# Tolerant Testing of Stabilizer States with Mixed State Inputs

arXiv: https://arxiv.org/abs/2411.08765 · HTML: https://mlsanity.com/paper/2411.08765/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2024.

## Built on by (most cited first, 3 of 3)

- [Mildly-Interacting Fermionic Unitaries are Efficiently Learnable](https://mlsanity.com/paper/2504.11318/) (2025)
- [Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more](https://mlsanity.com/paper/2510.06848/) (2025)
- [Parameterised graph theory for tensor networks: entanglement rerouting, structural simplification, and agnostic tomography](https://mlsanity.com/paper/2609.04165/) (2026)

## Abstract (arXiv)

We study the problem of tolerant testing of stabilizer states. In particular, we give the first such algorithm that accepts mixed state inputs. Formally, given a mixed state ρ that either has fidelity at least varepsilon1 with some stabilizer pure state or fidelity at most varepsilon2 with all such states, where varepsilon2 ≤ varepsilon1O(1), our algorithm distinguishes the two cases with sample complexity poly(1/varepsilon1) and time complexity O(n · poly(1/varepsilon1)).