Hardware-Matched Adaptive Dynamical Decoupling: When It Helps, When It Hurts, and How to Choos

Dynamical decoupling (DD) is a leading technique for preserving quantum coherence, yet standard periodic protocols fail to adapt to hardware-specific noise regimes. This work presents AHCE-OMEGA (Adaptive Hilbert Coherence Enhancement - Omega), a dynamical decoupling framework that utilizes prime-gap aperiodic timing and phase coupling through a constant lambda-q to achieve superior coherence retention. Validation on IBM Torino (133-qubit Heron processor) demonstrates up to 26.4% improvement in Bell state fidelity and a 4.3x slower decoherence rate compared to standard XY-8 sequences. Crucially, we also report boundary conditions: on IonQ Forte Enterprise trapped-ion hardware with near-ceiling baseline coherence (>99.5%), the full protocol incurs overhead that degrades performance. We introduce a LITE variant with scaled phase coupling (s = 0.1) that recovers parity on ions, and propose an Adaptive Controller that selects protection intensity based on measured noise features. This dataset supports the conclusion that one-size-fits-all DD is suboptimal and provides the engineering framework for hardware-aware coherence protection. Dataset and Code ContentsThis repository contains the supplementary materials for the preprint. experiment_data.json: Raw and processed fidelity data from 12 controlled experiments on IBM Torino and IonQ Forte. Includes ablation studies (Move 2) and fidelity decay sweeps (Move 8). generate_figures.py: Python source code used to generate the fidelity decay curves and ablation comparison charts presented in the paper. AHCE_OMEGA_Thinking_Paper.txt: Full text of the preprint including mathematical formulations for the Prime-Gap Timing and Lambda-Q Phase Coupling.