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

Shang Ling Hung^1*, Nien-Ting Ko¹, Hong-Bin Chen^1,2,3

¹Department of Engineering Science, National Cheng Kung University, Tainan, Taiwan
²Center for Quantum Frontiers of Research & Technology, National Cheng Kung University, Tainan, Taiwan
³Physics Division, National Center for Theoretical Sciences, Taipei, Taiwan

* Presenter:Shang Ling Hung, email:n96131281@gs.ncku.edu.tw

Characterizing of nonclassical traits of dynamical processes continues to attract significant attention in the study of open quantum systems. The canonical Hamiltonian ensemble representation (CHER), originally proposed to describe dynamical processes in the frequency domain, provides a framework for quantifying the nonclassicality of such processes. However, current experimental limitations in implementing CHER theory impose a trade-off between achievable precision and experimental cost.

To address this challenge, 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 (FID) process in NV centers. Moreover, recent studies in variational quantum machine learning have investigated the origin of barren plateaus and their relation to circuit design. In this context, we demonstrate that QNNs can be designed with consideration of key experimental factors, consistent with prior findings. We further analyze their training landscapes and circuit structures through the dynamical Lie algebra (DLA) of different ansätze, based on the Lie-algebraic framework established in previous theoretical work. In addition, we examine data-encoding effects that enrich the model’s frequency spectrum, effectively expressing the quantum model as a partial Fourier series in the input data. Overall, this approach represents a practical application of QNNs to learn the nonclassicality for pure dephasing dynamics.

Keywords: Quantum Neuron Network, Nonclassicality, NV-Center, Free Induction Decay