title: A Direct Mapping of Max k-SAT and High Order Parity Checks to a Chimera Graph.
abstract: We demonstrate a direct mapping of max k-SAT problems (and weighted max k-SAT) to a Chimera graph, which is the non-planar hardware graph of the devices built by D-Wave Systems Inc. We further show that this mapping can be used to map a similar class of maximum satisfiability problems where the clauses are replaced by parity checks over potentially large numbers of bits. The latter is of specific interest for applications in decoding for communication. We discuss an example in which the decoding of a turbo code, which has been demonstrated to perform near the Shannon limit, can be mapped to a Chimera graph. The weighted max k-SAT problem is the most general class of satisfiability problems, so our result effectively demonstrates how any satisfiability problem may be directly mapped to a Chimera graph. Our methods faithfully reproduce the low energy spectrum of the target problems, so therefore may also be used for maximum entropy inference.
authors.affiliation: Department of Physics, Durham University, South Road, Durham, UK.
authors.forename: N
authors.initials: N
authors.lastname: Chancellor
authors.affiliation: Department of Materials, University of Oxford, Parks Road, Oxford, UK.|Department of Engineering Science, University of Oxford, Parks Road, Oxford, UK.
authors.forename: S
authors.initials: S
authors.lastname: Zohren
authors.affiliation: London Centre for Nanotechnology 19 Gordon St, London, UK.|Department of Electronic and Electrical Engineering, UCL, Torrington Place, London, UK.
authors.forename: P A
authors.initials: PA
authors.lastname: Warburton
authors.affiliation: Department of Materials, University of Oxford, Parks Road, Oxford, UK.
authors.forename: S C
authors.initials: SC
authors.lastname: Benjamin
authors.affiliation: Department of Engineering Science, University of Oxford, Parks Road, Oxford, UK.
authors.forename: S
authors.initials: S
authors.lastname: Roberts