Autonomous Estimation of High-Dimensional Coulomb Diamonds from Sparse Measurements

Quantum dot arrays possess ground states governed by Coulomb energies, utilized prominently by singly occupied quantum dots, each implementing a spin qubit. For such quantum processors, the con-trolled transitions between ground states are of operational significance, as these allow the control of quantum information within the array such as qubit initialization and entangling gates. For few-dot arrays, ground states are traditionally mapped out by performing dense raster-scan measurements in control -voltage space. These become impractical for larger arrays due to the large number of measurements needed to sample the high-dimensional gate-voltage hypercube and the comparatively little information extracted. We develop a hardware-triggered detection method based on reflectometry, to acquire measure-ments directly corresponding to transitions between ground states. These measurements are distributed sparsely within the high-dimensional voltage space by executing line searches proposed by a learning algorithm. Our autonomous software-hardware algorithm accurately estimates the polytope of Coulomb blockade boundaries, experimentally demonstrated in a 2 x 2 array of silicon quantum dots.