# A Quantum Computational Approach to Correspondence Problems on Point Sets

arXiv: https://arxiv.org/abs/1912.12296 · HTML: https://mlsanity.com/paper/1912.12296/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2019.

## Built on by (most cited first, 23 of 23)

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- [Quantum Motion Segmentation](https://mlsanity.com/paper/2203.13185/) (2022)
- [Quantum Multi-Model Fitting](https://mlsanity.com/paper/2303.15444/) (2023)
- [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)
- [Matching Point Sets with Quantum Circuit Learning](https://mlsanity.com/paper/2102.06697/) (2021)
- [Quantum Visual Feature Encoding Revisited](https://mlsanity.com/paper/2405.19725/) (2024)
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- [Quantum Annealing for Single Image Super-Resolution](https://mlsanity.com/paper/2304.08924/) (2023)
- [3D-QAE: Fully Quantum Auto-Encoding of 3D Point Clouds](https://mlsanity.com/paper/2311.05604/) (2023)
- [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)
- [Qsco: A Quantum Scoring Module for Open-set Supervised Anomaly Detection](https://mlsanity.com/paper/2405.16368/) (2024)
- [Outlier-Robust Multi-Model Fitting on Quantum Annealers](https://mlsanity.com/paper/2504.13836/) (2025)
- [Quantum Multiple Rotation Averaging](https://mlsanity.com/paper/2602.10115/) (2026)
- [Fast Simultaneous Gravitational Alignment of Multiple Point Sets](https://mlsanity.com/paper/2106.11308/) (2021)
- [Quantum-Enhanced Similarity Measures for Polarimetric Materials Classification](https://mlsanity.com/paper/2606.07766/) (2026)

## Abstract (arXiv)

Modern adiabatic quantum computers (AQC) are already used to solve difficult combinatorial optimisation problems in various domains of science. Currently, only a few applications of AQC in computer vision have been demonstrated. We review AQC and derive a new algorithm for correspondence problems on point sets suitable for execution on AQC. Our algorithm has a subquadratic computational complexity of the state preparation. Examples of successful transformation estimation and point set alignment by simulated sampling are shown in the systematic experimental evaluation. Finally, we analyse the differences in the solutions and the corresponding energy values.