Estimation of Convex Polytopes for Automatic Discovery of Charge State Transitions in Quantum Dot Arrays

In spin based quantum dot arrays, material or fabrication imprecisions affect the behaviour of the device, which must be taken into account when controlling it. This requires measuring the shape of specific convex polytopes. We present an algorithm that automatically discovers count, shape and size of the facets of a convex polytope from measurements by alternating a phase of model-fitting with a phase of querying new measurements, based on the fitted model. We evaluate the algorithm on simulated polytopes and devices, as well as a real 2 x 2 spin qubit array. Results show that we can reliably find the facets of the convex polytopes, including small facets with sizes on the order of the measurement precision.