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 G: a subset of graph minors which contain any remaining minor of the graph as a subgraph. Any graph that can be embedded into 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 KN , N has a MSC of N minors, from which KN + 1 is identified as the largest clique minor of KN , N. The case of determining the largest clique minor of hardware with faults is briefly discussed but remains an open question.
Original language | English |
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Article number | 94 |
Journal | Quantum Information Processing |
Volume | 16 |
Issue number | 4 |
DOIs | |
State | Published - Apr 1 2017 |
Funding
This work was supported by the US Department of Defense and used resources of the Computational Research and Development Programs at Oak Ridge National Laboratory. This manuscript has been authored by UT-Battelle, LLC, under Contract No. DE-AC0500OR22725 with the US Department of Energy. The US Government retains and the publisher, by accepting the article for publication, acknowledges that the US Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for the US Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan.
Keywords
- Adiabatic quantum computing
- Clique minor
- Graph theory
- Minor embedding
- Quantum annealing