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

TL;DR

This paper evaluates the effectiveness of simple error correcting and error avoiding quantum codes, and their concatenation, in handling correlated noise models, showing that concatenation can be particularly beneficial for certain correlated noise regimes.

Contribution

It introduces an analysis of concatenated quantum codes for correlated noise models, highlighting their performance advantages in specific regimes.

Findings

Error correcting codes work well with high correlations in errors.

Error avoiding codes are effective with low correlations.

Concatenation improves performance in partial correlation regimes for certain models.

Abstract

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.