  The current generation of D-Wave quantum annealing processor is designed to
minimize the energy of an Ising spin configuration whose pairwise interactions
lie on the edges of a {\em Chimera} graph $\mathcal C_{M,N,L}$. In order to
solve an Ising spin problem with arbitrary pairwise interaction structure, the
corresponding graph must be minor-embedded into a Chimera graph. We define a
combinatorial class of {\em native clique minors} in Chimera graphs with vertex
images of uniform, near minimal size, and provide a polynomial-time algorithm
that finds a maximum native clique minor in a given induced subgraph of a
Chimera graph. These minors allow improvement over recent work and have
immediate practical applications in the field of quantum annealing.
