# Surveying structural complexity in quantum many-body systems

## TL;DR

This survey explores the structural complexity of quantum many-body systems using information-theoretic measures, providing insights into their non-classical behaviors and advancing understanding of quantum structure and dynamics.

## Contribution

It systematically reviews how complexity science tools reveal different features of quantum many-body systems, focusing on the Ising and Bose-Hubbard models.

## Key findings

- Different measures identify distinct structural features.
- Complexity measures reveal non-classical behaviors.
- Enhanced understanding of quantum system structures.

## Abstract

Quantum many-body systems exhibit a rich and diverse range of exotic behaviours, owing to their underlying non-classical structure. These systems present a deep structure beyond those that can be captured by measures of correlation and entanglement alone. Using tools from complexity science, we characterise such structure. We investigate the structural complexities that can be found within the patterns that manifest from the observational data of these systems. In particular, using two prototypical quantum many-body systems as test cases - the one-dimensional quantum Ising and Bose-Hubbard models - we explore how different information-theoretic measures of complexity are able to identify different features of such patterns. This work furthers the understanding of fully-quantum notions of structure and complexity in quantum systems and dynamics.