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/.

翻译：现有三维表示学习方法均在经典硬件上训练和测试深度神经网络。量子机器学习架构虽在速度和表征能力方面具有理论优势，但迄今尚未被用于处理三维数据或相关任务。本文首次提出针对三维点云的量子自编码器。我们的3D-QAE方法是完全量子的，即其所有数据处理组件均专为量子硬件设计。该方法通过三维点云集合训练以生成压缩表示。在设计此类完全量子模型时，除寻找合适架构外，核心挑战还包括三维数据归一化与参数优化，我们针对这两个问题分别提出了解决方案。在模拟门量子硬件上的实验表明，本方法优于简单经典基线方法，为三维计算机视觉开辟了新的研究方向。源代码见https://4dqv.mpi-inf.mpg.de/QAE3D/。