Engineering Non-Linear Decay Dynamics: Pulse-Level Control and Software-Defined Qubit Rescue on Superconducting Processors

The scalability of Noisy Intermediate-Scale Quantum (NISQ) devices is currently constrained by material defects, specifically Two-Level Systems (TLS) that induce resonant decoherence in superconducting qubits. This study presents a comprehensive experimental analysis using the IBM Quantum ibm_fez processor to demonstrate "Software-Defined Hardware" optimization. By employing a novel "Instruction-Level Calibration Injection" technique, we bypass standard compiler constraints to inject continuous off-resonant AC Stark drives ($N_{shots} = 4096$). Methodology The experiment utilizes a Floquet engineering approach to perform pulse-level Hamiltonian engineering. We implement custom instruction-level calibrations to…