Universality of Z3 parafermions via edge mode interaction and quantum simulation of topological space evolution with Rydberg atoms

TL;DR

This paper explores the properties of Z3 parafermions, demonstrating how edge mode interactions create dynamical phase gates, and proposes a Rydberg atom-based experiment to simulate topological state evolutions.

Contribution

It reveals how short-range interactions induce non-Clifford gates in Z3 parafermions and proposes a feasible quantum simulation using Rydberg atoms.

Findings

Interaction induces non-Clifford dynamical phase gates.

Strongest interactions generate gates in higher Clifford hierarchy levels.

Proposed Rydberg atom experiment to simulate topological braiding.

Abstract

Parafermions are Zn generalisations of Majorana quasiparticles, with fractional non-Abelian statistics. They can be used to encode topological qudits and perform Clifford operations by their braiding. We study the simplest case of the Z3 parafermion chain and investigate the form of the non-topological gate that arises through direct short-range interaction of the parafermion edge modes. We show that such an interaction gives rise to a dynamical phase gate on the encoded ground space, with the strongest order of the interaction generating a non-Clifford gate which can be tuned to belong to even levels of the Clifford hierarchy. We also illustrate the accessibility of highly non-contextual states using this dynamical gate. Finally, we propose an experiment that simulates the braiding and dynamical evolutions of the Z3 topological states with Rydberg atom technology.