Non-linear Optics Quantum Information Processing with Microwave Photons

One approach to quantum information processing\footnote{``A Scheme for Efficient Quantum Computation with Linear Optics,'' E. Knill, R. Laflamme, G.J. Milburn (Nature, Vol 409, 4 January 2001)} is to use photons as quantum bits and rely on the robustness of linear optical elements. However, some optical non-linearity is necessary to enable universal quantum computing. Here we suggest a circuit-QED approach to~ implementing a deterministic two-photon phase gate for such computing. Our specific example considers an LC resonator coupled to a flux qubit. Using this model, we show how fast two-qubit gates between photons are possible, and compute limitations of these ideas based on current technology.