Emulating quantum teleportation of a Majorana zero mode qubit

TL;DR

This paper demonstrates a quantum simulation of teleporting a Majorana zero mode qubit using a superconducting processor, showcasing fault-tolerant features and error detection in topological quantum computing.

Contribution

It presents the first quantum simulation of Majorana-based topological qubit teleportation using braiding operations on a superconducting quantum processor.

Findings

Achieved teleportation fidelity improved from 70.76% to 84.60%.

Successfully implemented braiding operations with Clifford gates.

Demonstrated error detection with Majorana encoding.

Abstract

Topological quantum computation based on anyons is a promising approach to achieve fault-tolerant quantum computing. The Majorana zero modes in the Kitaev chain are an example of non-Abelian anyons where braiding operations can be used to perform quantum gates. Here we perform a quantum simulation of topological quantum computing, by teleporting a qubit encoded in the Majorana zero modes of a Kitaev chain. The quantum simulation is performed by mapping the Kitaev chain to its equivalent spin version, and realizing the ground states in a superconducting quantum processor. The teleportation transfers the quantum state encoded in the spin-mapped version of the Majorana zero mode states between two Kitaev chains. The teleportation circuit is realized using only braiding operations, and can be achieved despite being restricted to Clifford gates for the Ising anyons. The Majorana encoding is a quantum error detecting code for phase flip errors, which is used to improve the average fidelity of the teleportation for six distinct states from $70.76 \pm 0.35 \% $ to $84.60 \pm 0.11 \%$, well beyond the classical bound in either case.