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

Ancilla postselection is a common means of achieving fault tolerance in quantum error correction. However, it can lead to additional data errors due to movement or wait operations. Alternatives to postselection may achieve lower overall failure rates due to avoiding such errors. We present numerical simulation results comparing the logical error rates for the fault-tolerant [[ 7,1,3]] Steane code using techniques of ancilla verification vs the newer method of ancilla decoding, as described in Phys. Rev. Lett. 98, 020501 (2007). We simulate QEC procedures in which the possibility of ancilla verification failures requires the creation and storage of additional ancillae and/ or additional waiting of the data until a new ancilla can be created. We find that the decoding method, which avoids verification failures, is advantageous in terms of overall error rate in various cases, even when measurement operations are no slower than others. We analyze the effect of different classes of physical error on the relative performance of these two methods.