Concatenated coding in the presence of dephasing

We investigate the use of concatenated coding to protect against dephasing in the absence of other types of error in order to carry out large quantum computations. This analysis is based on a well-known three-bit quantum code. Fault tolerant methods for carrying out gate operations, ancilla preparation, and syndrome identification are discussed and the maximum (or threshold) error rate which can be tolerated (if quantum coherence is to be maintained for arbitrarily long computations) is estimated. The methods for performing fault tolerant gate operations are compared to the methods appropriate for the seven-bit code and it is concluded that the three-bit code is not likely to be useful for large-scale quantum computation.