# Physics-Informed Bayesian Optimization of Variational Quantum Circuits

arXiv: https://arxiv.org/abs/2406.06150 · HTML: https://mlsanity.com/paper/2406.06150/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 64 references that are in the map.
- First posted on arXiv 10 Jun 2024.

## Builds on (most cited first, 5 of 5)

- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Predictive Entropy Search for Efficient Global Optimization of Black-box Functions](https://mlsanity.com/paper/1406.2541/) (2014)
- [Constrained Bayesian Optimization with Noisy Experiments](https://mlsanity.com/paper/1706.07094/) (2017)
- [Reinforcement learning for optimization of variational quantum circuit architectures](https://mlsanity.com/paper/2103.16089/) (2021)

## Built on by (most cited first, 7 of 7)

- [End-to-End Optimal Detector Design with Mutual Information Surrogates](https://mlsanity.com/paper/2503.14342/) (2025)
- [Enhancing Brain Source Reconstruction by Initializing 3D Neural Networks with Physical Inverse Solutions](https://mlsanity.com/paper/2411.00143/) (2024)
- [Machine-Learning-Enhanced Optimization of Noise-Resilient Variational Quantum Eigensolvers](https://mlsanity.com/paper/2501.17689/) (2025)
- [Replay-buffer engineering for noise-aware quantum circuit optimization](https://mlsanity.com/paper/2604.21863/) (2026)
- [Bayesian Parameter Shift Rule in Variational Quantum Eigensolvers](https://mlsanity.com/paper/2502.02625/) (2025)
- [Supervised Quantum Machine Learning: A Future Outlook from Qubits to Enterprise Applications](https://mlsanity.com/paper/2505.24765/) (2025)
- [Balancing Expressivity and Learnability in Quantum Kernel Bandit Optimization](https://mlsanity.com/paper/2607.01080/) (2026)

## Abstract (arXiv)

In this paper, we propose a novel and powerful method to harness Bayesian optimization for Variational Quantum Eigensolvers (VQEs) -- a hybrid quantum-classical protocol used to approximate the ground state of a quantum Hamiltonian. Specifically, we derive a VQE-kernel which incorporates important prior information about quantum circuits: the kernel feature map of the VQE-kernel exactly matches the known functional form of the VQE's objective function and thereby significantly reduces the posterior uncertainty. Moreover, we propose a novel acquisition function for Bayesian optimization called Expected Maximum Improvement over Confident Regions (EMICoRe) which can actively exploit the inductive bias of the VQE-kernel by treating regions with low predictive uncertainty as indirectly ``observed''. As a result, observations at as few as three points in the search domain are sufficient to determine the complete objective function along an entire one-dimensional subspace of the optimization landscape. Our numerical experiments demonstrate that our approach improves over state-of-the-art baselines.