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This content will become publicly available on February 23, 2018

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