# Adiabatic Quantum Linear Regression

arXiv: https://arxiv.org/abs/2008.02355 · HTML: https://mlsanity.com/paper/2008.02355/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Aug 2020.

## Built on by (most cited first, 17 of 17)

- [Quantum Annealing Formulation for Binary Neural Networks](https://mlsanity.com/paper/2107.02751/) (2021)
- [A Hybrid Quantum-Classical Neural Network Architecture for Binary Classification](https://mlsanity.com/paper/2201.01820/) (2022)
- [Quantum Hamiltonian Descent](https://mlsanity.com/paper/2303.01471/) (2023)
- [Quantum Langevin Dynamics for Optimization](https://mlsanity.com/paper/2311.15587/) (2023)
- [QuAnt: Quantum Annealing with Learnt Couplings](https://mlsanity.com/paper/2210.08114/) (2022)
- [A Novel Stochastic LSTM Model Inspired by Quantum Machine Learning](https://mlsanity.com/paper/2305.10212/) (2023)
- [Adiabatic Quantum Feature Selection for Sparse Linear Regression](https://mlsanity.com/paper/2106.02357/) (2021)
- [Quantum Speedup of Natural Gradient for Variational Bayes](https://mlsanity.com/paper/2106.05807/) (2021)
- [An Introduction to Quantum Computing for Statisticians and Data Scientists](https://mlsanity.com/paper/2112.06587/) (2021)
- [Adaptive Learning for Quantum Linear Regression](https://mlsanity.com/paper/2408.02833/) (2024)
- [Solving the Traveling Salesman Problem via Different Quantum Computing Architectures](https://mlsanity.com/paper/2502.17725/) (2025)
- [Outlier-Robust Multi-Model Fitting on Quantum Annealers](https://mlsanity.com/paper/2504.13836/) (2025)
- [Quantum-Assisted Support Vector Regression](https://mlsanity.com/paper/2111.09304/) (2021)
- [Efficient correlation-based discretization of continuous variables for annealing machines](https://mlsanity.com/paper/2301.07244/) (2023)
- [Adiabatic Quantum Support Vector Machines](https://mlsanity.com/paper/2401.12485/) (2024)
- [Hybrid Heuristic Algorithms for Adiabatic Quantum Machine Learning Models](https://mlsanity.com/paper/2407.21062/) (2024)
- [Non-Negative Matrix Factorization Using Non-Von Neumann Computers](https://mlsanity.com/paper/2512.00675/) (2025)

## Abstract (arXiv)

A major challenge in machine learning is the computational expense of training these models. Model training can be viewed as a form of optimization used to fit a machine learning model to a set of data, which can take up significant amount of time on classical computers. Adiabatic quantum computers have been shown to excel at solving optimization problems, and therefore, we believe, present a promising alternative to improve machine learning training times. In this paper, we present an adiabatic quantum computing approach for training a linear regression model. In order to do this, we formulate the regression problem as a quadratic unconstrained binary optimization (QUBO) problem. We analyze our quantum approach theoretically, test it on the D-Wave 2000Q adiabatic quantum computer and compare its performance to a classical approach that uses the Scikit-learn library in Python. Our analysis shows that the quantum approach attains up to 2.8x speedup over the classical approach on larger datasets, and performs at par with the classical approach on the regression error metric.