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:

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 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science Mathematics Division
 Publication Date:
 Grant/Contract Number:
 AC0500OR22725
 Type:
 Accepted Manuscript
 Journal Name:
 Quantum Information Processing
 Additional Journal Information:
 Journal Volume: 16; Journal Issue: 4; Journal ID: ISSN 15700755
 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/s1112801615137.
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/s1112801615137.
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/s1112801615137. 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/s1112801615137},
journal = {Quantum Information Processing},
number = 4,
volume = 16,
place = {United States},
year = {2017},
month = {2}
}