  We introduce the novel class $(E_\alpha)_{\alpha \in [-\infty,1)}$ of reverse
map projection embeddings, each one defining a unique new method of encoding
classical data into quantum states. Inspired by well-known map projections from
the unit sphere onto its tangent planes, used in practice in cartography, these
embeddings address the common drawback of the amplitude embedding method,
wherein scalar multiples of data points are identified and information about
the norm of data is lost.
  We show how reverse map projections can be utilised as equivariant embeddings
for quantum machine learning. Using these methods, we can leverage symmetries
in classical datasets to significantly strengthen performance on quantum
machine learning tasks.
  Finally, we select four values of $\alpha$ with which to perform a simple
classification task, taking $E_\alpha$ as the embedding and experimenting with
both equivariant and non-equivariant setups. We compare their results alongside
those of standard amplitude embedding.
