# Matching Point Sets with Quantum Circuit Learning

arXiv: https://arxiv.org/abs/2102.06697 · HTML: https://mlsanity.com/paper/2102.06697/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 57 references that are in the map.
- First posted on arXiv 12 Feb 2021.

## Builds on (most cited first, 13 of 13)

- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [PointContrast: Unsupervised Pre-training for 3D Point Cloud Understanding](https://mlsanity.com/paper/2007.10985/) (2020)
- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [PREDATOR: Registration of 3D Point Clouds with Low Overlap](https://mlsanity.com/paper/2011.13005/) (2020)
- [PointNetLK: Robust & Efficient Point Cloud Registration using PointNet](https://mlsanity.com/paper/1903.05711/) (2019)
- [Self-Supervised Pretraining of 3D Features on any Point-Cloud](https://mlsanity.com/paper/2101.02691/) (2021)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Differentiable Learning of Quantum Circuit Born Machine](https://mlsanity.com/paper/1804.04168/) (2018)
- [The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine](https://mlsanity.com/paper/1904.02214/) (2019)
- [Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines](https://mlsanity.com/paper/1712.04144/) (2017)
- [Quantum Permutation Synchronization](https://mlsanity.com/paper/2101.07755/) (2021)
- [A Quantum Computational Approach to Correspondence Problems on Point Sets](https://mlsanity.com/paper/1912.12296/) (2019)

## Built on by (most cited first, 10 of 10)

- [Quantum Motion Segmentation](https://mlsanity.com/paper/2203.13185/) (2022)
- [CCuantuMM: Cycle-Consistent Quantum-Hybrid Matching of Multiple Shapes](https://mlsanity.com/paper/2303.16202/) (2023)
- [QClusformer: A Quantum Transformer-based Framework for Unsupervised Visual Clustering](https://mlsanity.com/paper/2405.19722/) (2024)
- [Quantum Visual Feature Encoding Revisited](https://mlsanity.com/paper/2405.19725/) (2024)
- [Robust Fitting on a Gate Quantum Computer](https://mlsanity.com/paper/2409.02006/) (2024)
- [Quantum-enhanced Computer Vision: Going Beyond Classical Algorithms](https://mlsanity.com/paper/2510.07317/) (2025)
- [QuAnt: Quantum Annealing with Learnt Couplings](https://mlsanity.com/paper/2210.08114/) (2022)
- [QUBO Decision Tree: Annealing Machine Extends Decision Tree Splitting](https://mlsanity.com/paper/2303.09772/) (2023)
- [Quantum-Hybrid Stereo Matching With Nonlinear Regularization and Spatial Pyramids](https://mlsanity.com/paper/2312.16118/) (2023)
- [Pre-training Tensor-Train Networks Facilitates Machine Learning with Variational Quantum Circuits](https://mlsanity.com/paper/2306.03741/) (2023)

## Abstract (arXiv)

In this work, we propose a parameterised quantum circuit learning approach to point set matching problem. In contrast to previous annealing-based methods, we propose a quantum circuit-based framework whose parameters are optimised via descending the gradients w.r.t a kernel-based loss function. We formulate the shape matching problem into a distribution learning task; that is, to learn the distribution of the optimal transformation parameters. We show that this framework is able to find multiple optimal solutions for symmetric shapes and is more accurate, scalable and robust than the previous annealing-based method. Code, data and pre-trained weights are available at the project page: hrefhttps://hansen7.github.io/qKChttps://hansen7.github.io/qKC