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

TL;DR

This paper compares ancilla verification and decoding methods in the [[7,1,3]] Steane code, showing that decoding often results in lower logical error rates by avoiding verification failures, based on numerical simulations.

Contribution

It provides a numerical comparison of ancilla verification versus decoding in fault-tolerant quantum error correction for the Steane code, highlighting the advantages of decoding.

Findings

Decoding reduces overall error rates compared to verification.

Decoding is advantageous even with similar measurement speeds.

Different physical error classes impact the relative performance.

Abstract

Ancilla post-selection 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 post-selection 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 [D.P. DiVincenzo and P. Aliferis, PRL 98, 020501 (2007)]. We simulate QEC procedures in which rhe possibility of ancilla verification failures requires the creation and storage of additional ancillas 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.