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Quantum Information Processing
Erschienen in: Quantum Information Processing 4/2017

01.04.2017

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

verfasst von: Kathleen E. Hamilton, Travis S. Humble

Erschienen in: Quantum Information Processing | Ausgabe 4/2017

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Abstract

Using quantum annealing to solve an optimization problem requires minor embedding a logic graph into a known hardware graph. In an effort to reduce the complexity of the minor embedding problem, we introduce the minor set cover (MSC) of a known graph \({\mathcal {G}}\): a subset of graph minors which contain any remaining minor of the graph as a subgraph. Any graph that can be embedded into \({\mathcal {G}}\) 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. 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 \(K_{N,N}\). The case of determining the largest clique minor of hardware with faults is briefly discussed but remains an open question.
Vorheriger Artikel Deterministic remote preparation via the Brown state
Nächster Artikel Uncertainty under quantum measures and quantum memory

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Fußnoten
1
Work presented at the Society for Industrial and Applied Mathematics Workshop on Network Science 2016, manuscript in progress.
 
2
See footnote 1
 
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Metadaten
Titel
Identifying the minor set cover of dense connected bipartite graphs via random matching edge sets
verfasst von
Kathleen E. Hamilton
Travis S. Humble
Publikationsdatum
01.04.2017
Verlag
Springer US
Erschienen in
Quantum Information Processing / Ausgabe 4/2017
Print ISSN: 1570-0755
Elektronische ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-016-1513-7

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