Scattering Quantum Random Walks on Square Grids and Randomly Generated Mazes

TL;DR

This paper investigates the effectiveness of scattering quantum random walks on square grid graphs for search tasks, demonstrating their robustness in hybrid quantum-classical algorithms even with random obstacles and vertex placement.

Contribution

It extends the application of scattering quantum random walks to grid graphs and analyzes their resilience to randomness and obstacles in search problems.

Findings

Quantum walk probability distributions are favorable for hybrid algorithms.

The hybrid algorithm remains effective despite random obstacle placement.

Resilience of the quantum walk-based search to various types of randomness.

Abstract

The Scattering Quantum Random Walk scheme has found success as a basis for search algorithms on highly symmetric graph structures. In this paper we examine its effectiveness at locating a specially marked vertex on square grid graphs, consisting of N$^2$ nodes. We simulate these quantum systems using classical computational methods, and find that the probability distributions that arise are very favorable for a hybrid quantum / classical algorithm. We then examine how this hybrid algorithm handles varying types of randomness in both location of the special vertex and later random obstacles placed throughout the geometry, showing that that the algorithm is resilient to both cases.