A quantum logic gate is also characterized by its operation time
ts. For an alternating magnetic field of 10 T, the pulse width is very
small ( 0.01 ns) and can be reduced more. Then, the CNOT gate
time is practically equal to the waiting time between the two
pulses, i.e., ts τ (see Fig. 1). For performing a large number of
operations, the decoherence time T2 should be much longer than
the gate time [30], while the sources of decoherence are multiple:
Fidelity is another measure that is used to characterize logic
gates. However, its definition is not unique and its physical
interpretation remains questionable. When the input and the
output states, jψ in〉 and jψ out 〉, are pure states as in the present
case, its definitions lead to F ¼ j〈ψ injψ out 〉jn with n ¼ 1 or 2 [44]. So,
it expresses the amplitude or the probability of finding the spin
system in the state jψ out 〉 while it has been prepared in the state
jψ in〉. We retrieve the previous results. Averaged over all input
states, the gate fidelity is close to the maximum (equal to 1).