Optimization on large interconnected graphs and networks using adiabatic quantum computation

Abstract

In this paper, we demonstrate that it is possible to create an adiabatic quantum computing algorithm that solves the shortest path between any two vertices on an undirected graph with at most [Formula: see text] qubits, where [Formula: see text] is the number of vertices of the graph. We do so without relying on any classical algorithms, aside from creating an ([Formula: see text]) adjacency matrix. The objective of this paper is to demonstrate the fact that it is possible to model large graphs on an adiabatic quantum computer using the maximum number of qubits available and random graph generators such as the Barabási–Albert and the Erdős–Rényi methods which can scale based on a power law.