Topological Computation by non-Abelian Braiding in Classical Metamaterials

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.