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

Abstract

A very important problem in combinatorial optimization is partitioning a network into communities of densely connected nodes; where the connectivity between nodes inside a particular community is large compared to the connectivity between nodes belonging to different ones. This problem is known as community detection, and has become very important in various fields of science including chemistry, biology and social sciences. The problem of community detection is a twofold problem that consists of determining the number of communities and, at the same time, finding those communities. This drastically increases the solution space for heuristics to work on, compared to traditional graph partitioning problems. In many of the scientific domains in which graphs are used, there is the need to have the ability to partition a graph into communities with the "highest quality" possible since the presence of even small isolated communities can become crucial to explain a particular phenomenon. We have explored community detection using the power of quantum annealers, and in particular the D-Wave 2X and 2000Q machines. It turns out that the problem of detecting at most two communities naturally fits into the architecture of a quantum annealer with almost no need of reformulation. This paper addresses a systematic study of detecting two or more communities in a network us-ing a quantum annealer.

On The Use of Optimization for Mining Clusters in Networks

“…However, as it has been investigated recently [19], [34]- [35], many enhancements to these algorithms have been considered when dealing with NP problems in order to get good outcomes in reasonable time and deal with their main shortcomings. This is particularly when the solution space is huge for heuristic approaches to tackle as with the community detection problem since it involves identifying the modules number as well as discovering these modules [8]. Examples of these enhancements are:…”

“…The modules discovering has been employed widely in various domains like biology, computer science, combinatorial optimization, and sociology [5], [8]. Its applications are reached out from subject discovering within collaborative tagging systems to occasion discovering within the social networks as well as modeling huge-scale networks in internet services [2].…”

“…Recently, studying networks has resurged because of the availability and capability of storing and generating data from various systems [8]. It is considered one of the liveliest multidisciplinary domains as they are represented using networks like computer science, sociology, and complex systems [3].…”

Quantum Bridge Analytics I: a tutorial on formulating and using QUBO models

“…Recent QUBO quantum computing applications, complementing earlier applications on classical computing systems, include those for graph partitioning problems in Mniszewski et al (2016) and Ushijima-Mwesigwa et al (2017); graph clustering (quantum community detection problems) in Negre et al (2018Negre et al ( , 2019; traffic-flow optimization in Neukart et al (2017); vehicle routing problems in Feld et al (2018), Clark et al (2019) and Ohzeki et al(2018); maximum clique problems in Chapuis et al (2018); cybersecurity problems in Munch et al (2018) and Reinhardt et al(2018); predictive health analytics problems in De Oliveira et al (2018) and Sahner et al (2018); and financial portfolio management problems in Elsokkary et al (2017) and Kalra et al (2018). In another recent development, QUBO models are being studied using the IBM neuromorphic computer at as reported in Alom et al (2017) and Aimone et al (2018).…”

Multistart Methods for Quantum Approximate optimization

“…That is, s i = −1 denotes vertex i as being assigned to the first community, and s j = +1 denotes that vertex j is assigned to the second community. Modularity maximization for general graphs is NP-hard [27] and has a variety of applications in complex systems [28]- [32].…”