# Quantum-Assisted Support Vector Regression

arXiv: https://arxiv.org/abs/2111.09304 · HTML: https://mlsanity.com/paper/2111.09304/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 70 references that are in the map.
- First posted on arXiv 17 Nov 2021.

## Builds on (most cited first, 10 of 10)

- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [HyperFace: A Deep Multi-task Learning Framework for Face Detection, Landmark Localization, Pose Estimation, and Gender Recognition](https://mlsanity.com/paper/1603.01249/) (2016)
- [Facial Landmark Detection: a Literature Survey](https://mlsanity.com/paper/1805.05563/) (2018)
- [Support vector machines on the D-Wave quantum annealer](https://mlsanity.com/paper/1906.06283/) (2019)
- [A practical heuristic for finding graph minors](https://mlsanity.com/paper/1406.2741/) (2014)
- [Fast Facial Landmark Detection and Applications: A Survey](https://mlsanity.com/paper/2101.10808/) (2021)
- [Adiabatic Quantum Linear Regression](https://mlsanity.com/paper/2008.02355/) (2020)
- [Facial Feature Point Detection: A Comprehensive Survey](https://mlsanity.com/paper/1410.1037/) (2014)
- [A regression algorithm for accelerated lattice QCD that exploits sparse inference on the D-Wave quantum annealer](https://mlsanity.com/paper/1911.06267/) (2019)
- [Solving large Minimum Vertex Cover problems on a quantum annealer](https://mlsanity.com/paper/1904.00051/) (2019)

## Abstract (arXiv)

A popular machine-learning model for regression tasks, including stock-market prediction, weather forecasting and real-estate pricing, is the classical support vector regression (SVR). However, a practically realisable quantum SVR remains to be formulated. We devise annealing-based algorithms, namely simulated and quantum-classical hybrid, for training two SVR models and compare their empirical performances against the SVR implementation of Python's scikit-learn package for facial-landmark detection (FLD), a particular use case for SVR. Our method is to derive a quadratic-unconstrained-binary formulation for the optimisation problem used for training a SVR model and solve this problem using annealing. Using D-Wave's hybrid solver, we construct a quantum-assisted SVR model, thereby demonstrating a slight advantage over classical models regarding FLD accuracy. Furthermore, we observe that annealing-based SVR models predict landmarks with lower variances compared to the SVR models trained by gradient-based methods. Our work is a proof-of-concept example for applying quantum-assisted SVR to a supervised-learning task with a small training dataset.