Implementation of Single-qubit and CNOT Gates by Anyonic Excitations of Two-body Topological Color Code

TL;DR

This paper demonstrates how to implement single-qubit and CNOT gates using anyonic excitations in a two-body topological color code model, which can be simulated in optical lattices and enables topological quantum computation.

Contribution

It introduces a method to realize quantum gates through anyonic excitations in a two-body topological color code, highlighting the potential for topological quantum computing.

Findings

Single-qubit gates implemented via anyonic excitations.

CNOT gates achieved through braiding of anyons.

Model suitable for simulation in optical lattices.

Abstract

The anyonic excitations of topological two-body color code model are used to implement a set of gates. Because of two-body interactions, the model can be simulated in optical lattices. The excitations have nontrivial mutual statistics, and are coupled to nontrivial gauge fields. The underlying lattice structure provides various opportunities for encoding the states of a logical qubit in anyonic states. The interactions make the transition between different anyonic states, so being logical operation in the computational bases of the encoded qubit. Two-qubit gates can be performed in a topological way using the braiding of anyons around each other.