# Quantum computation from fermionic anyons on a 1D lattice

## TL;DR

This paper introduces fermionic anyon models by deforming fermionic algebra, demonstrating that these models enable universal quantum computation through number-preserving quadratic Hamiltonians.

## Contribution

It defines fermionic anyon models and proves their capability for universal quantum computation, extending fermionic linear optics to anyonic systems.

## Key findings

- Fermionic anyon models are constructed by deforming fermionic algebra.
- Deformed models enable universal quantum computation.
- Number-preserving quadratic Hamiltonians are sufficient for universality.

## Abstract

Fermionic linear optics corresponds to the dynamics of free fermions, and is known to be efficiently simulable classically. We define fermionic anyon models by deforming the fermionic algebra of creation and annihilation operators, and consider the dynamics of number-preserving, quadratic Hamiltonians on these operators. We show that any such deformation results in an anyonic linear optical model which allows for universal quantum computation.