Braiding Majorana Fermions and Creating Quantum Logic Gates with Vortices on a Periodic Pinning Structure

TL;DR

This paper demonstrates how vortices with Majorana fermions on a periodic pinning array can be manipulated to perform quantum logic gates through braiding operations, with robustness against thermal effects.

Contribution

It introduces a method for vortex exchange and braiding on a periodic pinning structure to realize quantum gates like Hadamard and CNOT.

Findings

Successful realization of Hadamard and CNOT gates via vortex braiding.

Identification of two basic vortex operations: move and exchange.

Robustness of operations against thermal fluctuations with distinct force signatures.

Abstract

We show how vortices that support Majorana fermions when placed on a periodic pinning array can be used for vortex exchange and independent braiding by performing a series of specific moves with a probe tip. Using these braiding operations, we demonstrate realizations of a Hadamard and a CNOT gate. We specifically consider the first matching field at which there is one vortex per pinning site, and we show that there are two basic dynamic operations, move and exchange, from which basic braiding operations can be constructed in order to create specific logic gates. The periodic pinning array permits both control of the world lines of the vortices and freedom for vortex manipulation using a set of specific moves of the probe during which the probe tip strength and height remain unchanged. We measure the robustness of the different moves against thermal effects and show that the three different operations produce distinct force signatures on the moving tip.