| Summary: | We show how a superconducting circuit consisting of three identical nonlinear 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 controlled-not gate or a spin transistor. Including nonsymmetric 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.
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