# Many-body topological invariants from randomized measurements

## TL;DR

This paper introduces randomized measurement protocols to experimentally determine many-body topological invariants in one-dimensional interacting bosonic systems, enabling classification of symmetry-protected topological phases.

## Contribution

It proposes a versatile, experimentally feasible method using local random unitaries to measure topological invariants in interacting quantum systems.

## Key findings

- Protocols applicable to all symmetry types of 1D bosonic systems
- Uses randomized measurements with local unitaries for invariant detection
- Facilitates experimental classification of SPT phases

## Abstract

The classification of symmetry-protected topological (SPT) phases in one dimension has been recently achieved, and had a fundamental impact in our understanding of quantum phases in condensed matter physics. In this framework, SPT phases can be identified by many-body topological invariants, which are quantized non-local correlators for the many-body wavefunction. While SPT phases can now be realized in interacting synthethic quantum systems, the direct measurement of quantized many-body topological invariants has remained so far elusive. Here, we propose measurement protocols for many-body topological invariants for all types of protecting symmetries of one-dimensional interacting bosonic systems. Our approach relies on randomized measurements implemented with local random unitaries, and can be applied to any spin system with single-site addressability and readout. Our scheme thus provides a versatile toolbox to experimentally classify interacting SPT phases.