Nonlinear optics quantum computing with circuit QED

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 non-linearity is necessary to enable universal quantum computing. We consider a circuit-QED approach to linear optics quantum computing in the microwave regime, including a deterministic two-photon phase gate. Our model is a hybrid quantum system comprising an LC resonator coupled to a flux or phase superconducting qubit, which will be used to implement a non-linear two photon phase shift operation. Using this model, we show how fast, low-noise two-qubit gates between photons are possible, and discuss limitations of these ideas based on current technology.