Topological Seonggil-Magnetic Graph Quantum Computing Framework (TSMG-QC): Unifying Rabi Dynamics, Phase Frustration, and Scalable Architecture

The generalized Quantum Rabi Model (QRM), when interpreted as a bipartite magnetic graph, reveals the deep structural topology of atom-light interactions. This paper elevates the Magnetic Graph Quantum Dynamics (MGQD) framework by fusing it with Rough Operator Algebra (ROA) and Seonggil Matrix Theory (SMT). By mapping the NP-hard subgraph disconnection cost C(η) to the polynomial-time invariant eigenvalue λ_max(S_M) and redefining quantum measurement as a Sashangmugak dimensional collapse at the Seonggil Critical Horizon, we establish a fully unified computational operating system for superposition, entanglement, compiling, and error mitigation in scalable quantum hardware.