  We present a comprehensive investigation into the learning capabilities of a
simple d-level system (qudit). Our study is specialized for classification
tasks using real-world databases, specifically the Iris, breast cancer, and
MNIST datasets. We explore various learning models in the metric learning
framework, along with different encoding strategies. In particular, we employ
data re-uploading techniques and maximally orthogonal states to accommodate
input data within low-dimensional systems.
  Our findings reveal optimal strategies, indicating that when the dimension of
input feature data and the number of classes are not significantly larger than
the qudit's dimension, our results show favorable comparisons against the best
classical models. This trend holds true even for small quantum systems, with
dimensions d<5 and utilizing algorithms with a few layers (L=1,2). However, for
high-dimensional data such as MNIST, we adopt a hybrid approach involving
dimensional reduction through a convolutional neural network. In this context,
we observe that small quantum systems often act as bottlenecks, resulting in
lower accuracy compared to their classical counterparts.
