  Based on the amplitude behavior of quantum Rabi oscillation driven by a
coherent field we show that there exists an upper bound to the number of
logical operation performed on any single qubit within one error-correction
period of a quantum computation. We introduce a parameter to depict the maximum
of this number and estimate its decoherence limit. The analysis shows that a
generally accepted error-rate threshold of quantum logic gates limits the
parameter to so small a number that even a double of fault-tolerant Toffoli
gates can hardly be implemented reliably within one error-correction period.
This result suggests that the design of feasible fault-tolerant quantum
circuits is still an arduous task.
