Autonomous estimation of high-dimensional Coulomb diamonds from sparse measurements.

Arrays of coupled quantum dots possess ground states governed by Coulomb energies, utilized prominently by singly occupied quantum dots that each implement a spin qubit. For such quantum processors, the controlled transitions between one ground state to another are of significant operational significance, as these allow movements of quantum information within the array (single-electron shuttling and qubit initialization) or wave function overlap of one spin with another (entangling gates and teleportation). For few-dot arrays, the ground state regions (Coulomb diamonds) are traditionally mapped out by performing dense measurements in control-voltage space. For larger dot arrays, such raster scans become impractical, due to the large number of measurements needed to sample the high-dimensional gate-voltage hypercube, and the comparatively little information one extracts from such dense scans (boundaries of Coulomb diamonds). In this work, we use adaptive low-dimensional line searches proposed by a learning algorithm within a high-dimensional voltage space and combine this with a hardware triggered detection method based on reflectometry, to acquire sparse measurements that directly correspond to transitions between different ground states within the array. Our autonomous software-hardware algorithm terminates by accurately estimating the polytope of Coulomb blockade boundaries, which we experimentally demonstrate in a 2$\times$2 array of silicon quantum dots.