Topological phases with parafermions: theory and blueprints

TL;DR

This paper reviews the theoretical foundations and experimental blueprints for realizing parafermions, exotic particles that extend Majorana fermions, and explores their potential for topological quantum computing.

Contribution

It provides a comprehensive overview of parafermion theory, experimental realization strategies, and their application in fault-tolerant quantum computing architectures.

Findings

Parafermions are linked to Z_3-symmetric spin chains with topological edge modes.

Multiple experimental platforms are proposed for realizing parafermion zero modes.

Coupled parafermion arrays could enable universal topological quantum computation.

Abstract

We concisely review the recent evolution in the study of parafermions -- exotic emergent excitations that generalize Majorana fermions and similarly underpin a host of novel phenomena. First we illustrate the intimate connection between Z_3-symmetric "spin" chains and one-dimensional parafermion lattice models, highlighting how the latter host a topological phase featuring protected edge zero modes. We then tour several blueprints for the laboratory realization of parafermion zero modes -- focusing on quantum Hall/superconductor hybrids, quantum Hall bilayers, and two-dimensional topological insulators -- and describe striking experimental fingerprints that they provide. Finally, we discuss how coupled parafermion arrays in quantum Hall architectures yield topological phases that potentially furnish hardware for a universal, intrinsically decoherence-free quantum computer.