We show how a superconducting circuit consisting of three identical, non-linear oscillators in series considered in terms of its electrical modes can implement a strong, native three-body interaction among qubits. Because of strong interactions, part of the qubit-subspace is coupled to higher levels. The remaining qubit states can be used to implement a restricted Fredkin gate, which in turn implements a CNOT-gate or a spin transistor. Including non-symmetric contributions from couplings to ground and external control we alter the circuit slightly to compensate, and find average fidelities for our implementation of the above gates above 99.5% with operation times on the order of a nanosecond. Additionally we show how to analytically include all orders of the cosine contributions from Josephson junctions to the Hamiltonian of a superconducting circuit.
@article{arxiv.1910.08741,
title = {Native three-body interaction in superconducting circuits},
author = {Simon Panyella Pedersen and Kasper Sangild Christensen and Nikolaj Thomas Zinner},
journal= {arXiv preprint arXiv:1910.08741},
year = {2019}
}