# How to Apply the Neyman-Pearson Lemma to Quantum Supremacy Claims via the Monte Carlo Method

### I could easily have goofed up one or more of the formulas, so please comment or e-mail me if you find an error!

The background for this post can be found in ‘Supplementary information for “Quantum supremacy using a programmable superconducting processor”’ (Google AI Quantum and collaborators) 10/8/19, at the start of section F. Distribution of bit string probabilities.1

The goal here is to map the notation in the above article for application of my earlier post, and thereby produce a (nearly) most (statistically) powerful test of the claim.

#### Notation:

#### Models for the null (uniform distribution) and alternative (Porter-Thomas distribution) hypotheses:

#### Relative log likelihood:

1

If you ‘Go to Page…’ 37, this will take you to the first page of section F, which is numbered page 36 in the article.

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