Automatic, adaptive and sparse acquisition of Coulomb-blockade boundaries in quantum-dot arrays (Part 2)*

One practical challenge of realizing spin-based quantum processors is the tuning of many different control voltages to a desirable region within its high-dimensional gate-voltage space. For a capacitively-coupled network of quantum dots, Coulomb blockade can stabilize many different charge configurations depending on applied gate voltages. In gate-voltage space, each ground state is associated with a region that is (within the constant-interaction model) a convex polytope. A common method of locating these polytopes is by dense rastering of gate-voltage space. From these charge stability maps information of Coulomb-blockade boundaries is extracted, thereby diminishing the information content of most measured pixels and making this approach expensive for larger arrays.
To learn Coulomb-blockade boundaries from only a sparse set of measurements, we develop a convex-polytope-finding algorithm based on active learning and large-margin classifiers suitable for noisy measurements. By applying this algorithm to a quadruple dot implemented in silicon we demonstrate the automatic discovery of charge-state transitions from a small number of noisy measurements obtained via high-frequency reflectometry off one gate electrode.