# Graph-Based Bayesian Optimization for Quantum Circuit Architecture Search with Uncertainty Calibrated Surrogates

arXiv: https://arxiv.org/abs/2512.09586 · HTML: https://mlsanity.com/paper/2512.09586/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 59 references that are in the map.
- First posted on arXiv 10 Dec 2025.

## Builds on (most cited first, 19 of 19)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Variational Quantum Circuits for Deep Reinforcement Learning](https://mlsanity.com/paper/1907.00397/) (2019)
- [QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits](https://mlsanity.com/paper/2107.10845/) (2021)
- [Quantum circuit architecture search for variational quantum algorithms](https://mlsanity.com/paper/2010.10217/) (2020)
- [Bayesian Optimization of Combinatorial Structures](https://mlsanity.com/paper/1806.08838/) (2018)
- [Quantum Architecture Search: A Survey](https://mlsanity.com/paper/2406.06210/) (2024)
- [Financial Fraud Detection: A Comparative Study of Quantum Machine Learning Models](https://mlsanity.com/paper/2308.05237/) (2023)
- [Enhancing Quantum Support Vector Machines through Variational Kernel Training](https://mlsanity.com/paper/2305.06063/) (2023)
- [Simulation of a Variational Quantum Perceptron using Grover's Algorithm](https://mlsanity.com/paper/2305.11040/) (2023)
- [Comparative Performance Analysis of Quantum Machine Learning Architectures for Credit Card Fraud Detection](https://mlsanity.com/paper/2412.19441/) (2024)
- [HQNN-FSP: A Hybrid Classical-Quantum Neural Network for Regression-Based Financial Stock Market Prediction](https://mlsanity.com/paper/2503.15403/) (2025)
- [Quantum State Tomography using Quantum Machine Learning](https://mlsanity.com/paper/2308.10327/) (2023)
- [Circuit Transformations for Quantum Architectures](https://mlsanity.com/paper/1902.09102/) (2019)
- [Incorporating Quantum Advantage in Quantum Circuit Generation through Genetic Programming](https://mlsanity.com/paper/2501.09682/) (2025)

## Built on by (most cited first, 3 of 3)

- [Hybrid Quantum-Classical Neural Architecture Search](https://mlsanity.com/paper/2605.18345/) (2026)
- [Q-PhotoNAS: Hybrid Quantum Neural Architecture Search Framework on Photonic Devices](https://mlsanity.com/paper/2605.22097/) (2026)
- [MDQEC-QAS: Meta-Decoding for Quantum Error Correction with Hardware-Aware VQC Search and Confidence-Gated Recovery](https://mlsanity.com/paper/2607.10707/) (2026)

## Abstract (arXiv)

Quantum circuit design is a key bottleneck for practical quantum machine learning on complex, real-world data. We present an automated framework that discovers and refines variational quantum circuits (VQCs) using graph-based Bayesian optimization with a graph neural network (GNN) surrogate. Circuits are represented as graphs and mutated and selected via an expected improvement acquisition function informed by surrogate uncertainty with Monte Carlo dropout. Candidate circuits are evaluated with a hybrid quantum-classical variational classifier on the next generation firewall telemetry and network internet of things (NF-ToN-IoT-V2) cybersecurity dataset, after feature selection and scaling for quantum embedding. We benchmark our pipeline against an MLP-based surrogate, random search, and greedy GNN selection. The GNN-guided optimizer consistently finds circuits with lower complexity and competitive or superior classification accuracy compared to all baselines. Robustness is assessed via a noise study across standard quantum noise channels, including amplitude damping, phase damping, thermal relaxation, depolarizing, and readout bit flip noise. The implementation is fully reproducible, with time benchmarking and export of best found circuits, providing a scalable and interpretable route to automated quantum circuit discovery.