  A number of composite pulse (CP) sequences for four basic quantum phase gates
-- the Z, S, T and general phase gates -- are presented. The CP sequences
contain up to 18 pulses and can compensate up to eight orders of experimental
errors in the pulse amplitude and duration. The short CP sequences (up to 8
pulses) are calculated analytically and the longer ones numerically. The
results demonstrate the remarkable flexibility of CPs accompanied by extreme
accuracy and robustness to errors -- three features that cannot be
simultaneously achieved by any other coherent control technique. These CP
sequences, in particular the Z, S and T gates, can be very useful quantum
control tools in quantum information applications, because they provide a
variety of options to find the optimal balance between ultrahigh fidelity,
error range and speed, which may be different in different physical
applications.
