We study a recently demonstrated design for a high-performance tunable coupler suitable for superconducting Xmon and planar transmon qubits [Y. Chen et al., arXiv:1402.7367]. The coupler circuit uses a single flux-biased Josephson junction and acts as a tunable current divider. We calculate the effective qubit-qubit interaction Hamiltonian by treating the nonlinearity of the qubit and coupler junctions perturbatively. We find that the qubit nonlinearity has two principal effects: The first is to suppress the magnitude of the transverse XX coupling from that obtained in the harmonic approximation by about 15%. The second is to induce a small diagonal ZZ coupling. The effects of the coupler junction nonlinearity are negligible in the parameter regime considered.
@article{arxiv.1405.1915,
title = {Tunable coupler for superconducting Xmon qubits: Perturbative nonlinear model},
author = {Michael R. Geller and Emmanuel Donate and Yu Chen and Charles Neill and Pedram Roushan and John M. Martinis},
journal= {arXiv preprint arXiv:1405.1915},
year = {2015}
}