Automatic, adaptive and sparse acquisition of Coulomb-blockade boundaries in quantum-dot arrays (Part 1)

For spin-based quantum processors, controlled transitions in quantum-dot arrays between one ground state to other competing ground states are of significant operational significance, as these allow movements of quantum information within otherwise empty arrays (single-electron shuttling), or wave function overlap of one spin with another (coherent Heisenberg spin exchange). Even for small arrays, dense raster scans in control-voltage space become impractical, due to the large number of measurements needed to sample the high-dimensional gate-voltage cube, and the comparatively little information (Coulomb diamond boundaries) one gains.
Instead, we develop a hardware-triggered detection method using high-frequency reflectometry, to acquire sparse measurements directly corresponding to transitions between competing ground states within the array. Instead of digitizing reflectometry voltages, the acquisition computer only records timestamps (triggered changes in reflectometry signal) and reconstructs their location in gate-voltage space based on the applied voltage ramps. Applying this sparse acquisition technique to a quadruple quantum dot implemented in silicon, we find good agreement between our method and traditional raster scans.