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We study the performance of simple error correcting and error avoidingquantum codes together with their concatenation for correlated noise models.Specifically, we consider two error models: i) a bit-flip (phase-flip) noisyMarkovian memory channel (model I); ii) a memory channel defined as a memorydegree dependent linear combination of memoryless channels with Krausdecompositions expressed solely in terms of tensor products of X-Pauli(Z-Pauli) operators (model II). The performance of both the three-qubit bitflip (phase flip) and the error avoiding codes suitable for the considerederror models is quantified in terms of the entanglement fidelity. We explicitlyshow that while none of the two codes is effective in the extreme limit whenthe other is, the three-qubit bit flip (phase flip) code still works for highenough correlations in the errors, whereas the error avoiding code does notwork for small correlations. Finally, we consider the concatenation of suchcodes for both error models and show that it is particularly advantageous formodel II in the regime of partial correlations.

Concatenation of Error Avoiding with Error Correcting Quantum Codes for Correlated Noise Models