The potential energy surface (PES) of a quantum chemical system is notoriously hard to compute. In the past decades, tensor networks emerged as a promising tool to study many-body quantum systems. The framework of tensor networks was recently found to provide promising results on specific kinds of mathematical functions while being very sample-efficient using the so-called quantics tensor cross interpolation (QTCI) method. This work investigates the question of whether the QTCI method can also be applied to approximating PESs using a parsimonious amount of samples. We show that while leading to astonishing results on length-separating functions, the PES just might not be the problem where QTCIs have the edge over traditional machine learning methods.