# A note on polynomial-time tolerant testing stabilizer states

arXiv: https://arxiv.org/abs/2410.22220 · HTML: https://mlsanity.com/paper/2410.22220/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2024.

## Built on by (most cited first, 2 of 2)

- [Testing classical properties from quantum data](https://mlsanity.com/paper/2411.12730/) (2024)
- [Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more](https://mlsanity.com/paper/2510.06848/) (2025)

## Abstract (arXiv)

We show an improved inverse theorem for the Gowers-3 norm of n-qubit quantum states |psirangle which states that: for every γ≥ 0, if the textsfGowers(|psi rangle,3)8 ≥ γ then the stabilizer fidelity of |psirangle is at least γC for some constant C>1. This implies a constant-sample polynomial-time tolerant testing algorithm for stabilizer states which accepts if an unknown state is varepsilon1-close to a stabilizer state in fidelity and rejects when |psirangle is varepsilon2 ≤ varepsilon1C-far from all stabilizer states, promised one of them is the case.