Topological Computation by non-Abelian Braiding in Classical Metamaterials

• URL: http://arxiv.org/abs/2502.16006v1
• Date: Fri, 21 Feb 2025 23:44:10 GMT
• Title: Topological Computation by non-Abelian Braiding in Classical Metamaterials
• Authors: Liyuan Chen, Matthew Fuertes, Bolei Deng,
• Abstract summary: We propose a realization of the one-dimensional computation Kitaev topological superconductor in classical mechanical metamaterials.<n>We demonstrate that the system's mid-gap vibrational modes termed Major zero modes (MZMs), accurately reproduce statistics predicted by quantum theory.
• Score: 0.5714553194279463
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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