Topological Quantum Computation with the universal R matrix for Ising anyons

TL;DR

This paper demonstrates how the universal R matrix for Ising anyons can be used to understand topological quantum computation, aligning with Pfaffian wave function results while emphasizing the role of parity projection in entanglement.

Contribution

It introduces a braid-group extension framework for Ising anyons using the universal R matrix, connecting algebraic and wave function approaches in topological quantum computing.

Findings

Universal R matrix reproduces Pfaffian wave function results.

Parity projection is crucial for topological entanglement.

Braid-group extension offers a new perspective on Ising anyon computation.

Abstract

We show that the braid-group extension of the monodromy-based topological quantum computation scheme of Das Sarma et al. can be understood in terms of the universal R matrix for the Ising model giving similar results to those obtained by direct analytic continuation of multi-anyon Pfaffian wave functions. It is necessary, however, to take into account the projection on spinor states with definite total parity which is responsible for the topological entanglement in the Pfaffian topological quantum computer.