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]
- 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}
}
- Free Publicly Accessible Full Text
-
Accepted Manuscript (DOE)
- Publisher's Version of Record
- https://doi.org/10.1007/s11128-016-1513-7