Do Rydberg chains yield Fibonacci anyons?

TL;DR

This paper investigates whether Rydberg atom chains can realize Fibonacci anyons for topological quantum computing, concluding that generic local operators do not preserve the necessary topological symmetry, thus Rydberg chains do not produce Fibonacci anyons.

Contribution

The paper demonstrates that Rydberg chains do not naturally realize Fibonacci anyons due to the non-local nature of their operators and the lack of topological symmetry preservation.

Findings

Rydberg chains' local operators are non-local anyonic operators.

Rydberg chains do not preserve topological symmetry.

Quantum computation with Rydberg atoms is not topologically protected.

Abstract

Recent experiments have focused attention on the properties of chains of atoms in which the atoms are either in their ground states or in highly excited Rydberg states which block similar excitations in their immediate neighbors. As the low energy Hilbert space of such chains is isomorphic to that of a chain of Fibonacci anyons, they have been proposed as a platform for topological quantum computation and for simulating anyon dynamics. We show that generic local operators in the Rydberg chain correspond to non-local anyonic operators that do not preserve a topological symmetry of the physical anyons. Consequently, we argue that Rydberg chains do not yield Fibonacci anyons and quantum computation with Rydberg atoms is not topologically protected.