Learning Lindblad Dynamics of a Superconducting Quantum Processor

Accurate models of quantum processors are essential for understanding, calibrating, and improving their performance. In practice, model construction must balance physical detail against the experimental and computational effort required to reliably learn parameters. Compact descriptions therefore often rely on assumptions about which interactions, noise processes, or hidden degrees of freedom are relevant. Here we introduce LIMINAL, a data-driven framework for testing such assumptions and selecting minimal adequate Lindblad models. LIMINAL fits nested candidate models to time-resolved tomographic data and uses likelihood-ratio tests to decide when added physical mechanisms are warranted. We apply LIMINAL to a five-qubit superconducting processor, identifying an idling model with three-local Hamiltonian terms and two-local dissipation, while finding no support for three-local dissipation. We further apply it to recover driven single-qubit Hamiltonians, reconstruct a shaped-pulse Hamiltonian without assuming an analytic pulse model, and test hidden-qubit extensions in coupler-mediated dynamics, demonstrating the applicability of the framework for a wide range of tasks.