  Quantum annealing provides a way of solving optimization problems by encoding
them as Ising spin models which are implemented using physical qubits. The
solution of the optimization problem then corresponds to the ground state of
the system. Quantum tunnelling is harnessed to enable the system to move to the
ground state in a potentially highly non-convex energy landscape. A major
difficulty in encoding optimization problems in physical quantum annealing
devices is the fact that many real world optimization problems require
interactions of higher connectivity as well as multi-body terms beyond the
limitations of the physical hardware. In this work we address the question of
how to implement multi-body interactions using hardware which natively only
provides two-body interactions. The main result is an efficient circuit design
of such multi-body terms using superconducting flux qubits in which effective
N-body interactions are implemented using N ancilla qubits and only two
inductive couplers. It is then shown how this circuit can be used as the unit
cell of a scalable architecture by applying it to a recently proposed embedding
technique for constructing an architecture of logical qubits with arbitrary
connectivity using physical qubits which have nearest-neighbor four-body
interactions. It is further shown that this design is robust to non-linear
effects in the coupling loops as well as mismatches in some of the circuit
parameters.
