On braid statistics versus parastatistics

TL;DR

This paper explores advanced algebraic frameworks for paraparticles and anyons, demonstrating how these models can distinguish paraparticles from bosons/fermions and proposing a braided Majorana qubit for topological quantum computing.

Contribution

It introduces the use of (graded) Hopf algebras with braided tensor products to model paraparticles and anyons, and proposes a braided Majorana qubit for topological quantum computing.

Findings

Certain observables can discriminate paraparticles from bosons/fermions.

Toy models show the non-conventionality of parastatistics.

Introduction of braided Majorana qubits for topological quantum computing.

Abstract

I report the recent advances in applying (graded) Hopf algebras with braided tensor product in two scenarios: i) paraparticles beyond bosons and fermions living in any space dimensions and transforming under the permutation group; ii) physical models of anyons living in two space-dimensions and transforming under the braid group. In the first scenario simple toy models based on the so-called $2$-bit parastatistics show that, in the multiparticle sector, certain observables can discriminate paraparticles from ordinary bosons/fermions (thus, providing a counterexample to the widespread belief of the "conventionality of parastatistics" argument). In the second scenario the notion of (braided) Majorana qubit is introduced as the simplest building block to implement the Kitaev's proposal of a topological quantum computer which protects from decoherence.