# 3D-QAE: Fully Quantum Auto-Encoding of 3D Point Clouds

arXiv: https://arxiv.org/abs/2311.05604 · HTML: https://mlsanity.com/paper/2311.05604/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 76 references that are in the map.
- First posted on arXiv 9 Nov 2023.

## Builds on (most cited first, 30 of 42)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [AMASS: Archive of Motion Capture as Surface Shapes](https://mlsanity.com/paper/1904.03278/) (2019)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Generating 3D faces using Convolutional Mesh Autoencoders](https://mlsanity.com/paper/1807.10267/) (2018)
- [Transfer learning in hybrid classical-quantum neural networks](https://mlsanity.com/paper/1912.08278/) (2019)
- [Information-theoretic bounds on quantum advantage in machine learning](https://mlsanity.com/paper/2101.02464/) (2021)
- [Quantum machine learning beyond kernel methods](https://mlsanity.com/paper/2110.13162/) (2021)
- [Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation](https://mlsanity.com/paper/1905.02876/) (2019)
- [Variational Autoencoders for Deforming 3D Mesh Models](https://mlsanity.com/paper/1709.04307/) (2017)
- [Theory for Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.08566/) (2022)
- [Fully Convolutional Mesh Autoencoder using Efficient Spatially Varying Kernels](https://mlsanity.com/paper/2006.04325/) (2020)
- [Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks](https://mlsanity.com/paper/2210.09974/) (2022)
- [Implicit Autoencoder for Point-Cloud Self-Supervised Representation Learning](https://mlsanity.com/paper/2201.00785/) (2022)
- [Representation Theory for Geometric Quantum Machine Learning](https://mlsanity.com/paper/2210.07980/) (2022)
- [Recent Advances for Quantum Neural Networks in Generative Learning](https://mlsanity.com/paper/2206.03066/) (2022)
- [On Circuit-based Hybrid Quantum Neural Networks for Remote Sensing Imagery Classification](https://mlsanity.com/paper/2109.09484/) (2021)
- [Quantum Permutation Synchronization](https://mlsanity.com/paper/2101.07755/) (2021)
- [Q-Match: Iterative Shape Matching via Quantum Annealing](https://mlsanity.com/paper/2105.02878/) (2021)
- [A Quantum Computational Approach to Correspondence Problems on Point Sets](https://mlsanity.com/paper/1912.12296/) (2019)
- [Adiabatic Quantum Computing for Multi Object Tracking](https://mlsanity.com/paper/2202.08837/) (2022)
- [Hybrid Quantum-Classical Graph Convolutional Network](https://mlsanity.com/paper/2101.06189/) (2021)
- [Quantum Neural Networks: Concepts, Applications, and Challenges](https://mlsanity.com/paper/2108.01468/) (2021)
- [DEMEA: Deep Mesh Autoencoders for Non-Rigidly Deforming Objects](https://mlsanity.com/paper/1905.10290/) (2019)
- [A Hybrid Quantum-Classical Algorithm for Robust Fitting](https://mlsanity.com/paper/2201.10110/) (2022)
- [Multiclass classification using quantum convolutional neural networks with hybrid quantum-classical learning](https://mlsanity.com/paper/2203.15368/) (2022)
- [Semiconductor Defect Detection by Hybrid Classical-Quantum Deep Learning](https://mlsanity.com/paper/2208.03514/) (2022)

## Built on by (most cited first, 5 of 5)

- [Quantum Visual Fields with Neural Amplitude Encoding](https://mlsanity.com/paper/2508.10900/) (2025)
- [Quantum-enhanced Computer Vision: Going Beyond Classical Algorithms](https://mlsanity.com/paper/2510.07317/) (2025)
- [Quantum Implicit Neural Representations for Novel View Synthesis](https://mlsanity.com/paper/2601.05250/) (2026)
- [Universality of Many-body Projected Ensemble for Learning Quantum Data Distribution](https://mlsanity.com/paper/2601.18637/) (2026)
- [Latent-Conditioned Parameterized Quantum Circuits as Universal Approximators for Distributions over Quantum States](https://mlsanity.com/paper/2605.28690/) (2026)

## Abstract (arXiv)

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/.