  A new paradigm for data science has emerged, with quantum data, quantum
models, and quantum computational devices. This field, called Quantum Machine
Learning (QML), aims to achieve a speedup over traditional machine learning for
data analysis. However, its success usually hinges on efficiently training the
parameters in quantum neural networks, and the field of QML is still lacking
theoretical scaling results for their trainability. Some trainability results
have been proven for a closely related field called Variational Quantum
Algorithms (VQAs). While both fields involve training a parametrized quantum
circuit, there are crucial differences that make the results for one setting
not readily applicable to the other. In this work we bridge the two frameworks
and show that gradient scaling results for VQAs can also be applied to study
the gradient scaling of QML models. Our results indicate that features deemed
detrimental for VQA trainability can also lead to issues such as barren
plateaus in QML. Consequently, our work has implications for several QML
proposals in the literature. In addition, we provide theoretical and numerical
evidence that QML models exhibit further trainability issues not present in
VQAs, arising from the use of a training dataset. We refer to these as
dataset-induced barren plateaus. These results are most relevant when dealing
with classical data, as here the choice of embedding scheme (i.e., the map
between classical data and quantum states) can greatly affect the gradient
scaling.
