Errors and pseudo-thresholds for incoherent and coherent noise

TL;DR

This paper investigates how incoherent and coherent errors affect the logical error rate in quantum error correction, revealing key differences and the limitations of common approximations through exact simulations.

Contribution

It provides an exact simulation comparison of incoherent and coherent errors on the Steane code, highlighting differences in error models and the impact on pseudo-threshold estimates.

Findings

Pauli twirling approximates incoherent errors well but not coherent errors.

Pessimistic physical error channels lead to pessimistic logical error rates.

Pseudo-threshold varies significantly depending on the error metric used.

Abstract

We compare the effect of single qubit incoherent and coherent errors on the logical error rate of the Steane [[7,1,3]] quantum error correction code by performing an exact full-density-matrix simulation of an error correction step. We find that the effective 1-qubit process matrix at the logical level reveals the key differences between the error models and provides insight into why the Pauli twirling approximation is a good approximation for incoherent errors and a poor approximation for coherent ones. Approximate channels composed of Clifford operations and Pauli measurement operators that are pessimistic at the physical level result in pessimistic error rates at the logical level. In addition, we observe that the pseudo-threshold can differ by a factor of five depending on whether the error is calculated using the fidelity or the distance.