Quantum Machine Learning
Graph-Based Bayesian Optimization for Quantum Circuit Architecture Search with Uncertainty Calibrated Surrogates
Prashant Kumar Choudhary, Muhammad Shafique, Nouhaila Innan, Rajeev Singh
December 10, 2025
Quantum circuit design is a key bottleneck for practical quantum machine learning on complex, real-world data. This paper presents 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, 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.
Executive Impact & Key Metrics
This paper introduces a novel graph-based Bayesian Optimization (BO) pipeline for automated quantum circuit architecture search, specifically targeting hybrid quantum-classical classification tasks. By leveraging Graph Neural Networks (GNNs) as structure-aware surrogates with Monte Carlo dropout for uncertainty calibration, the framework effectively navigates the complex, high-dimensional search space of Variational Quantum Circuits (VQCs). The approach demonstrates superior performance in discovering robust and efficient quantum circuits with lower complexity and competitive or superior classification accuracy compared to baselines, even under various quantum noise models. The methodology provides a scalable and interpretable route to automated quantum circuit discovery for near-term quantum devices.
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Peak Accuracy (12Q)
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Noise Robustness Gain
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BO Iterations
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Methodology Overview
Key Results & Efficiency
Noise Robustness Analysis
Our proposed pipeline performs hardware-realistic circuit discovery end-to-end. It begins with data preparation and a fixed VQC model, then configures noise and decoherence models. Graph encoding and GNN surrogates with MC-dropout uncertainty are used, alongside feature-based MLP scores and a cost- and noise-aware EI acquisition. The hardware-constrained search space and mutation operators generate candidate circuits, which are then evaluated and used to update the surrogate.
The GNN-guided optimizer consistently finds circuits with lower complexity and competitive or superior classification accuracy compared to all baselines. Across 8, 10, and 12 qubits, BO+VQC+GNN and BO+VQC+MLP show comparable end-to-end runtimes, indicating that wall-clock cost is dominated by candidate training/evaluation of the hybrid VQC rather than the surrogate itself. The GNN-based pipeline scales smoothly as qubit count increases.
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 learned circuits retain strong performance and, in several cases, even benefit from modest stochasticity. This indicates the pipeline's ability to identify cost-optimal architectures that sustain strong accuracy under practical compilation and coherence constraints.
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Average Validation Accuracy (8Q)
Quantum Circuit Discovery Process
Data Prep & Feature Engineering
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Circuit Generation & Encoding
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GNN Surrogate Scoring
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Cost & Noise-Aware Acquisition
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VQC Evaluation
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Update Surrogate & Retrain
| Method | Validation Accuracy (%) | Test Accuracy (%) | Key Advantages |
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| BO + VQC + GNN (Our Method) | 92.32% | 94.25% |
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| BO + VQC + MLP (No Graph) | 86.25% | 92.95% |
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| Greedy GNN | 80.65% | 83.35% |
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| Random Search | 80.15% | 83.55% |
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Noise Robustness in Action
Our learned circuits demonstrate strong performance even under various noise scenarios. For instance, with Amplitude Damping, the test accuracy improved to 86.70%, a +3.45% gain relative to the noise-free baseline. Thermal relaxation also showed a +3.30% gain. This indicates the pipeline's ability to find architectures that are inherently robust to common quantum noise, crucial for NISQ devices. Depolarizing noise was the most detrimental, causing a modest -3.24% drop, but overall resilience remained high.
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Amplitude Damping Accuracy
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BO Loop Wall Time (8Q, in s)
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