Generalization of CNOT-based Discrete Circular Quantum Walk: Simulation and Effect of Gate Errors

TL;DR

This paper explores implementing discrete circular quantum walks using CNOT and single-qubit gates, simulates them on IBM quantum hardware, and analyzes how gate errors affect circuit fidelity.

Contribution

It introduces a generalized CNOT-based quantum circular walk and evaluates the impact of gate errors through simulation on IBM quantum hardware.

Findings

Successful implementation of circular quantum walk circuits on IBM-Q

Gate errors significantly reduce circuit fidelity

Generalized circuit design enhances understanding of quantum walk dynamics

Abstract

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.