Extended Data Table 1 Code parameters of Bivariate Bicycle codes

From: High-threshold and low-overhead fault-tolerant quantum memory

  1. Small examples of Bivariate Bicycle LDPC codes and their parameters. All codes have weight-6 checks, thickness-2 Tanner graph, and a depth-7 syndrome measurement circuit. Code distance was computed by the mixed integer programming approach of ref. 68. The notation ≤d indicates that only an upper bound on the code distance is known at the time of this writing. We round r down to the nearest inverse integer. The codes have check matrices HX = (A∣B) and HZ = (BT∣AT) with A and B defined in the last two columns. The matrices x, y obey xℓ  =  ym  =  1 and xy  =  yx.
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