Quantum-assisted cluster analysis

TL;DR

This paper introduces a quantum-assisted clustering algorithm using D-Wave's quantum processing unit, demonstrating its equivalence in accuracy to classical methods and explaining how to formulate clustering as a QUBO problem for quantum annealing.

Contribution

It presents a novel approach to quantum-assisted clustering by formulating the problem as a QUBO and utilizing quantum annealing hardware, without claiming superiority over classical algorithms.

Findings

Quantum-assisted clustering matches classical accuracy.

The problem is effectively expressed as a QUBO.

The paper explains how to implement clustering on a D-Wave QPU.

Abstract

We present an algorithm for quantum-assisted cluster analysis (QACA) that makes use of the topological properties of a D-Wave 2000Q quantum processing unit (QPU). Clustering is a form of unsupervised machine learning, where instances are organized into groups whose members share similarities. The assignments are, in contrast to classification, not known a priori, but generated by the algorithm. We explain how the problem can be expressed as a quadratic unconstrained binary optimization (QUBO) problem, and show that the introduced quantum-assisted clustering algorithm is, regarding accuracy, equivalent to commonly used classical clustering algorithms. Quantum annealing algorithms belong to the class of metaheuristic tools, applicable for solving binary optimization problems. Hardware implementations of quantum annealing, such as the quantum annealing machines produced by D-Wave Systems, have been subject to multiple analyses in research, with the aim of characterizing the technology's usefulness for optimization, sampling, and clustering. Our first and foremost aim is to explain how to represent and solve parts of these problems with the help of the QPU, and not to prove supremacy over every existing classical clustering algorithm.