Topological Computation by non-Abelian Braiding in Classical Metamaterials

TL;DR

This paper demonstrates how classical mechanical metamaterials can simulate topological quantum computation by implementing braiding protocols that produce Majorana zero modes and perform quantum gates, all within a robust, classical system.

Contribution

It introduces a classical analog of a topological superconductor that can simulate quantum braiding and quantum gate operations using mechanical metamaterials.

Findings

Successfully simulated braiding of Majorana zero modes in classical systems

Implemented all single-qubit Clifford gates via braiding protocols

Proved topological robustness against mechanical defects

Abstract

We propose a realization of the one-dimensional Kitaev topological superconductor in classical mechanical metamaterials. By designing appropriate braiding protocols, we demonstrate that the system's mid-gap vibrational modes, termed classical Majorana zero modes (MZMs), accurately reproduce the braiding statistics predicted by quantum theory. Encoding four MZMs as a classical analog of a qubit, we implement all single-qubit Clifford gates through braiding, enabling the simulation of topological quantum computation in a classical system. Furthermore, we establish the system's topological protection by demonstrating its robustness against mechanical defects. This work provides a novel framework for exploring topological quantum computation using classical metamaterials and offers a pathway to realizing stable vibrational systems protected by topology.