Lie-Wedge Stratification Classifies 13 Control Strata for Drift-Free Single-Qubit Systems

Wang et al. from the primary arXiv submission derive the stratification by combining the control algebra with four channel properties. In each stratum the reversible directions coincide exactly with coherent controls, while five strata require extra channel data to decide stabilizability and one exceptional case needs averaging of two dissipative directions inside the wedge to reach a unique globally attractive pure state. This geometry distinguishes reversible from irreversible generators, information erased by ordinary Lie-algebra methods.

Standard Lie-algebra controllability tests applied to open quantum systems routinely overlook dissipation directionality, leading to over-optimistic claims about single-channel stabilization. The wedge approach recovers the missing distinction and shows that five strata remain conditionally stabilizable while one cannot be stabilized by any single rotated dissipator. The result directly affects hardware designs that rely on minimal control resources for state preparation and error suppression.

Next steps include mapping the stratification onto concrete device Hamiltonians and jump operators in superconducting and trapped-ion platforms, followed by numerical verification of the averaging protocol in the exceptional stratum. Experimental tests will require calibrated single-channel dissipation and precise tomography to confirm global attractivity thresholds predicted by the wedge geometry.