Cycle discrete-time quantum walks on a noisy quantum computer

TL;DR

This paper evaluates the current capabilities of IBM's quantum computers to simulate cycle discrete-time quantum walks, highlighting the significant noise reduction needed for larger, more complex walks.

Contribution

It demonstrates the implementation of quantum walks on real quantum hardware and develops a noise model to estimate fidelity requirements for larger walks.

Findings

Current IBM quantum devices can simulate small quantum walks with limited fidelity.

A noise reduction of at least 94% is necessary for larger, more complex quantum walks.

The study provides insights into hardware limitations and noise impacts on quantum walk simulations.

Abstract

The rapid development of quantum computing has led to increasing interest in quantum algorithms for a variety of different applications. Quantum walks have also experienced a surge in interest due to their potential use in quantum algorithms. Using the qiskit software package, we test how accurately the current generation of quantum computers provided by IBM can simulate a cycle discrete-time quantum walk. Implementing an 8-node, 8-step walk and a simpler 4-node, 4-step discrete-time quantum walk on an IBM quantum device known as ibmq_quito, the results for each step of the respective walks are presented. A custom noise model is developed in order to estimate that noise levels in the ibmq_santiago quantum device would need to be reduced by at least 94% in order to execute a 16-node, 16-step cycle discrete-time quantum walk to a reasonable level of fidelity.