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

Source: arXiv - 2512.09586v1

Overview

Designing variational quantum circuits (VQCs) that are both expressive and hardware‑friendly is one of the biggest hurdles for bringing quantum machine learning (QML) to real‑world problems. The paper introduces a graph‑based Bayesian optimization (BO) framework that automatically discovers and refines VQC architectures using a graph neural network (GNN) surrogate model. By treating circuits as graphs and leveraging uncertainty‑aware BO, the authors achieve competitive (often better) classification performance on a cybersecurity dataset while keeping circuit depth and gate count low.

Key Contributions

• Graph representation of VQCs: Encodes qubits, gates, and connectivity as a directed graph, enabling systematic mutations (add/remove gates, rewire connections).
• Uncertainty‑calibrated GNN surrogate: Trains a GNN to predict circuit performance and quantifies prediction uncertainty via Monte‑Carlo dropout, feeding this into the BO acquisition function.
• Expected Improvement (EI) acquisition with uncertainty: Guides the search toward promising yet under‑explored circuit designs, balancing exploitation and exploration.
• Comprehensive benchmark: Compared against an MLP surrogate, random search, and a greedy GNN selector on the NF‑ToN‑IoT‑V2 cybersecurity dataset, showing lower circuit complexity and equal or higher accuracy.
• Robustness analysis: Evaluated discovered circuits under a suite of realistic quantum noise channels (amplitude/phase damping, thermal relaxation, depolarizing, readout errors).
• Open‑source, reproducible pipeline: Includes time‑benchmarking, export of best circuits, and scripts for data preprocessing, quantum embedding, and training.

Methodology

1. Data preparation – The raw NF‑ToN‑IoT‑V2 telemetry is filtered, feature‑selected, and scaled to fit the limited qubit count of near‑term devices. Classical features are encoded into quantum states using amplitude or angle embedding.
2. Circuit graph construction – Each VQC is turned into a graph where nodes represent quantum gates (e.g., Rx, CNOT) and edges capture the temporal order and qubit wiring.
3. Surrogate modeling – A GNN ingests these graphs and learns to predict the validation accuracy of the corresponding hybrid quantum‑classical classifier. Monte‑Carlo dropout is applied at inference time to produce a mean prediction and a variance (uncertainty).
4. Bayesian optimization loop
   • Acquisition: Expected Improvement (EI) is computed using both the surrogate mean and its uncertainty.
   • Mutation: The top‑scoring circuits are mutated (gate insertion, deletion, rewiring) to generate a candidate pool.
   • Evaluation: Candidates are run on a quantum simulator (or real hardware) to obtain true accuracy, which is fed back to retrain the GNN.
5. Stopping criteria – The loop stops after a fixed budget of circuit evaluations or when EI falls below a threshold.

The whole pipeline is modular, allowing developers to swap out the surrogate (e.g., replace the GNN with a transformer) or the acquisition function without rewriting the core search logic.

Results & Findings

• The GNN‑BO consistently discovers shallower circuits with fewer entangling gates, which translates to lower error rates on noisy hardware.
• Accuracy remains on par or better than baselines, demonstrating that the surrogate’s uncertainty guidance does not sacrifice performance.
• Noise robustness tests show ≤ 2 % degradation under realistic depolarizing noise (p = 0.01), whereas deeper circuits from random search lose > 5 % accuracy.

Practical Implications

• Accelerated QML prototyping: Developers can plug in their own datasets and let the BO engine suggest hardware‑ready VQCs, cutting weeks of manual architecture tuning.
• Hardware‑aware design: By penalizing depth and two‑qubit gates, the framework naturally yields circuits that fit within coherence times of current superconducting or trapped‑ion devices.
• Cost‑effective experimentation: The surrogate dramatically reduces the number of expensive quantum‑hardware runs needed—only a few dozen full evaluations are enough to converge.
• Transferable to other domains: The graph‑based representation is agnostic to the task; it can be reused for quantum chemistry ansätze, reinforcement‑learning policies, or any variational algorithm.
• Open‑source tooling: The provided codebase can be integrated into existing quantum SDKs (Qiskit, Pennylane, Cirq), enabling seamless CI pipelines that automatically evolve circuit architectures as hardware improves.

Limitations & Future Work

• Scalability to larger qubit counts: The current experiments are limited to ≤ 8 qubits due to simulator constraints; extending the surrogate to handle > 20 qubits may require hierarchical graph encodings or sparsity‑aware GNNs.
• Surrogate training cost: Although cheaper than full quantum evaluations, training the GNN still needs a modest GPU budget and a curated set of labeled circuits.
• Dataset specificity: The study focuses on a cybersecurity telemetry dataset; performance on image or natural‑language tasks remains to be validated.
• Noise model fidelity: Simulated noise channels approximate real hardware but cannot capture all cross‑talk and calibration drift; future work will involve closed‑loop optimization on actual quantum processors.

Overall, the paper delivers a compelling, developer‑friendly recipe for automated quantum circuit discovery, bridging the gap between theoretical QML research and production‑grade quantum applications.

Authors

• Prashant Kumar Choudhary
• Nouhaila Innan
• Muhammad Shafique
• Rajeev Singh

Paper Information

• arXiv ID: 2512.09586v1
• Categories: quant-ph, cs.AI, cs.LG, cs.NE, cs.NI
• Published: December 10, 2025
• PDF: Download PDF