Experimentally Probing Topological Order and Its Breakdown via Modular Matrices

TL;DR

This paper demonstrates that experimental techniques can accurately reconstruct modular matrices, fundamental signatures of topological order, even with disorder and perturbations, confirming the robustness of topological phases and their potential for quantum computing.

Contribution

It provides the first experimental reconstruction of modular matrices for topological order under realistic conditions, showing robustness and technological feasibility.

Findings

Modular matrices can be reconstructed with high accuracy experimentally.

Topological order signatures are robust against disorder and detuning.

Current technologies can probe phases of matter beyond ideal models.

Abstract

The modern conception of phases of matter has undergone tremendous developments since the first observation of topologically ordered states in fractional quantum Hall systems in the 1980s. In this paper, we explore the question: How much detail of the physics of topological orders can in principle be observed using state of the art technologies? We find that using surprisingly little data, namely the toric code Hamiltonian in the presence of generic disorders and detuning from its exactly solvable point, the modular matrices -- characterizing anyonic statistics that are some of the most fundamental finger prints of topological orders -- can be reconstructed with very good accuracy solely by experimental means. This is a first experimental realization of these fundamental signatures of a topological order, a test of their robustness against perturbations, and a proof of principle -- that current technologies have attained the precision to identify phases of matter and, as such, probe an extended region of phase space around the soluble point before its breakdown. Given the special role of anyonic statistics in quantum computation, our work promises myriad applications both in probing and realistically harnessing these exotic phases of matter.