Circuit design for multi-body interactions in superconducting quantum annealing system with applications to a scalable architecture

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 optimisation 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 optimisation 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. It is then shown how this circuit can be used as a 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-neighbour four-body interactions.