Probing topological entanglement on large scales

TL;DR

This paper introduces a protocol that efficiently measures topological entanglement in large quantum systems by using local adiabatic deformations, enabling practical certification of topological order through small subsystem measurements.

Contribution

It presents a novel, general method to extract topological entanglement features from small subsystems, reducing measurement complexity in large quantum systems.

Findings

Protocol successfully applied to string-net models of topological phases.

Numerical simulations demonstrate feasibility on neutral atom tweezer arrays.

Method reduces measurement complexity from exponential to polynomial time.

Abstract

Topologically ordered quantum matter exhibits intriguing long-range patterns of entanglement, which reveal themselves in subsystem entropies. However, measuring such entropies, which can be used to certify topological order, on large partitions is challenging and becomes practically unfeasible for large systems. We propose a protocol based on local adiabatic deformations of the Hamiltonian which extracts the universal features of long-range topological entanglement from measurements on small subsystems of finite size, trading an exponential number of measurements against a polynomial-time evolution. Our protocol is general and readily applicable to various quantum simulation architectures. We apply our method to various string-net models representing both abelian and non-abelian topologically ordered phases, and illustrate its application to neutral atom tweezer arrays with numerical simulations.