Room-Temperature Stability of Topological Qubits: From Topological Protection Gap to Full-Scale Quantum Error Correction Analysis拓扑量子比特的室温稳定性:从拓扑保护能隙到量子纠错的全尺度分析

The central promise of topological quantum computing is that quantum information is stored in topological invariants, thereby naturally immune to local noise. However, the extent to which this promise can be realised depends on a critical parameter — the topological protection gap . Within the established unifified framework of topologicalΔE phonon coupling, this paper presents a rigorous full-scale analysis of the roomtemperature stability of topological qubits across four material systems ( -RuCl , TBG, α 3 TMD moir\'{e} superlattices, and cuprates). From fifirst principles, we derive the quantitative relation between decoherence rate and , temperature , and phonon ΔE T heat-bath spectral density, demonstrating that topological protection is not "all or nothing" but is exponentially suppressed as . We further construct a exp(−ΔE/kB T) complete error model encompassing three distinct noise channels — thermally excited virtual errors, non-adiabatic transitions, and quasiparticle poisoning — and map it onto the fault-tolerance threshold framework of the surface code. The core quantitative conclusion: the SV-MPTP (Q = 2 mode) in TMD moir\'{e} superlattices achieves a logical error rate as low as per gate operation at 300 K, far exceeding the threshold for 10 −18 practical fault-tolerant quantum computing; cuprate CSPTSs exhibit comparable stability below ; while TBG and -RuCl require moderate cooling to approximately 250 K and T ∗ α 3150 K, respectively. This paper provides a complete noise analysis and optimisation roadmap for the engineering design of topological-phonon qubits.