Relative performance of ancilla verification and decoding in the [[7,1,3]] Steane code

We present numerical simulation results comparing the logical error rates for the fault-tolerant [[7,1,3]] Steane code using standard ancilla verifications techniques vs. the newer method of ancilla decoding, as described in [1]. We simulate a realistic QEC procedure in which failed ancilla creation requires storing the data until a new ancilla can be created; we expect the decoding method, which avoids the need for such storage, to be advantageous when the failure probability is sufficiently high. For the [[7,1,3]] code, we analyze the effect of both different syndrome extraction techniques and of different classes of physical error (initialization, measurement, hold etc.) on the relative performance of these two methods.\\ $\bf 1$. David P. DiVincenzo and Panos Aliferis, Phy. Rev. Lett. $\bf 98$ 020501(2007).