Universal quantum computation using Ising anyons from a non-semisimple Topological Quantum Field Theory

TL;DR

This paper introduces a new non-semisimple topological quantum field theory framework that extends Ising anyons, enabling universal quantum computation through braiding, which was not possible with conventional Ising anyons alone.

Contribution

It presents a novel non-semisimple TQFT that adds a new anyon type to Ising models, achieving universal quantum computation via braiding.

Findings

Adding one new anyon type enables universality.

Non-semisimple theories provide more powerful models.

Potential for fault-tolerant quantum computing.

Abstract

We propose a framework for topological quantum computation using newly discovered non-semisimple analogs of topological quantum field theories in 2+1 dimensions. These enhanced theories offer more powerful models for quantum computation. The conventional theory of Ising anyons, which is believed to describe excitations in the $\nu = 5/2$ fractional quantum Hall state, is not universal for quantum computation via braiding of quasiparticles. However, we show that the non-semisimple theory introduces new anyon types that extend the Ising framework. By adding just one new anyon type, universal quantum computation can be achieved through braiding alone. This result opens new avenues for realizing fault-tolerant quantum computing in topologically ordered systems.