We study the performance of simple error correcting and error avoiding
quantum codes together with their concatenation for correlated noise models.
Specifically, we consider two error models: i) a bit-flip (phase-flip) noisy
Markovian memory channel (model I); ii) a memory channel defined as a memory
degree dependent linear combination of memoryless channels with Kraus
decompositions expressed solely in terms of tensor products of X-Pauli
(Z-Pauli) operators (model II). The performance of both the three-qubit bit
flip (phase flip) and the error avoiding codes suitable for the considered
error models is quantified in terms of the entanglement fidelity. We explicitly
show that while none of the two codes is effective in the extreme limit when
the other is, the three-qubit bit flip (phase flip) code still works for high
enough correlations in the errors, whereas the error avoiding code does not
work for small correlations. Finally, we consider the concatenation of such
codes for both error models and show that it is particularly advantageous for
model II in the regime of partial correlations.Comment: 16 pages, 3 figure
