Empirical Validation of the Ait Zaouit Law v3.1: Achieving 78.83% Fidelity in High-Depth Quantum Circuits on IBM Heron Architecture

Overview: This report introduces and validates the Ait Zaouit Law v3.1, a proprietary quantum error mitigation (QEM) protocol designed to address systematic phase drifts in high-depth quantum circuits. The protocol was benchmarked on IBM’s latest Heron-class processors (ibm_torino, ibm_fez), demonstrating a significant breakthrough in maintaining qubit coherence at depths previously considered dominated by stochastic noise. Key Experimental Results: The Ait Zaouit protocol was subjected to rigorous stress-testing and symmetry validation: Mirror Symmetry Test (Depth 100): Achieved an unprecedented 78.83% return-to-zero fidelity on ibm_torino, proving near-perfect phase reversibility. Extreme Depth Stability (Depth 150): Maintained 40.92% fidelity on ibm_fez, successfully preventing the total information collapse observed in standard circuits. Comparative Benchmark: Outperformed industry-standard optimization models (Level 3) at a critical circuit depth of 111 gates. Methodology (Black-Box Summary): The Ait Zaouit Law utilizes a Deterministic Phase-Shielding mechanism. It functions as a pre-emptive stabilizing layer that injects compensatory virtual rotations (RZ) based on the specific gate depth and the hardware's coherent noise profile. This approach shifts the paradigm from gate-reduction to Phase Engineering, allowing for deeper and more complex quantum algorithms without additional hardware overhead. Intellectual Property & Disclosure: The specific mathematical constants, the non-linear scaling index, and the algorithmic source code are proprietary assets of Ait Zaouit Quantum Research. This publication serves as an official disclosure of the empirical results and the efficacy of the methodology. Full technical disclosure for peer-review or institutional collaboration is available under a Non-Disclosure Agreement (NDA). Keywords: Quantum Error Mitigation, Ait Zaouit Law, IBM Heron, Phase Shielding, Qiskit, Circuit Depth, Quantum Fidelity.