Introduction to Topological Superconductivity and Majorana Fermions for Quantum Engineers

TL;DR

This tutorial introduces topological superconductivity and Majorana fermions, explaining their mathematical foundations, physical properties, and potential for quantum computing applications, especially in topological qubit engineering.

Contribution

It provides a comprehensive introduction with detailed derivations and explanations of Majorana fermions and topological superconductivity for quantum engineers.

Findings

Mathematical derivation of the Kitaev model and BdG Hamiltonian

Explanation of Majorana fermions and Non-Abelian statistics

Guidance on engineering topological qubits using Majoranas

Abstract

In this tutorial paper, we provide an introduction to the briskly expanding research field of Majorana fermions in topological superconductors. We discuss several aspects of topological superconductivity and the advantages it brings to quantum computing. Mathematical derivation of the Kitaev model and BdG Hamiltonian is carried out to explain the phenomena of superconductivity and Majorana fermions. The Majorana fermions and the Non-Abelian statistics are described in detail along with their significance for quantum engineers. The theory provided led towards the engineering of the topological qubits using Majoranas.