# Efficient Tomography of Non-Interacting Fermion States

arXiv: https://arxiv.org/abs/2102.10458 · HTML: https://mlsanity.com/paper/2102.10458/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 51 references that are in the map.
- First posted on arXiv 20 Feb 2021.

## Builds on (most cited first, 2 of 2)

- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Efficient quantum tomography II](https://mlsanity.com/paper/1612.00034/) (2016)

## Built on by (most cited first, 7 of 7)

- [A survey on the complexity of learning quantum states](https://mlsanity.com/paper/2305.20069/) (2023)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Efficient Learning of Quantum States Prepared With Few Non-Clifford Gates](https://mlsanity.com/paper/2305.13409/) (2023)
- [Agnostic Tomography of Stabilizer Product States](https://mlsanity.com/paper/2404.03813/) (2024)
- [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)
- [Efficient Learning of Quantum States Prepared With Few Non-Clifford Gates II: Single-Copy Measurements](https://mlsanity.com/paper/2308.07175/) (2023)

## Abstract (arXiv)

We give an efficient algorithm that learns a non-interacting fermion state, given copies of the state. For a system of n non-interacting fermions and m modes, we show that O(m3 n2 log(1/δ) / ε4) copies of the input state and O(m4 n2 log(1/δ)/ ε4) time are sufficient to learn the state to trace distance at most ε with probability at least 1 - δ. Our algorithm empirically estimates one-mode correlations in O(m) different measurement bases and uses them to reconstruct a succinct description of the entire state efficiently.