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We study a comprehensive list of quantum codes as candidates for codes used at the physical level in a fault-tolerant code architecture. Using the Aliferis-Gottesman-Preskill (AGP) ex-Rec method we calculate the pseudo-threshold for these codes against depolarizing noise at various levels of overhead. We estimate the logical noise rate as a function of overhead at a physical error rate of p0 = 1 × 10-4. The Bacon-Shor codes and the Golay code are the best performers in our study.

A comparative code study for quantum fault tolerance