Ultrafast Quantum Gates in Circuit QED
  We present a method of implementing ultrafast two-qubit gates valid for the ultrastrong coupling (USC) and deep strong coupling (DSC) regimes of light-matter interaction, considering state-of-the-art circuit quantum electrodynamics (QED) technology. Our proposal includes a suitable qubit architecture and is based on a four-step sequential displacement of an intracavity mode, operating at a time proportional to the inverse of the resonator frequency. Through ab initio calculations, we show that these quantum gates can be performed at subnanosecond time scales, while keeping the fidelity above 99%. 
G. Romero, D. Ballester, Y. M. Wang, V. Scarani, and E. Solano
quant-ph cond-mat.supr-con