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We demonstrate a direct mapping of max k-SAT problems (and weighted maxk-SAT) to a Chimera graph, which is the non-planar hardware graph of thedevices built by D-Wave Systems Inc. We further show that this mapping can beused to map a similar class of maximum satisfiability problems where theclauses are replaced by parity checks over potentially large numbers of bits.The latter is of specific interest for applications in decoding forcommunication. 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 toa Chimera graph. The weighted max k-SAT problem is the most general class ofsatisfiability problems, so our result effectively demonstrates how anysatisfiability problem may be directly mapped to a Chimera graph. Our methodsfaithfully reproduce the low energy spectrum of the target problems, sotherefore may also be used for maximum entropy inference.

A Direct Mapping of Max k-SAT and High Order Parity Checks to a Chimera Graph