Optimization on Large Interconnected Graphs and Networks Using Adiabatic Quantum Computation

TL;DR

This paper presents an adiabatic quantum algorithm capable of solving shortest path problems on large, interconnected graphs using a number of qubits proportional to the number of vertices, demonstrating scalability with random graph models.

Contribution

It introduces a novel quantum algorithm for shortest path problems that scales with graph size and does not rely on classical algorithms beyond adjacency matrix creation.

Findings

Algorithm can solve shortest path with up to 3V qubits

Scales with random graph models like Barabasi-Albert and Erdos-Renyi

Demonstrates feasibility of modeling large graphs on quantum hardware

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 3V qubits, where V is the number of vertices of the graph. We do so without relying on any classical algorithms, aside from creating a (V x V) 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 Barabasi-Albert and the Erdos-Renyi methods which can scale based on a power law.