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

Hamilton, Kathleen E.; Humble, Travis S.

doi:10.1007/s11128-016-1513-7

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

Journal Article · Thu Feb 23 00:00:00 EST 2017 · Quantum Information Processing

DOI:https://doi.org/10.1007/s11128-016-1513-7· OSTI ID:1361309

Hamilton, Kathleen E. ^[1]; Humble, Travis S. ^[1]

Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science Mathematics Division

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.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1361309

Journal Information:: Quantum Information Processing, Vol. 16, Issue 4; ISSN 1570-0755

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 12 works

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Embedding Equality Constraints of Optimization Problems into a Quantum Annealer Vyskocil, Tomas; Djidjev, Hristo Algorithms, Vol. 12, Issue 4 https://doi.org/10.3390/a12040077	journal	April 2019
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Title: Identifying the minor set cover of dense connected bipartite graphs via random matching edge sets

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