Parametrically-induced tunable coupling between flux qubits - dependence on the coupler bias

We have studied a tunable coupling scheme of two superconducting flux qubits biased at the degeneracy point. The qubits are coupled parametrically under microwave driving, via nonlinear inductance of a third qubit biased slightly away from the degeneracy point. The observed on-state coupling as well as the off-state residual coupling depend non-monotonically on the coupler bias point and agree quantitatively with calculations based on a three-qubit Hamiltonian. This simple model is useful to optimize the parameters for a large on/off ratio.