A Z₃-Graded Topological Quantum Computing Architecture Based on the Discrete 44-Vector Vacuum Lattice

Current quantum computing platforms, primarily based on Z2-graded qubits, suffer from fragility against decoherence and limited error correction thresholds. Here, we propose a topological quantum computing architecture founded on the finite-dimensional 19-dimensional Z3-graded Lie superalgebra and its emergent discrete 44-vector vacuum lattice—a minimal, closed geometric realization of ternary symmetry in 3D embedding space. The lattice supports stable non-Abelian anyonic excitations encoded as native qutrits, with triality-protected braiding offering intrinsic topological error correction and enhanced coherence times. We derive universal gate operations from graded bracket closure, estimate fault-tolerance thresholds exceeding 1.5% noise (significantly surpassing conventional surface code thresholds of ∼0.7–1%), and outline near-term experimental pathways in photonic lattices, cold atoms, and superconducting circuits. This Z3 framework provides a promising candidate for scalable, decoherenceresistant quantum computation, potentially resolving current bottlenecks in qubit-based platforms while bridging algebraic unification with practical quantum hardware.