  Exploiting the power of quantum computation to realise superior machine
learning algorithmshas been a major research focus of recent years, but the
prospects of quantum machine learning (QML) remain dampened by considerable
technical challenges. A particularly significant issue is that generic QML
models suffer from so-called barren plateaus in their training landscapes --
large regions where cost function gradients vanish exponentially in the number
of qubits employed, rendering large models effectively untrainable. A leading
strategy for combating this effect is to build problem-specific models which
take into account the symmetries of their data in order to focus on a smaller,
relevant subset of Hilbert space. In this work, we introduce a family of
rotationally equivariant QML models built upon the quantum Fourier transform,
and leverage recent insights from the Lie-algebraic study of QML models to
prove that (a subset of) our models do not exhibit barren plateaus. In addition
to our analytical results we numerically test our rotationally equivariant
models on a dataset of simulated scanning tunnelling microscope images of
phosphorus impurities in silicon, where rotational symmetry naturally arises,
and find that they dramatically outperform their generic counterparts in
practice.
