# Quantum error correction failure distributions: comparison of coherent and stochastic error models

## TL;DR

This paper compares failure distributions in quantum error correction circuits under stochastic and coherent error models, revealing significant differences and highlighting the complexity of coherent errors for quantum computing reliability.

## Contribution

It provides a detailed comparison of failure distributions for coherent and stochastic errors using fully coherent simulations, showing the inadequacy of simple error model mappings.

## Key findings

- Coherent errors produce broad, heavy-tailed failure distributions.
- Output distributions differ markedly between error models.
- Mean statistics may not capture the impact of coherent errors.

## Abstract

We compare failure distributions of quantum error correction circuits for stochastic errors and coherent errors. We utilize a fully coherent simulation of a fault tolerant quantum error correcting circuit for a $d=3$ Steane and surface code. We find that the output distributions are markedly different for the two error models, showing that no simple mapping between the two error models exists. Coherent errors create very broad and heavy-tailed failure distributions. This suggests that they are susceptible to outlier events and that mean statistics, such as pseudo-threshold estimates, may not provide the key figure of merit. This provides further statistical insight into why coherent errors can be so harmful for quantum error correction. These output probability distributions may also provide a useful metric that can be utilized when optimizing quantum error correcting codes and decoding procedures for purely coherent errors.