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

TL;DR

This paper introduces a graph-based Bayesian optimization framework utilizing GNN surrogates to automate the discovery and refinement of variational quantum circuits for quantum machine learning, demonstrating superior performance and robustness.

Contribution

It presents a novel graph neural network-based Bayesian optimization method for quantum circuit architecture search, improving automation and efficiency in quantum machine learning.

Findings

GNN-guided optimizer finds lower complexity circuits with competitive accuracy.

The approach outperforms MLP-based surrogate, random search, and greedy GNN selection.

Robustness verified across various quantum noise channels.

Abstract

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.