# Efficient Learning of Quantum States Prepared With Few Non-Clifford Gates II: Single-Copy Measurements

arXiv: https://arxiv.org/abs/2308.07175 · HTML: https://mlsanity.com/paper/2308.07175/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 44 references that are in the map.
- First posted on arXiv 14 Aug 2023.

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

- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Information-theoretic bounds on quantum advantage in machine learning](https://mlsanity.com/paper/2101.02464/) (2021)
- [Efficient quantum tomography II](https://mlsanity.com/paper/1612.00034/) (2016)
- [Exponential separations between learning with and without quantum memory](https://mlsanity.com/paper/2111.05881/) (2021)
- [Improved Stabilizer Estimation via Bell Difference Sampling](https://mlsanity.com/paper/2304.13915/) (2023)
- [Fast and robust quantum state tomography from few basis measurements](https://mlsanity.com/paper/2009.08216/) (2020)
- [Optimal algorithms for learning quantum phase states](https://mlsanity.com/paper/2208.07851/) (2022)
- [Efficient Tomography of Non-Interacting Fermion States](https://mlsanity.com/paper/2102.10458/) (2021)
- [Low-Stabilizer-Complexity Quantum States Are Not Pseudorandom](https://mlsanity.com/paper/2209.14530/) (2022)

## Abstract (arXiv)

Recent work has shown that n-qubit quantum states output by circuits with at most t single-qubit non-Clifford gates can be learned to trace distance ε using mathsfpoly(n,2t,1/ε) time and samples. All prior algorithms achieving this runtime use entangled measurements across two copies of the input state. In this work, we give a similarly efficient algorithm that learns the same class of states using only single-copy measurements.