Topological Quantum Computation on Supersymmetric Spin Chains

TL;DR

This paper demonstrates how supersymmetric spin chains can host non-Abelian anyons suitable for topological quantum computation, providing a new physical realization that enhances error prevention in quantum gates.

Contribution

It establishes a precise mapping between anyonic fusion spaces and zero modes of Nicolai-like supersymmetric spin chains, enabling braid group operations for quantum computing.

Findings

Fusion spaces mapped to supersymmetric spin chain zero modes

Braid group operations realized on these zero modes

Potential for error-resistant quantum gates

Abstract

Quantum gates built out of braid group elements form the building blocks of topological quantum computation. They have been extensively studied in $SU(2)_k$ quantum group theories, a rich source of examples of non-Abelian anyons such as the Ising ($k=2$), Fibonacci ($k=3$) and Jones-Kauffman ($k=4$) anyons. We show that the fusion spaces of these anyonic systems can be precisely mapped to the product state zero modes of certain Nicolai-like supersymmetric spin chains. As a result, we can realize the braid group on the product state zero modes of these supersymmetric systems. These operators kill all the other states in the Hilbert space, thus preventing the occurrence of errors while processing information, making them suitable for quantum computing.