# A Short Introduction to Topological Quantum Computation

## TL;DR

This paper provides an accessible overview of topological quantum computation using anyons, highlighting its error-resilient features, key concepts, challenges, and experimental realizations, especially focusing on Majorana zero modes in nanowires.

## Contribution

It offers an introductory synthesis of topological quantum computation, emphasizing the role of anyons, and discusses recent experimental models like topological superconducting nanowires.

## Key findings

- Topological quantum computation uses anyons for error-resistant quantum information processing.
- Majorana zero modes in nanowires are promising candidates for realizing topological qubits.
- The review identifies key challenges and future directions in experimental implementations.

## Abstract

This review presents an entry-level introduction to topological quantum computation -- quantum computing with anyons. We introduce anyons at the system-independent level of anyon models and discuss the key concepts of protected fusion spaces and statistical quantum evolutions for encoding and processing quantum information. Both the encoding and the processing are inherently resilient against errors due to their topological nature, thus promising to overcome one of the main obstacles for the realisation of quantum computers. We outline the general steps of topological quantum computation, as well as discuss various challenges faced by it. We also review the literature on condensed matter systems where anyons can emerge. Finally, the appearance of anyons and employing them for quantum computation is demonstrated in the context of a simple microscopic model -- the topological superconducting nanowire -- that describes the low-energy physics of several experimentally relevant settings. This model supports localised Majorana zero modes that are the simplest and the experimentally most tractable types of anyons that are needed to perform topological quantum computation.