# General scheme for preparation of different topological states on the cluster states

## TL;DR

This paper presents a general method for generating various topological quantum states, including non-Abelian anyons, from cluster states using specific measurement patterns, aiding experimental realization.

## Contribution

Introduces a universal scheme to find measurement patterns for creating diverse topological states and anyons from cluster states, with a graphical notation for state conversion.

## Key findings

- Developed a measurement pattern for non-Abelian anyons on cluster states.
- Provided a graphical method to convert CSS topological states to cluster states.
- Supported scheme for experimental realization of topological states and anyons.

## Abstract

Although it is well known that all quantum states can be produced by single qubit measurements on the cluster states, it is not a simple task to explicitly find which measurement patterns on the cluster states can generate different quantum states. In this paper we introduce a general scheme to find measurement patterns corresponding to different topological CSS states containing Kitaev's toric code states and color code states on different lattices and in different dimensions. Furthermore, we find a measurement pattern for generating non abelian anyons where measurement induced defects on a toric code state play the role of Ising anyons. We also support our scheme by a graphical notation where, by following a few simple graphical transformations, one will be able to convert a CSS topological state to a cluster state. Our scheme can be also used for experimental realization of anyons on cluster states.