Fault-Tolerance of the [[8, 1, 3]] Non-CSS Code

Abstract

We present a fault-tolerant [[8, 1, 3]] non-CSS quantum error correcting code and study its logical error rates. We modify Gottesman's encoding procedure for stabilizer codes to suit a class of non-CSS quantum codes. We adopt the bare ancilla method presented by Brown et al. to reorder the measurement sequence in the syndrome extraction step and upgrade it to obtain higher pseudo-thresholds and lower leading order terms of logical error rates under the standard depolarizing and anisotropic noise models.