  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. We
optimize the cQED system parameters 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 [H. Goto and K. Ichimura, Phys.
Rev. A 80, 040303(R) (2009)]. Our optimization greatly relaxes the requirements
for fault-tolerant quantum computation in some parameter regions, compared with
the conventional optimization method where only the photon loss is minimized
without considering the shape distortion [H. Goto and K. Ichimura, Phys. Rev. A
82, 032311 (2010)]. 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.
