# Agnostic Tomography of Stabilizer Product States

arXiv: https://arxiv.org/abs/2404.03813 · HTML: https://mlsanity.com/paper/2404.03813/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 50 references that are in the map.
- First posted on arXiv 4 Apr 2024.

## Builds on (most cited first, 9 of 9)

- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [A survey on the complexity of learning quantum states](https://mlsanity.com/paper/2305.20069/) (2023)
- [Learning shallow quantum circuits](https://mlsanity.com/paper/2401.10095/) (2024)
- [Improved Stabilizer Estimation via Bell Difference Sampling](https://mlsanity.com/paper/2304.13915/) (2023)
- [Optimal algorithms for learning quantum phase states](https://mlsanity.com/paper/2208.07851/) (2022)
- [On the Hardness of PAC-learning Stabilizer States with Noise](https://mlsanity.com/paper/2102.05174/) (2021)
- [Efficient Tomography of Non-Interacting Fermion States](https://mlsanity.com/paper/2102.10458/) (2021)
- [Efficient Learning of Quantum States Prepared With Few Non-Clifford Gates](https://mlsanity.com/paper/2305.13409/) (2023)
- [High-Temperature Gibbs States are Unentangled and Efficiently Preparable](https://mlsanity.com/paper/2403.16850/) (2024)

## Built on by (most cited first, 4 of 4)

- [Mildly-Interacting Fermionic Unitaries are Efficiently Learnable](https://mlsanity.com/paper/2504.11318/) (2025)
- [Efficient learning of bosonic Gaussian unitaries](https://mlsanity.com/paper/2510.05531/) (2025)
- [Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more](https://mlsanity.com/paper/2510.06848/) (2025)
- [Finding Gaussian Structure in Bosonic States](https://mlsanity.com/paper/2610.06810/) (2026)

## Abstract (arXiv)

We define a quantum learning task called agnostic tomography, where given copies of an arbitrary state ρ and a class of quantum states C, the goal is to output a succinct description of a state that approximates ρ at least as well as any state in C (up to some small error varepsilon). This task generalizes ordinary quantum tomography of states in C and is more challenging because the learning algorithm must be robust to perturbations of ρ. We give an efficient agnostic tomography algorithm for the class C of n-qubit stabilizer product states. Assuming ρ has fidelity at least τ with a stabilizer product state, the algorithm runs in time nO(log(2/τ)) / varepsilon2, which is mathsfpoly(n/varepsilon) for any constant τ.