Abstract: In this talk, we will explore the universality of Selective Number-dependent Arbitrary Phase (SNAP) and Displacement gates for quantum control in 'Qudit-based' systems. However, optimizing the parameters of these gates poses a challenging task. The main focus is to investigate the sensitivity of training any of the SNAP parameters in the SNAP-Displacement protocol. I will analyze conditions that could potentially lead to the Barren Plateau problem in a qudit system and draw comparisons with multi-qubit systems. The parameterized ansatz consists of blocks, where each block is composed of hardware operations, namely SNAP and Displacement gates. Applying Variational Quantum Algorithm (VQA) with observable and gate cost functions, techniques common in literatures are applied along with the concept of t−design. Through this analysis, I will show that: (a) The trainability of a SNAP-parameter does not exhibit a preference for any particular direction within our cost function landscape, (b) By leveraging the first and second moments properties of Haar measures, I will establish new lemmas concerning the expectation of certain polynomial functions, and (c) utilizing these new lemmas, a general condition that indicates an expected trainability advantage in a qudit system when compared to multi-qubit systems will be shown.