Quantum Architectonics: A Unified Framework for Substrate Engineering via Topological Genesis, Signal-Worker Dynamics, and Multi-Modal Control

The engineering of robust, decoherence-resistant topological qubits is currently impeded by a fragmented approach to material design that often treats control parameters in isolation. This study introduces and computationally supports the “Superconducting Quadrangle,” a unified framework integrating four cardinal axes—Geometry (G), Light (L), Heat (H), and Pressure (P)—for the predictive design of topological substrates. We identify a critical “thermodynamic bottleneck” governed by the coupling between Light and Heat, which constrains the utility of active Floquet engineering. In response, we propose the “Tensor Coupling” of Pressure and Geometry (PxG) as a thermodynamically efficient alternative. We demonstrate that this coupling creates an effective “analogue gravity” metric within the material, giving rise to a “tensor-locked” topological phase. Crucially, we provide direct computational evidence that this phase maintains a robust topological gap in the presence of strong local potential disorder, offering a deterministic, active alternative to the current reliance on passive geometric confinement. This work bridges the gap between abstract theoretical unification and physical realism, offering a rigorous blueprint for the next generation of fault-tolerant quantum materials.