# Efficient Classical Shadow Tomography through Many-body Localization Dynamics

**Authors:** Tian-Gang Zhou, Pengfei Zhang  
**arXiv:** [2309.01258](https://arxiv.org/abs/2309.01258)  
**Date:** 2023-09-03  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2309.01258v1/

## Key points

- Introduction of a new approach to classical shadow tomography by Tian-Gang Zhou and Pengfei Zhang
- Avoidance of random two-qubit gates in the method, beneficial for quantum simulators like ultracold atomic gases
- Utilization of many-body localization dynamics instead, commonly observed in optical lattices
- Efficiency demonstrated through analytical exploration with a phenomenological model and numerical simulations using the TEBD algorithm
- Exponential advantage over traditional Pauli measurement protocols for few-body measurements shown through direct numerical simulations
- Methodology showcases remarkable efficiency comparable to shallow circuits or measurement-induced criticality
- Research highlights how many-body localization dynamics can enhance classical shadow tomography and provide insights into extracting information from complex quantum systems efficiently

## Summary

In their work titled "Efficient Classical Shadow Tomography through Many-body Localization Dynamics," Tian-Gang Zhou and Pengfei Zhang introduce a new approach to classical shadow tomography, a powerful tool for extracting properties from complex quantum many-body systems with minimal measurements. This alternative method avoids the use of random two-qubit gates, which can be challenging on certain quantum simulators like ultracold atomic gases. Instead, it utilizes the dynamics of many-body localization, a phenomenon commonly observed in optical lattices. Through analytical exploration using a phenomenological model and numerical simulations with the TEBD algorithm, the researchers demonstrate that their scheme achieves remarkable efficiency comparable to shallow circuits or measurement-induced criticality. This exponential advantage over traditional Pauli measurement protocols for few-body measurements is supported by direct numerical simulations covering the entire sampling and reconstruction processes, showcasing a compelling methodology for analyzing output states of quantum simulators. Overall, this research sheds light on how many-body localization dynamics can enhance classical shadow tomography and offers insights into more efficient ways to extract information from complex quantum systems.