and propose a a generalized version of the all CNOT based
quantum discrete circular walk. We simulated these circuits on an IBM quantum
supercomputer London IBM-Q with 5 qubits. This quantum computer has non perfect
gates based on superconducting qubits, therefore we analyze the impact of
errors on the fidelity of the Walker circuit.
Iyed Ben Slimen Amor Gueddana Vasudevan Lakshminarayanan