  Existing methods for learning 3D representations are deep neural networks
trained and tested on classical hardware. Quantum machine learning
architectures, despite their theoretically predicted advantages in terms of
speed and the representational capacity, have so far not been considered for
this problem nor for tasks involving 3D data in general. This paper thus
introduces the first quantum auto-encoder for 3D point clouds. Our 3D-QAE
approach is fully quantum, i.e. all its data processing components are designed
for quantum hardware. It is trained on collections of 3D point clouds to
produce their compressed representations. Along with finding a suitable
architecture, the core challenges in designing such a fully quantum model
include 3D data normalisation and parameter optimisation, and we propose
solutions for both these tasks. Experiments on simulated gate-based quantum
hardware demonstrate that our method outperforms simple classical baselines,
paving the way for a new research direction in 3D computer vision. The source
code is available at https://4dqv.mpi-inf.mpg.de/QAE3D/.
