Performance of non-CSS LDGM-based quantum codes over the misidentified depolarizing channel

Quantum Low Density Generator Matrix (QLDGM) codes based on Calderbank-Steane-Shor (CSS) constructions have shown unprecedented error correction capabilities in the paradigm of quantum communication. Recently, a strategy based on non-CSS quantum codes derived from QLDGM CSS codes has been shown to surpass other Quantum Low Density Parity Check (QLDPC) schemes proposed in the literature over the depolarizing channel. Given the importance of quantum channel estimation and the impact it has on the performance of QLDPC codes, in this article, we study the behaviour of non-CSS QLDGM codes under the umbrella of channel mismatch. We begin by showing how a relatively accurate estimate of the quantum channel is pivotal for these codes to perform appropriately. We follow this by analyzing an off-line and an on-line quantum channel parameter estimation technique, as well as discussing how these methods affect the Quantum Error Correction (QEC) codes under consideration. Finally, we show how the on-line methodology yields similar performance to the perfect channel knowledge scenario despite its relative simplicity.

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