  One approach to quantum information processing is to use photons as quantum
bits and rely on linear optical elements for most operations. However, some
optical nonlinearity is necessary to enable universal quantum computing. Here,
we suggest a circuit-QED approach to nonlinear optics quantum computing in the
microwave regime, including a deterministic two-photon phase gate. Our specific
example uses a hybrid quantum system comprising a LC resonator coupled to a
superconducting flux qubit to implement a nonlinear coupling. Compared to the
self-Kerr nonlinearity, we find that our approach has improved tolerance to
noise in the qubit while maintaining fast operation.
