# Quantum Gaussian Process Regression for Bayesian Optimization

arXiv: https://arxiv.org/abs/2304.12923 · HTML: https://mlsanity.com/paper/2304.12923/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 56 references that are in the map.
- First posted on arXiv 25 Apr 2023.

## Builds on (most cited first, 20 of 20)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Quantum machine learning beyond kernel methods](https://mlsanity.com/paper/2110.13162/) (2021)
- [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021)
- [Training Quantum Embedding Kernels on Near-Term Quantum Computers](https://mlsanity.com/paper/2105.02276/) (2021)
- [Towards understanding the power of quantum kernels in the NISQ era](https://mlsanity.com/paper/2103.16774/) (2021)
- [Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning](https://mlsanity.com/paper/1910.06151/) (2019)
- [Quantum support vector machine for big data classification](https://mlsanity.com/paper/1307.0471/) (2013)
- [Quantum machine learning of large datasets using randomized measurements](https://mlsanity.com/paper/2108.01039/) (2021)
- [Quantum assisted Gaussian process regression](https://mlsanity.com/paper/1512.03929/) (2015)
- [An analytic comparison of regularization methods for Gaussian Processes](https://mlsanity.com/paper/1602.00853/) (2016)
- [Faster variational quantum algorithms with quantum kernel-based surrogate models](https://mlsanity.com/paper/2211.01134/) (2022)

## Built on by (most cited first, 9 of 9)

- [Reduction of finite sampling noise in quantum neural networks](https://mlsanity.com/paper/2306.01639/) (2023)
- [QuaCK-TSF: Quantum-Classical Kernelized Time Series Forecasting](https://mlsanity.com/paper/2408.12007/) (2024)
- [sQUlearn -- A Python Library for Quantum Machine Learning](https://mlsanity.com/paper/2311.08990/) (2023)
- [Old Rules in a New Game: Mapping Uncertainty Quantification to Quantum Machine Learning](https://mlsanity.com/paper/2507.14919/) (2025)
- [Bringing Quantum Algorithms to Automated Machine Learning: A Systematic Review of AutoML Frameworks Regarding Extensibility for QML Algorithms](https://mlsanity.com/paper/2310.04238/) (2023)
- [AutoQML: A Framework for Automated Quantum Machine Learning](https://mlsanity.com/paper/2502.21025/) (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)
- [Balancing Expressivity and Learnability in Quantum Kernel Bandit Optimization](https://mlsanity.com/paper/2607.01080/) (2026)

## Abstract (arXiv)

Gaussian process regression is a well-established Bayesian machine learning method. We propose a new approach to Gaussian process regression using quantum kernels based on parameterized quantum circuits. By employing a hardware-efficient feature map and careful regularization of the Gram matrix, we demonstrate that the variance information of the resulting quantum Gaussian process can be preserved. We also show that quantum Gaussian processes can be used as a surrogate model for Bayesian optimization, a task that critically relies on the variance of the surrogate model. To demonstrate the performance of this quantum Bayesian optimization algorithm, we apply it to the hyperparameter optimization of a machine learning model which performs regression on a real-world dataset. We benchmark the quantum Bayesian optimization against its classical counterpart and show that quantum version can match its performance.