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 apply continuous off-resonant AC Stark drives, effectively modifying the qubit frequency to avoid resonant interactions with defect states. Key Findings The application of this protocol yielded three primary results: Spectral Decoupling: Successfully restored Ramsey fringes in a defect-limited qubit (Q150), achieving a coherence time of $T_2^* \approx 6.36 \: \mu\text{s}$. Protocol Benchmarking: The "Stark Rescue" protocol demonstrated a statistical advantage over standard CPMG dynamical decoupling. It extended coherence time by 11.3% ($T_2^{Stark} = 8.17 \: \mu\text{s}$ vs. $T_2^{CPMG} = 7.34 \: \mu\text{s}$; $p = 0.042$, Bootstrap t-test). Topological Simulation: Digital simulation of a topological domain wall under engineered correlated noise revealed a sigmoidal stability threshold ($SSE \approx 0.0008$), significantly outperforming standard exponential models ($SSE \approx 0.0085$). Conclusion These results confirm that pulse-level Hamiltonian engineering can effectively reclaim compromised hardware resources on current NISQ platforms. Keywords NISQ, Superconducting Qubits, Two-Level Systems (TLS), Floquet Engineering, AC Stark Effect, IBM Quantum, Dynamical Decoupling, Quantum Control.