Embedding quadratization gadgets on Chimera and Pegasus graphs

We group all known quadratizations of cubic and quartic terms in binary optimization problems into six and seven unique graphs respectively. We then perform a minor embedding of these graphs onto the well-known Chimera graph, and the brand new Pegasus graph. We conclude with recommendations for which gadgets are best to use when aiming to reduce the total number of qubits required to embed a problem.