  The limited connectivity of current and next-generation quantum annealers
motivates the need for efficient graph-minor embedding methods. These methods
allow non-native problems to be adapted to the target annealer's architecture.
The overhead of the widely used heuristic techniques is quickly proving to be a
significant bottleneck for solving real-world applications. To alleviate this
difficulty, we propose a systematic and deterministic embedding method,
exploiting the structures of both the input graph of the specific problem and
the quantum annealer. We focus on the specific case of the Cartesian product of
two complete graphs, a regular structure that occurs in many problems. We
divide the embedding problem by first embedding one of the factors of the
Cartesian product in a repeatable pattern. The resulting simplified problem
consists of the placement and connecting together of these copies to reach a
valid solution. Aside from the obvious advantage of a systematic and
deterministic approach with respect to speed and efficiency, the embeddings
produced are easily scaled for larger processors and show desirable properties
for the number of qubits used and the chain length distribution. To conclude,
we briefly address the problem of circumventing inoperable qubits by presenting
possible extensions of the method.
