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

Negre, Christian F.  A.; Ushijima-Mwesigwa, Hayato; Mniszewski, Susan M.

doi:10.1371/journal.pone.0227538

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

Abstract

A very important problem in combinatorial optimization is the partitioning of 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 papermore »« less

Authors:

Negre, Christian F. A. ^[1];

^[2]; Mniszewski, Susan M. ^[2]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Div.
Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Computer, Computational & Statistical Division

Publication Date:: Thu Feb 13 00:00:00 EST 2020

Research Org.:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1628969

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: PLoS ONE

Additional Journal Information:: Journal Volume: 15; Journal Issue: 2; Journal ID: ISSN 1932-6203

Publisher:: Public Library of Science

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING

Citation Formats


                    Negre, Christian F.  A., Ushijima-Mwesigwa, Hayato, and Mniszewski, Susan M. Detecting multiple communities using quantum annealing on the D-Wave system.  United States: N. p., 2020. 
Web.  doi:10.1371/journal.pone.0227538.

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                    Negre, Christian F.  A., Ushijima-Mwesigwa, Hayato, & Mniszewski, Susan M. Detecting multiple communities using quantum annealing on the D-Wave system.  United States.  https://doi.org/10.1371/journal.pone.0227538

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                    Negre, Christian F.  A., Ushijima-Mwesigwa, Hayato, and Mniszewski, Susan M. Thu .  
"Detecting multiple communities using quantum annealing on the D-Wave system".  United States.  https://doi.org/10.1371/journal.pone.0227538.  https://www.osti.gov/servlets/purl/1628969.

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@article{osti_1628969,

  title        = {Detecting multiple communities using quantum annealing on the D-Wave system},

  author       = {Negre, Christian F.  A. and Ushijima-Mwesigwa, Hayato and Mniszewski, Susan M.},

  abstractNote = {A very important problem in combinatorial optimization is the partitioning of 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 using a quantum annealer.},

  doi          = {10.1371/journal.pone.0227538},

  journal      = {PLoS ONE},

  number       = 2,

  volume       = 15,

  place        = {United States},

  year         = {Thu Feb 13 00:00:00 EST 2020},

  month        = {Thu Feb 13 00:00:00 EST 2020}

}

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

Abstract

Citation Formats

Graph-based linear scaling electronic structure theory journal, June 2016

Allosteric pathways in imidazole glycerol phosphate synthase journal, May 2012

Community detection in networks: A user guide journal, November 2016

Graph Partitioning using Quantum Annealing on the D-Wave System conference, January 2017

Community structure in social and biological networks journal, June 2002

Fast algorithm for detecting community structure in networks journal, June 2004

Fast unfolding of communities in large networks journal, October 2008

Optimization by Simulated Annealing journal, May 1983

Community detection in graphs journal, February 2010

Optimization with Extremal Dynamics journal, June 2001

Community detection in complex networks using extremal optimization journal, August 2005

Modularity and community structure in networks journal, May 2006

Normalized cuts and image segmentation journal, January 2000

Hierarchical Grouping to Optimize an Objective Function journal, March 1963

Quantum-Assisted Cluster Analysis on a Quantum Annealing Device journal, June 2018

Resolution limit in community detection journal, December 2006

Performance of modularity maximization in practical contexts journal, April 2010

Improving heuristics for network modularity maximization using an exact algorithm journal, January 2014

An Information Flow Model for Conflict and Fission in Small Groups journal, December 1977

The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations journal, September 2003

Comparative Analysis of Quality Metrics for Community Detection in Social Networks Using Genetic Algorithm journal, January 2016

Demonstration of a Scaling Advantage for a Quantum Annealer over Simulated Annealing journal, July 2018

The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations journal, September 2003

Sheep meat production in the Brazilian semi-arid region: crossing between indigenous breeds journal, October 2021

Improving heuristics for network modularity maximization using an exact algorithm journal, January 2014

Community detection in graphs journal, February 2010

Community detection in networks: A user guide journal, November 2016

Resolution limit in community detection journal, December 2006

Allosteric pathways in imidazole glycerol phosphate synthase journal, May 2012

Eigenvector centrality for characterization of protein allosteric pathways journal, December 2018

Finding community structure in very large networks journal, December 2004

Task-based Parallel Computation of the Density Matrix in Quantum-based Molecular Dynamics using Graph Partitioning journal, January 2017

A community detection algorithm using network topologies and rule-based hierarchical arc-merging strategies journal, November 2017

Algorithm AS 136: A K-Means Clustering Algorithm journal, January 1979

Quantum-Assisted Cluster Analysis on a Quantum Annealing Device journal, June 2018

The Anatomy of the Facebook Social Graph preprint, January 2011

Entanglement in a quantum annealing processor text, January 2014

Demonstration of a scaling advantage for a quantum annealer over simulated annealing text, January 2017

Community Detection Across Emerging Quantum Architectures preprint, January 2018

Text Mining using Nonnegative Matrix Factorization and Latent Semantic Analysis preprint, January 2019

The large-scale organization of metabolic networks text, January 2000

Functional cartography of complex metabolic networks text, January 2005

Quantum isomer search journal, January 2020

Multilevel Combinatorial Optimization Across Quantum Architectures text, January 2019

The prospects of quantum computing in computational molecular biology text, January 2020

Constrained-optimization Approach Delivers Superior Classical Performance for Graph Partitioning via Quantum-ready Method preprint, January 2020

Graph-based linear scaling electronic structure theory
journal, June 2016

Allosteric pathways in imidazole glycerol phosphate synthase
journal, May 2012

Community detection in networks: A user guide
journal, November 2016

Graph Partitioning using Quantum Annealing on the D-Wave System
conference, January 2017

Community structure in social and biological networks
journal, June 2002

Fast algorithm for detecting community structure in networks
journal, June 2004

Fast unfolding of communities in large networks
journal, October 2008

Optimization by Simulated Annealing
journal, May 1983

Community detection in graphs
journal, February 2010

Optimization with Extremal Dynamics
journal, June 2001

Community detection in complex networks using extremal optimization
journal, August 2005

Modularity and community structure in networks
journal, May 2006

Normalized cuts and image segmentation
journal, January 2000

Hierarchical Grouping to Optimize an Objective Function
journal, March 1963

Quantum-Assisted Cluster Analysis on a Quantum Annealing Device
journal, June 2018

Resolution limit in community detection
journal, December 2006

Performance of modularity maximization in practical contexts
journal, April 2010

Improving heuristics for network modularity maximization using an exact algorithm
journal, January 2014

An Information Flow Model for Conflict and Fission in Small Groups
journal, December 1977

The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations
journal, September 2003

Comparative Analysis of Quality Metrics for Community Detection in Social Networks Using Genetic Algorithm
journal, January 2016

Demonstration of a Scaling Advantage for a Quantum Annealer over Simulated Annealing
journal, July 2018

The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations
journal, September 2003

Sheep meat production in the Brazilian semi-arid region: crossing between indigenous breeds
journal, October 2021

Improving heuristics for network modularity maximization using an exact algorithm
journal, January 2014

Community detection in graphs
journal, February 2010

Community detection in networks: A user guide
journal, November 2016

Resolution limit in community detection
journal, December 2006

Allosteric pathways in imidazole glycerol phosphate synthase
journal, May 2012

Eigenvector centrality for characterization of protein allosteric pathways
journal, December 2018

Finding community structure in very large networks
journal, December 2004

Task-based Parallel Computation of the Density Matrix in Quantum-based Molecular Dynamics using Graph Partitioning
journal, January 2017

A community detection algorithm using network topologies and rule-based hierarchical arc-merging strategies
journal, November 2017

Algorithm AS 136: A K-Means Clustering Algorithm
journal, January 1979

Quantum-Assisted Cluster Analysis on a Quantum Annealing Device
journal, June 2018

The Anatomy of the Facebook Social Graph
preprint, January 2011

Entanglement in a quantum annealing processor
text, January 2014

Demonstration of a scaling advantage for a quantum annealer over simulated annealing
text, January 2017

Community Detection Across Emerging Quantum Architectures
preprint, January 2018

Text Mining using Nonnegative Matrix Factorization and Latent Semantic Analysis
preprint, January 2019

The large-scale organization of metabolic networks
text, January 2000

Functional cartography of complex metabolic networks
text, January 2005

Quantum isomer search
journal, January 2020

Multilevel Combinatorial Optimization Across Quantum Architectures
text, January 2019

The prospects of quantum computing in computational molecular biology
text, January 2020

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preprint, January 2020