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We study the performance of common quantum stabilizer codes in the presenceof asymmetric and correlated errors. Specifically, we consider the depolarizingnoisy quantum memory channel and perform quantum error correction via the fiveand seven-qubit stabilizer codes. We characterize these codes by means of theentanglement fidelity as function of the error probability and the degree ofmemory. We show that their performances are lowered by the presence ofcorrelations and we compute the error probability threshold values for codeseffectiveness. Furthermore, we uncover that the asymmetry in the errorprobabilities does not affect the performance of the five-qubit code while itdoes affect the performance of the seven-qubit code which results lesseffective when considering correlated and symmetric depolarizing errors butmore effective for correlated and asymmetric errors.

Quantum Stabilizer Codes for Correlated and Asymmetric Depolarizing Errors