  The states needed in a quantum computation are extremely affected by
decoherence. Several methods have been proposed to control error spreading.
They use two main tools: fault-tolerant constructions and concatenated quantum
error correcting codes. In this work, we estimate the threshold conditions
necessary to make a long enough quantum computation. The [[7,1,3]] CSS quantum
code, together with the Shor method to measure the error syndrome is used. No
concatenation is included. The decoherence is introduced by means of the
depolarizing channel error model, obtaining several thresholds from the
numerical simulation. Regarding the maintenance of a qubit stabilized in the
memory, the error probability must be smaller than 2.9 10-5. In order to
implement a one or two qubit encoded gate in an effective fault-tolerant way,
it is possible to choose an adequate non-encoded noisy gate if the memory error
probability is smaller than 1.3 10-5. In addition, fulfilling this last
condition permits us to assume a more efficient behaviour compared to the
equivalent non-encoded process.
