Four Body Local Interactions in a Superconducting Flux Qubit Coupling Architecture

Quantum annealing is a promising candidate to realize quantum computation and break the limit of classical computers.
Since all naturally arising interactions in these systems are two local, it is important to answer the question how to get higher local interactions. In this work we study four superconducting flux qubits coupled via an additional flux qubit. To get analytical expressions for the coupling strength for high coupler nonlinearities, we use the Schrieffer-Wolff transformation to derive an effective Hamiltonian. We show that the right system parameter choice and specific values of the coupler nonlinearity lead to a regime where four local interactions are the leading effect in the system, up to three orders of magnitude larger than all other coupling effects.
Quantum annealing is equivalent to the circuit model quanutm computer, as long as it includes at least three body local interactions. Therefoere one could build a universal quantum annealer using these four local interactions.