  The realization of high fidelity quantum gates in a multi-qubit system, with
a typical target set at 99.9%, is a critical requirement for the implementation
of fault-tolerant quantum computation. To reach this level of fidelity, one
needs to carefully analyze the noises and imperfections in the experimental
system and optimize the gate operations to mitigate their effects. Here, we
consider one of the leading experimental systems for the fault-tolerant quantum
computation, ions in an anharmonic linear Paul trap, and optimize entangling
quantum gates using segmented laser pulses with the assistance of all the
collective transverse phonon modes of the ion crystal. We present detailed
analyses of the effects of various kinds of intrinsic experimental noises as
well as errors from imperfect experimental controls. Through explicit
calculations, we find the requirements on these relevant noise levels and
control precisions to achieve the targeted high fidelity of 99.9% for the
entangling quantum gates in a multi-ion crystal.
