Weighing unequal parameter importance and measurement expense in adaptive quantum sensing

A large class of experiments consists of measuring the parameters of physical models. In these experiments, the goal is to learn about these parameters as accurately and, often, quickly as possible. Adaptive experiment design works by yielding instrument control to Bayesian-based algorithms that alter instrument settings based on potential information gain about the parameters. By actively learning from data in real-time where to measure instead of determining instrument settings <i>a priori</i>, striking improvements in experiment efficiency are possible. Here, two new algorithms that improve upon previous implementations of adaptive experiment design are introduced. The first algorithm focuses on learning the model parameters that matter the most. The second algorithm considers the expense of a measurement and prioritizes information that can be gained at a lower cost. We demonstrate the remarkable improvement in efficiency and sensitivity that these algorithms provide for quantum sensing, specifically magnetometry, with nitrogen-vacancy centers in diamond. Most notably, we find an almost five-fold improvement in magnetic field sensitivity.