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 controlled 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 measurements 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$\times$2 array of silicon quantum dots.