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Title: Identifying the minor set cover of dense connected bipartite graphs via random matching edge sets

Using quantum annealing to solve an optimization problem requires minor embedding a logic graph into a known hardware graph. We introduce the minor set cover (MSC) of a known graph GG : a subset of graph minors which contain any remaining minor of the graph as a subgraph, in an effort to reduce the complexity of the minor embedding problem. Any graph that can be embedded into GG will be embeddable into a member of the MSC. Focusing on embedding into the hardware graph of commercially available quantum annealers, we establish the MSC for a particular known virtual hardware, which is a complete bipartite graph. Furthermore, we show that the complete bipartite graph K N,N has a MSC of N minors, from which K N+1 is identified as the largest clique minor of K N,N. In the case of determining the largest clique minor of hardware with faults we briefly discussed this open question.
Authors:
 [1] ;  [1]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science Mathematics Division
Publication Date:
Grant/Contract Number:
AC05-00OR22725
Type:
Accepted Manuscript
Journal Name:
Quantum Information Processing
Additional Journal Information:
Journal Volume: 16; Journal Issue: 4; Journal ID: ISSN 1570-0755
Publisher:
Springer
Research Org:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Minor embedding; Adiabatic quantum computing; Quantum annealing; Clique minor; Graph theory
OSTI Identifier:
1361309

Hamilton, Kathleen E., and Humble, Travis S.. Identifying the minor set cover of dense connected bipartite graphs via random matching edge sets. United States: N. p., Web. doi:10.1007/s11128-016-1513-7.
Hamilton, Kathleen E., & Humble, Travis S.. Identifying the minor set cover of dense connected bipartite graphs via random matching edge sets. United States. doi:10.1007/s11128-016-1513-7.
Hamilton, Kathleen E., and Humble, Travis S.. 2017. "Identifying the minor set cover of dense connected bipartite graphs via random matching edge sets". United States. doi:10.1007/s11128-016-1513-7. https://www.osti.gov/servlets/purl/1361309.
@article{osti_1361309,
title = {Identifying the minor set cover of dense connected bipartite graphs via random matching edge sets},
author = {Hamilton, Kathleen E. and Humble, Travis S.},
abstractNote = {Using quantum annealing to solve an optimization problem requires minor embedding a logic graph into a known hardware graph. We introduce the minor set cover (MSC) of a known graph GG : a subset of graph minors which contain any remaining minor of the graph as a subgraph, in an effort to reduce the complexity of the minor embedding problem. Any graph that can be embedded into GG will be embeddable into a member of the MSC. Focusing on embedding into the hardware graph of commercially available quantum annealers, we establish the MSC for a particular known virtual hardware, which is a complete bipartite graph. Furthermore, we show that the complete bipartite graph KN,N has a MSC of N minors, from which KN+1 is identified as the largest clique minor of KN,N. In the case of determining the largest clique minor of hardware with faults we briefly discussed this open question.},
doi = {10.1007/s11128-016-1513-7},
journal = {Quantum Information Processing},
number = 4,
volume = 16,
place = {United States},
year = {2017},
month = {2}
}