  We present a detailed error analysis of a Rydberg blockade mediated
controlled-NOT quantum gate between two neutral atoms as demonstrated recently
in Phys. Rev. Lett. 104, 010503 (2010) and Phys. Rev. A 82, 030306 (2010).
Numerical solutions of a master equation for the gate dynamics, including all
known sources of technical error, are shown to be in good agreement with
experiments. The primary sources of gate error are identified and suggestions
given for future improvements. We also present numerical simulations of quantum
process tomography to find the intrinsic fidelity, neglecting technical errors,
of a Rydberg blockade controlled phase gate. The gate fidelity is characterized
using trace overlap and trace distance measures. We show that the trace
distance is linearly sensitive to errors arising from the finite Rydberg
blockade shift and introduce a modified pulse sequence which corrects the
linear errors. Our analysis shows that the intrinsic gate error extracted from
simulated quantum process tomography can be under 0.002 for specific states of
$^{87}$Rb or Cs atoms. The relation between the process fidelity and the gate
error probability used in calculations of fault tolerance thresholds is
discussed.
