# Quantum assisted Gaussian process regression

arXiv: https://arxiv.org/abs/1512.03929 · HTML: https://mlsanity.com/paper/1512.03929/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2015.

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

- [Towards provably efficient quantum algorithms for large-scale machine-learning models](https://mlsanity.com/paper/2303.03428/) (2023)
- [A survey on the complexity of learning quantum states](https://mlsanity.com/paper/2305.20069/) (2023)
- [Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applications](https://mlsanity.com/paper/2307.00908/) (2023)
- [The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning](https://mlsanity.com/paper/2103.04913/) (2021)
- [Quantum Gaussian Process Regression for Bayesian Optimization](https://mlsanity.com/paper/2304.12923/) (2023)
- [Advantage of Quantum Machine Learning from General Computational Advantages](https://mlsanity.com/paper/2312.03057/) (2023)
- [Training Hybrid Classical-Quantum Classifiers via Stochastic Variational Optimization](https://mlsanity.com/paper/2201.08629/) (2022)
- [sQUlearn -- A Python Library for Quantum Machine Learning](https://mlsanity.com/paper/2311.08990/) (2023)
- [Quantum advantage for learning shallow neural networks with natural data distributions](https://mlsanity.com/paper/2503.20879/) (2025)
- [Quantum Machine Learning For Classical Data](https://mlsanity.com/paper/2105.03684/) (2021)
- [Assessing Quantum Advantage for Gaussian Process Regression](https://mlsanity.com/paper/2505.22502/) (2025)
- [Old Rules in a New Game: Mapping Uncertainty Quantification to Quantum Machine Learning](https://mlsanity.com/paper/2507.14919/) (2025)
- [Non-variational supervised quantum kernel methods: a review](https://mlsanity.com/paper/2604.07896/) (2026)
- [Quantum-assisted Gaussian process regression using random Fourier features](https://mlsanity.com/paper/2507.22629/) (2025)
- [Distributed Quantum Gaussian Processes for Multi-Agent Systems](https://mlsanity.com/paper/2602.15006/) (2026)
- [Spectral Anatomy of Quantum Gaussian Process Kernels](https://mlsanity.com/paper/2605.30952/) (2026)
- [A Quantum-Inspired Dequantization Method for Diagonally Weighted Matrix Functions: Application to Learning with Optimized Random Features](https://mlsanity.com/paper/2609.10729/) (2026)

## Abstract (arXiv)

Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires O(n3) logic gates. We show that the quantum linear systems algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] can be applied to Gaussian process regression (GPR), leading to an exponential reduction in computation time in some instances. We show that even in some cases not ideally suited to the quantum linear systems algorithm, a polynomial increase in efficiency still occurs.