Maximum entropy for fine-tuning quantum dot arrays

Quantum dots are a promising platform to realize practical quantum computing. However, before they can be used as qubits, quantum dots must be carefully tuned to the correct regime in the voltage space to trap individual electrons. Moreover, realizable quantum computing requires tuning of large arrays, which translates to a significant increase in the number of parameters that need to be controlled and calibrated. This necessitates the development of robust and automated methods to bring the device into an operational state. Building upon previous ray-based tuning methods, we explore the utility of the ray-based measurements to accurately extract the interdot and dot-to-gate capacitive coupling. Using the geometric information from the quantum dot charge stability diagram, we derive the probability that the quantum dot system is in the (n,m) state. We achieve this by automatically extracting the fisher information to navigate the probability manifold. This, in turn, gives us both the probability of being in the (m,n) state (charge tuning) and a way to measure the probability of going from (n,m) to (n,m+1) as the plunger gates are changed. This method not only enhances ray-based navigation but also provides a measure of uncertainty for transitioning between different charge occupations. Our work is an important step in establishing reliable fine-tuning methods for calibrating quantum dots to work as qubits.