# Derandomized shallow shadows: Efficient Pauli learning with bounded-depth circuits

arXiv: https://arxiv.org/abs/2412.18973 · HTML: https://mlsanity.com/paper/2412.18973/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 99 references that are in the map.
- First posted on arXiv 25 Dec 2024.

## Builds on (most cited first, 5 of 5)

- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [TensorNetwork: A Library for Physics and Machine Learning](https://mlsanity.com/paper/1905.01330/) (2019)
- [Demonstration of Robust and Efficient Quantum Property Learning with Shallow Shadows](https://mlsanity.com/paper/2402.17911/) (2024)
- [Hardware-efficient learning of quantum many-body states](https://mlsanity.com/paper/2212.06084/) (2022)
- [GFlowNets for Hamiltonian decomposition in groups of compatible operators](https://mlsanity.com/paper/2410.16041/) (2024)

## Built on by (most cited first, 1 of 1)

- [Generative Learning for Quantum Measurement Design](https://mlsanity.com/paper/2608.11396/) (2026)

## Abstract (arXiv)

Efficiently estimating large numbers of non-commuting observables is an important subroutine of many quantum science tasks. We present the derandomized shallow shadows (DSS) algorithm for efficiently learning a large set of non-commuting observables, using shallow circuits to rotate into measurement bases. Exploiting tensor network techniques to ensure polynomial scaling of classical resources, our algorithm outputs a set of shallow measurement circuits that approximately minimizes the sample complexity of estimating a given set of Pauli strings. We numerically demonstrate systematic improvement, in comparison with state-of-the-art techniques, for energy estimation of quantum chemistry benchmarks and verification of quantum many-body systems, and we observe DSS's performance consistently improves as one allows deeper measurement circuits. These results indicate that in addition to being an efficient, low-depth, stand-alone algorithm, DSS can also benefit many larger quantum algorithms requiring estimation of multiple non-commuting observables.