Reducing Sensing Time through Offline Experimental Design for Nuclear Spin Detection

The characterization of nuclear spin environments in solid-state devices plays an important role in advancing quantum technologies, yet traditional methods often demand long measurement times. To address this challenge, we integrate surrogate information gain (SIG) into our deep learning model based on the SALI architecture. By using SIG for data point selection, we achieve a significant reduction in experimental time while maintaining high precision in nuclear spin detection. SIG is a figure of merit based on the expected variance of the signal, which is more straightforward to compute than the expected information gain (EIG) rooted in Bayesian estimation, and, crucially, it selects experiments that are more robust to experimental imperfections. We demonstrate our approach on a nitrogen-vacancy (NV) center in diamond coupled to $^{13}$C nuclei. In the high-field regime, our variance-based optimization is validated with experimental data, resulting in an 85$\%$ reduction in measurement time for a modest reduction in performance. In the low-field regime, we explore the model's performance on simulated data, predicting a 60$\%$ reduction in the total experimental time by improving the temporal resolution of the measurements and applying SIG. This demonstrates the potential of integrating deep learning with optimized signal selection to enhance the efficiency of quantum sensing and nuclear spin characterization, paving the way for scaling these techniques to larger nuclear spin systems.