Experimental observation of saddle points over the quantum control landscape of a two-spin system

The growing successes in performing quantum control experiments motivated the development of control landscape analysis as a basis to explain these findings. When a quantum system is controlled by an electromagnetic field, the observable as a functional of the control field forms a landscape. Theoretical analyses have predicted the existence of critical points over the landscapes, including saddle points with indefinite Hessians. This paper presents a systematic experimental study of quantum control landscape saddle points. Nuclear magnetic resonance control experiments are performed on a coupled two-spin system in a C-13-labeled chloroform ((CHCl3)-C-13) sample. We address the saddles with a combined theoretical and experimental approach, measure the Hessian at each identified saddle point, and study how their presence can influence the search effort utilizing a gradient algorithm to seek an optimal control outcome. The results have significance beyond spin systems, as landscape saddles are expected to be present for the control of broad classes of quantum systems

NMR Landscapes for Chemical Shift Prediction

The ability to reliably predict NMR chemical shifts plays an important role in elucidating the structure of organic molecules. Additionally, an intriguing question is how the multitude of variable factors (structural, electronic, and environmental) correlate with the actual electromagnetic shielding effect that determines the chemical shift value. This work presents NMRscape as a new tool for understanding these correlations by constructing the landscape that describes the relationship between the chemical shift value and the moieties bonded to a molecular scaffold. The scaffold may be as small as a single atom probed by NMR or a larger molecular framework containing the probed atom. NMRscape operates with only a list of the chemical moieties bonded to the scaffold, without utilizing any potentially biasing chemometric descriptors. The corresponding chemical shift landscape is constructed based on fundamental physical principles, which makes NMRscape a credible chemical shift prediction and analysis tool. As an illustration, we demonstrate that NMRscape can predict ¹³C chemical shifts with an accuracy exceeding the substituent chemical shift (SCS) increment, hierarchical organization of spherical environments (HOSE), and neural networks (NN), methods for three distinct families of molecules sharing a common scaffold structure with moieties placed at two variable sites. The constructed NMR landscapes confirmed known empirical rules relating chemical shift values to the variation of chemical moieties on a scaffold, as well as uncovered hitherto hidden relationships. The practical importance of NMRscape is discussed