# How to estimate the number of false positives

### Prelude: the topological gap protocol preprint¶

In arXiv:2207.02472 Microsoft Quantum reported validating and then applying the *topological gap protocol*. I summarized my overall opinion about it in a commentary. However, even after finishing the commentary, I was confused about how the manuscript estimates the chance that they found false positives. Because I am not trained in statistics, I've used this opportunity to learn how to make such an analysis properly. Here's what I found.