Network Community Detection On Small Quantum Computers

TL;DR

This paper introduces a hybrid quantum local search method for network community detection that effectively utilizes small quantum computers, achieving solutions comparable to classical solvers on graphs with up to 410 vertices.

Contribution

It presents a hardware-agnostic hybrid quantum local search approach for community detection, demonstrating its effectiveness on small quantum devices and scalability to practical problem sizes.

Findings

Q-LS performs similarly on IBM and D-Wave quantum computers.

Capable of solving community detection on graphs up to 410 vertices.

Achieves solutions comparable to state-of-the-art classical methods.

Abstract

In recent years a number of quantum computing devices with small numbers of qubits became available. We present a hybrid quantum local search (QLS) approach that combines a classical machine and a small quantum device to solve problems of practical size. The proposed approach is applied to the network community detection problem. QLS is hardware-agnostic and easily extendable to new quantum computing devices as they become available. We demonstrate it to solve the 2-community detection problem on graphs of size up to 410 vertices using the 16-qubit IBM quantum computer and D-Wave 2000Q, and compare their performance with the optimal solutions. Our results demonstrate that QLS perform similarly in terms of quality of the solution and the number of iterations to convergence on both types of quantum computers and it is capable of achieving results comparable to state-of-the-art solvers in terms of quality of the solution including reaching the optimal solutions.