Nonpairwise interactions induced by virtual transitions in four coupled artificial atoms

The field of quantum information has matured and various protocols implementing a quantum computer are being pursued. Most similar to a classical computer is the circuit model. In 2007 Aharonov et al. showed the equivalence between the circuit model and a quantum annealer, and with this proofed the universality of quantum annealing. Here the system starts in an easily preparable ground state and evolves adiabatically to a final ground state which yields the solution of the computational problem. However, equivalence with the circuit model requires multi-local interactions, i.e. interaction terms involving more than two subsystems. Natural interactions are only two-local, hence the construction or simulation of higher order couplers is indispensable for a universal quantum annealer. Also, four-local couplers allow compact implementation of error correction with the Bacon-Shor code. Four-local interactions can further serve as a tool for basic research. Here we show that in a specific flux qubit coupler design without ancilla qubits, four body interactions are induced by virtual coupler excitations. For specific parameter regimes they are even the leading effect and can be tuned up to the GHz range.