  We investigate the performance of a three qubit error correcting code in the
framework of superconducting qubit implementations. Such a code can recover a
quantum state perfectly in the case of dephasing errors but only in situations
where the dephasing rate is low. Numerical studies in previous work have
however shown that the code does increase the fidelity of the encoded state
even in the presence of high error probability, during both storage and
processing. In this work we give analytical expressions for the fidelity of
such a code. We consider two specific schemes for qubit-qubit interaction
realizable in superconducting systems; one $\sigma_z\sigma_z$-coupling and one
cavity mediated coupling. With these realizations in mind, and considering
errors during storing as well as processing, we calculate the maximum operation
time allowed in order to still benefit from the code. We show that this limit
can be reached with current technology.
