# Robust Fitting on a Gate Quantum Computer

arXiv: https://arxiv.org/abs/2409.02006 · HTML: https://mlsanity.com/paper/2409.02006/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 68 references that are in the map.
- First posted on arXiv 3 Sep 2024.

## Builds on (most cited first, 30 of 32)

- [DSAC - Differentiable RANSAC for Camera Localization](https://mlsanity.com/paper/1611.05705/) (2016)
- [GDRNPP: A Geometry-guided and Fully Learning-based Object Pose Estimator](https://mlsanity.com/paper/2102.12145/) (2021)
- [Experimental Quantum Generative Adversarial Networks for Image Generation](https://mlsanity.com/paper/2010.06201/) (2020)
- [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)
- [Robust Fitting in Computer Vision: Easy or Hard?](https://mlsanity.com/paper/1802.06464/) (2018)
- [Nonnegative/binary matrix factorization with a D-Wave quantum annealer](https://mlsanity.com/paper/1704.01605/) (2017)
- [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)
- [Certifiably Optimal Outlier-Robust Geometric Perception: Semidefinite Relaxations and Scalable Global Optimization](https://mlsanity.com/paper/2109.03349/) (2021)
- [Adiabatic Quantum Graph Matching with Permutation Matrix Constraints](https://mlsanity.com/paper/2107.04032/) (2021)
- [Quantum-soft QUBO Suppression for Accurate Object Detection](https://mlsanity.com/paper/2007.13992/) (2020)
- [An Evaluation of Feature Matchers for Fundamental Matrix Estimation](https://mlsanity.com/paper/1908.09474/) (2019)
- [Quantum Motion Segmentation](https://mlsanity.com/paper/2203.13185/) (2022)
- [Semiconductor Defect Detection by Hybrid Classical-Quantum Deep Learning](https://mlsanity.com/paper/2208.03514/) (2022)
- [MosaiQ: Quantum Generative Adversarial Networks for Image Generation on NISQ Computers](https://mlsanity.com/paper/2308.11096/) (2023)
- [Image classification using quantum inference on the D-Wave 2X](https://mlsanity.com/paper/1905.13215/) (2019)
- [Quantum Robust Fitting](https://mlsanity.com/paper/2006.06986/) (2020)
- [Accelerating Globally Optimal Consensus Maximization in Geometric Vision](https://mlsanity.com/paper/2304.05156/) (2023)
- [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)
- [Outlier-Robust Spatial Perception: Hardness, General-Purpose Algorithms, and Guarantees](https://mlsanity.com/paper/1903.11683/) (2019)
- [Matching Point Sets with Quantum Circuit Learning](https://mlsanity.com/paper/2102.06697/) (2021)
- [Deterministic consensus maximization with biconvex programming](https://mlsanity.com/paper/1807.09436/) (2018)
- [Q-FW: A Hybrid Classical-Quantum Frank-Wolfe for Quadratic Binary Optimization](https://mlsanity.com/paper/2203.12633/) (2022)
- [QuACK: Accelerating Gradient-Based Quantum Optimization with Koopman Operator Learning](https://mlsanity.com/paper/2211.01365/) (2022)
- [A regression algorithm for accelerated lattice QCD that exploits sparse inference on the D-Wave quantum annealer](https://mlsanity.com/paper/1911.06267/) (2019)
- [Quantum Normalizing Flows for Anomaly Detection](https://mlsanity.com/paper/2402.02866/) (2024)
- [Unsupervised Learning for Robust Fitting:A Reinforcement Learning Approach](https://mlsanity.com/paper/2103.03501/) (2021)
- [Consensus Maximisation Using Influences of Monotone Boolean Functions](https://mlsanity.com/paper/2103.04200/) (2021)

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

- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [Quantum-enhanced Computer Vision: Going Beyond Classical Algorithms](https://mlsanity.com/paper/2510.07317/) (2025)
- [Outlier-Robust Multi-Model Fitting on Quantum Annealers](https://mlsanity.com/paper/2504.13836/) (2025)
- [Event-driven Robust Fitting on Neuromorphic Hardware](https://mlsanity.com/paper/2508.09466/) (2025)
- [Robust PnP on a Neuromorphic Processor for Object Pose Estimation](https://mlsanity.com/paper/2607.16834/) (2026)

## Abstract (arXiv)

Gate quantum computers generate significant interest due to their potential to solve certain difficult problems such as prime factorization in polynomial time. Computer vision researchers have long been attracted to the power of quantum computers. Robust fitting, which is fundamentally important to many computer vision pipelines, has recently been shown to be amenable to gate quantum computing. The previous proposed solution was to compute Boolean influence as a measure of outlyingness using the Bernstein-Vazirani quantum circuit. However, the method assumed a quantum implementation of an ℓ_∞ feasibility test, which has not been demonstrated. In this paper, we take a big stride towards quantum robust fitting: we propose a quantum circuit to solve the ℓ_∞ feasibility test in the 1D case, which allows to demonstrate for the first time quantum robust fitting on a real gate quantum computer, the IonQ Aria. We also show how 1D Boolean influences can be accumulated to compute Boolean influences for higher-dimensional non-linear models, which we experimentally validate on real benchmark datasets.