  We calculate the fidelity with which an arbitrary state can be encoded into a
[7,1,3] CSS quantum error correction code in a non-equiprobable Pauli operator
error environment with the goal of determining whether this encoding can be
used for practical implementations of quantum computation. This determination
is accomplished by applying ideal error correction to the encoded state which
demonstrates the correctability of errors that occurred during the encoding
process. We then apply single-qubit Clifford gates to the encoded state and
determine the accuracy with which these gates can be applied. Finally, fault
tolerant noisy error correction is applied to the encoded states in the
non-equiprobable Pauli operator error environment allowing us to compare noisy
(realistic) and perfect error correction implementations. We note that this
maintains the fidelity of the encoded state for certain error-probability
values. These results have implications for when non-fault tolerant procedures
may be used in practical quantum computation and whether quantum error
correction should be applied at every step in a quantum protocol.
