  The decoherence effect on Grover algorithm has been studied numerically
through a noise modelled by a depolarizing channel. Two types of error are
introduced characterizing the qubit time evolution and gate application, so the
noise is directly related to the quantum network construction. The numerical
simulation concludes an exponential damping law for the successive probability
of the maxima as time increases. We have obtained an allowed-error law for the
algorithm: the error threshold for the allowed noise behaves as Eth(N) ~ 1/N1.1
(N being the size of the data set). As the power of N is almost one, we
consider the Grover algorithm as robust to a certain extent against
decoherence. This law also provides an absolute threshold: if the free
evolution error is greater than 0.043, Grover algorithm does not work for any
number of qubits affected by the present error model. The improvement in the
probability of success, in the case of two qubits has been illustrated by using
a fault-tolerant encoding of the initial state by means of the [[7,1,3]]
quantum code.
