  A crucial building block for quantum information processing with trapped ions
is a controlled-NOT quantum gate. In this paper, two different sequences of
laser pulses implementing such a gate operation are analyzed using quantum
process tomography. Fidelities of up to 92.6(6)% are achieved for single gate
operations and up to 83.4(8)% for two concatenated gate operations. By process
tomography we assess the performance of the gates for different experimental
realizations and demonstrate the advantage of amplitude--shaped laser pulses
over simple square pulses. We also investigate whether the performance of
concatenated gates can be inferred from the analysis of the single gates.
