Many-body Chern number from statistical correlations of randomized measurements

TL;DR

This paper introduces an ancilla-free method using randomized measurements to experimentally determine the many-body Chern number, a key topological invariant, applicable to current quantum simulator geometries without prior Hamiltonian knowledge.

Contribution

It proposes a novel, experimentally feasible scheme to measure the many-body Chern number using statistical correlations of randomized measurements, avoiding the need for Hamiltonian information.

Findings

Applicable to disk-like geometries suitable for quantum simulators

Enables measurement of topological invariants without Hamiltonian knowledge

Uses statistical correlations of randomized measurements

Abstract

One of the main topological invariants that characterizes several topologically-ordered phases is the many-body Chern number (MBCN). Paradigmatic examples include several fractional quantum Hall phases, which are expected to be realized in different atomic and photonic quantum platforms in the near future. Experimental measurement and numerical computation of this invariant is conventionally based on the linear-response techniques which require having access to a family of states, as a function of an external parameter, which is not suitable for many quantum simulators. Here, we propose an ancilla-free experimental scheme for the measurement of this invariant, without requiring any knowledge of the Hamiltonian. Specifically, we use the statistical correlations of randomized measurements to infer the MBCN of a wavefunction. Remarkably, our results apply to disk-like geometries that are more amenable to current quantum simulator architectures.