# Quantum Robust Fitting

arXiv: https://arxiv.org/abs/2006.06986 · HTML: https://mlsanity.com/paper/2006.06986/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2020.

## Built on by (most cited first, 15 of 15)

- [Adiabatic Quantum Graph Matching with Permutation Matrix Constraints](https://mlsanity.com/paper/2107.04032/) (2021)
- [A Hybrid Quantum-Classical Algorithm for Robust Fitting](https://mlsanity.com/paper/2201.10110/) (2022)
- [Advances in Global Solvers for 3D Vision](https://mlsanity.com/paper/2602.14662/) (2026)
- [Quantum Multi-Model Fitting](https://mlsanity.com/paper/2303.15444/) (2023)
- [Q-FW: A Hybrid Classical-Quantum Frank-Wolfe for Quadratic Binary Optimization](https://mlsanity.com/paper/2203.12633/) (2022)
- [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)
- [Consensus Maximisation Using Influences of Monotone Boolean Functions](https://mlsanity.com/paper/2103.04200/) (2021)
- [QuAnt: Quantum Annealing with Learnt Couplings](https://mlsanity.com/paper/2210.08114/) (2022)
- [Probabilistic Sampling of Balanced K-Means using Adiabatic Quantum Computing](https://mlsanity.com/paper/2310.12153/) (2023)
- [Projected Stochastic Gradient Descent with Quantum Annealed Binary Gradients](https://mlsanity.com/paper/2310.15128/) (2023)
- [A Revisit of the Normalized Eight-Point Algorithm and A Self-Supervised Deep Solution](https://mlsanity.com/paper/2304.10771/) (2023)
- [Outlier-Robust Multi-Model Fitting on Quantum Annealers](https://mlsanity.com/paper/2504.13836/) (2025)
- [Quantum Levenberg--Marquardt Algorithm for optimization in Bundle Adjustment](https://mlsanity.com/paper/2203.02311/) (2022)
- [Event-driven Robust Fitting on Neuromorphic Hardware](https://mlsanity.com/paper/2508.09466/) (2025)

## Abstract (arXiv)

Many computer vision applications need to recover structure from imperfect measurements of the real world. The task is often solved by robustly fitting a geometric model onto noisy and outlier-contaminated data. However, recent theoretical analyses indicate that many commonly used formulations of robust fitting in computer vision are not amenable to tractable solution and approximation. In this paper, we explore the usage of quantum computers for robust fitting. To do so, we examine and establish the practical usefulness of a robust fitting formulation inspired by Fourier analysis of Boolean functions. We then investigate a quantum algorithm to solve the formulation and analyse the computational speed-up possible over the classical algorithm. Our work thus proposes one of the first quantum treatments of robust fitting for computer vision.