Finding paths in tree graphs with a quantum walk

TL;DR

This paper explores how quantum random walks can be used to efficiently find specific nodes in tree graphs, potentially outperforming classical search algorithms.

Contribution

It demonstrates the use of quantum scattering random walks to locate nodes in tree graphs, providing both numerical and analytical evidence of improved search efficiency.

Findings

Quantum walks can locate nodes faster than classical methods.

Analytical solutions confirm the efficiency of quantum search.

Numerical simulations support the theoretical results.

Abstract

In this paper, we analyze the potential for new types of searches using the formalism of scattering random walks on Quantum Computers. Given a particular type of graph consisting of nodes and connections, a "Tree Maze", we would like to find a selected final node as quickly as possible, faster than any classical search algorithm. We show that this can be done using a quantum random walk, both exactly through numerical calculations as well as analytically using eigenvectors and eigenvalues of the quantum system.