拓扑-声子耦合体系中非阿贝尔任意子编织的统一理论框架-A Unified Theoretical Framework for Non-Abelian Anyon Braiding inTopological-Phonon Coupled Systems

Based on the solid-state material verification line of Layer One, this paper proposes a unified theory of non-Abelian braiding that spans four material systems: α-RuCl₃, twisted bilayer graphene (TBG), TMD moiré superlattices, and cuprate high-temperature superconductors. Although the core quasiparticles of each system — OPTS, MPTP, SV-MPTP, and CSPTS — possess distinct microscopic constituents (Majorana fermions, valley-polarized electrons, spin-valley locked holes, charge-spin-phonon composites), their low-energy braiding dynamics are described by the same braid group ??, and the braiding generators share isomorphic matrix representations. We demonstrate that this universality is rooted in a deeper mathematical structure: all four quasiparticles are topological excitations of the ? 6 soliton potential within the topological-phonon coupling field theory, and their topological charge classification spaces all take the form ?(1) × ?, where ? is a material-specific discrete or continuous symmetry group. Based on this unified description, we propose a universal acoustic braiding hardware scheme applicable to all four systems — interdigital transducer (IDT) arrays as a platform for universal topological quantum gate operations — and rigorously derive the fidelity limits of braiding operations. This paper provides a materialindependent universal theoretical framework and an engineering implementation roadmap for topological-phonon quantum computation.