We analyze the requirements for fault-tolerant quantum computation with atom-atom gates based on cavity quantum electrodynamics (cQED) mediated by a photon with a finite pulse length. For short photon pulses, the distorted shape of the reflected pulses from the cQED system is a serious error source. In the previous study by Goto and Ichimura [Phys. Rev. A82, 032311 (2010)PLRAAN1050-294710.1103/PhysRevA.82.032311], only the photon loss is minimized without considering the shape distortion to optimize the system parameters. Here we show an improved optimization method to minimize the infidelity due to the shape distortion and the photon losses in a well-balanced manner for the fault-tolerant scheme using probabilistic gates [Phys. Rev. A80, 040303(R) (2009)PLRAAN1050-294710.1103/PhysRevA.80.040303]. Under this optimization, we discuss the fault-tolerant quantum computing requirement for short pulses. Finally, we show that reducing the cavity length is an effective way to reduce the errors of this type of gate in the case of short photon pulses.
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