Universal Quantum Computation with Continuous-Variable Abelian Anyons

TL;DR

This paper demonstrates how continuous-variable abelian anyons can be used for universal quantum computation by combining topological operations with non-Gaussian elements, expanding the capabilities of topological quantum computing.

Contribution

It introduces a protocol for universal quantum computation with continuous-variable abelian anyons, incorporating non-topological operations like squeezing and measurements.

Findings

Topological operations alone are insufficient for universality.

Non-Gaussian elements enable universal quantum computation.

Protocols for implementing quantum gates with continuous-variable anyons.

Abstract

We describe how continuous-variable abelian anyons, created on the surface of a continuous-variable analogue of Kitaev's lattice model can be utilized for quantum computation. In particular, we derive protocols for the implementation of quantum gates using topological operations. We find that the topological operations alone are insufficient for universal quantum computation which leads us to study additional non-topological operations such as offline squeezing and single-mode measurements. It is shown that these in conjunction with a non-Gaussian element allow for universal quantum computation using continuous-variable abelian anyons.