Non-perturbative CPMG scaling and qutrit-driven breakdown under compiled superconducting-qubit control: a single-qubit study

Abstract

Decoherence in superconducting qubits emerges from the interplay of multilevel dynamics and structured environmental noise, yet perturbative models cannot capture all resulting signatures. Here, EmuPlat couples instruction-set-architecture-level waveform generation to the hierarchical equations of motion (HEOM) under $1/f$ non-Markovian pure dephasing. In the resulting non-perturbative regime -- where filter-function predictions become quantitatively uninformative -- CPMG scaling of a three-level superconducting transmon yields one calibration result, two physical findings, and one structural null. Y-CPMG exhibits axis-dependent scaling-law breakdown -- non-monotonic decoherence, partial coherence revival, and pronounced X--Y population asymmetry ($0.204$ vs ${<}\,0.01$) -- driven by third-level anharmonicity amplified by bath memory; X-CPMG maintains well-behaved power-law scaling with a finite-$n$ transient excess consistent with non-Markovian bath-memory effects. The structural null is equally informative: waveform-level differences -- Standard versus VPPU realizations -- remain undetectable across all coupling strengths, establishing that rotating-frame pure-dephasing coupling renders control-layer detail invisible to scaling observables. These findings define testable predictions, the most experimentally accessible requiring only qualitative verification.