Quantum-Assisted Cluster Analysis on a Quantum Annealing Device

Abstract

We present an algorithm for quantum-assisted cluster analysis that makes use of the topological properties of a D-Wave 2000Q quantum processing unit. 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 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 [1], have been subject to multiple analyses in research, with the aim of characterizing the technology's usefulness for optimization, sampling, and clustering [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. 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.

Portfolio Asset Identification Using Graph Algorithms on a Quantum Annealer

“…Graph partitioning on D-Wave is studied in [Ushijima-Mwesigwa et al, 2017]. Graphs are used for in a quantumclassical hybird approach to cluster analysis in [Neukart et al, 2018]. Structured balance in signed networks is applied to the problem of analyzing social conflicts using the D-Wave machine in [Ambrosiano et al, 2017].…”

Semi-supervised time series classification method for quantum computing

“…Other works have also shown how to reformulate parts of classical clustering algorithms as quantum subroutines that can be executed on error-corrected gate-model QPUs (Alexander et al 2018;Aimeur et al 2013;Wiebe et al 2015;Horn and Gottlieb 2001). In quantum annealing, a similar approach has been shown in which the objective function of the clustering task (minimizing distance metrics between high-dimensional vectors) has been directly translated to a QUBO, with each vector's possible assignment represented via one-hot encoding to physical qubits (Kumar et al 2018;Neukart et al 2018).…”

Detecting multiple communities using quantum annealing on the D-Wave system

“…Other metrics and methods include k-means [23], spectral [24], hierarchical [25], modularity density [21], min-max cut [26], and normalized cut [24] among others. Moreover, Neukart, et al, implemented a quantum-assisted clustering method on the D-Wave system [27]. The modularity metric allows to quantify the quality of a community structure by comparing the connectivity of edges within communities with the connectivity of an equivalent network where edges would be placed randomly.…”