Learning the nonclassicality of FID dynamics in diamond NV center from sparse data with quantum neural networks

Characterization of nonclassical traits of dynamical processes continues to attract significant attention in the field of open quantum system theory. An approach based on the canonical Hamiltonian ensemble representation (CHER) has been proposed as a framework for quantifying the nonclassicality of dynamical processes. However, current experimental limitations in implementing CHER theory impose a trade-off between achievable precision and experimental cost. Here we propose a quantum machine learning approach that extracts physical information from experimentally accessible systems, with the nitrogen–vacancy (NV) center in diamond serving as a representative platform. Leveraging the power of quantum neural networks (QNNs), our method captures the nonclassical features of the free-induction-decay process in NV centers. Moreover, we demonstrate that QNNs can be designed with consideration of key experimental factors—consistent with prior studies—while also analyzing their training landscape and circuit structures through the dynamical Lie algebra of different ansätze and data-encoding effects. Overall, this work demonstrates a practical application of QNNs for learning and characterizing nonclassicality in pure dephasing dynamics.