Experimental Identification of Non-Abelian Topological Orders on a Quantum Simulator

TL;DR

This paper demonstrates how to identify different topological orders, including non-Abelian Fibonacci order, using a nuclear magnetic resonance quantum simulator by measuring their modular matrices, advancing topological quantum computing research.

Contribution

The study introduces a method to identify topological orders via modular matrix measurements on a quantum simulator, including non-Abelian Fibonacci order, a key step toward topological quantum computing.

Findings

Successfully measured modular S and T matrices for three topological phases

Identified non-Abelian Fibonacci order as a candidate for universal quantum computing

Established a new approach for investigating topological orders with quantum simulators

Abstract

Topological orders can be used as media for topological quantum computing --- a promising quantum computation model due to its invulnerability against local errors. Conversely, a quantum simulator, often regarded as a quantum computing device for special purposes, also offers a way of characterizing topological orders. Here, we show how to identify distinct topological orders via measuring their modular $S$ and $T$ matrices. In particular, we employ a nuclear magnetic resonance quantum simulator to study the properties of three topologically ordered matter phases described by the string-net model with two string types, including the $\Z_2$ toric code, doubled semion, and doubled Fibonacci. The third one, non-Abelian Fibonacci order is notably expected to be the simplest candidate for universal topological quantum computing. Our experiment serves as the basic module, built on which one can simulate braiding of non-Abelian anyons and ultimately topological quantum computation via the braiding, and thus provides a new approach of investigating topological orders using quantum computers.