Explainable Phenomenological Models for Multivariate Quantum Dot Readout

In physics, many complex, real-world phenomena resist rigorous modeling, particularly when measurements are multivariate. In gate-defined quantum dot (QD) tuning, the connection between multiple gates and the dot behavior is very challenging to explain with theoretical models, hindering automated tuning. We propose relaxing the requirements for strictly theoretical models, focusing instead on mathematical modeling of the behavior. Such models, composed of simple functions such as sigmoids and Gaussians, can approximate a wide range of phenomena while requiring significantly less data than the previously proposed, complex machine learning (ML) methods. By integrating these models with explainable ML techniques, we demonstrate their utility in automating QD autotuning processes. Specifically, we apply this approach to experiments performed at the Laboratory for Physical Sciences involving Pauli-spin blockade readout in HRL-fabricated six-dot SLEDGE devices, showing that mathematical models provide valuable insights into device behavior and can optimize the device for desirable operational regimes. This approach helps overcome the current limitations of insufficient theoretical grounding by offering a practical solution that leads to more actionable tuning.