Quantum Computing: Implementing Hitting Time for Coined Quantum Walks on Regular Graphs

TL;DR

This paper develops a quantum circuit for the MNRS algorithm to compute hitting times in quantum walks on regular graphs, demonstrating its effectiveness on noise-free and noisy IBM quantum simulators.

Contribution

It introduces a practical implementation of the MNRS quantum walk algorithm for hitting time estimation on regular graphs using IBM quantum simulators.

Findings

Hitting times match theoretical expectations on noise-free simulators

Noise significantly affects the accuracy of quantum walk outcomes

Implementation demonstrates feasibility of quantum walk algorithms on current hardware

Abstract

In recent years, quantum walks have been widely researched and have shown exciting properties. One such is a quadratic speed-up in hitting time compared to its classical counterpart. In this paper, we design a quantum circuit for the MNRS algorithm, which finds a marked node in a graph with a quantum walk, and use it to find a hitting time for the marked nodes in the walk. We do this by implementing the circuit on IBM quantum simulators and show that the execution on a noise-free simulator results in hitting times that agree with the theoretical expectations. We also run the algorithm on a mock backend that simulates the noise of the IBM Melbourne computer. As expected, the noise has an extensive impact on the output, resulting in outcomes far from the noise-free simulation.