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arXiv:2609.12980

Transpilation-Aware Runtime Prediction for Noisy Quantum Circuit Simulation

Davud Azizov, Javier Vela-Tambo, Tian Guo

quant-phcs.PFSubmitted Sep 11, 2026• Announced Sep 14, 2026• 0 citations
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Abstract

Predicting the runtime of noisy quantum circuit simulations is important for scheduling, resource allocation, and performance optimization. However, accurate prediction is challenging because backend-aware transpilation can substantially alter the original circuit structure, while the backend-derived noise model and simulator execution behavior can introduce additional runtime variation. We study the effectiveness of graph neural networks (GNNs) and conventional regression methods in predicting Qiskit Aer simulation runtime measured after transpilation. We construct a dataset from a benchmark pool of 1,402 unique circuits spanning 22 circuit families, two Qiskit fake-backend configurations, and four transpiler optimization levels. Specifically, we compare a source GNN using original circuit information, hybrid GNN combining source-level graph with post-transpilation features, and transpiled GNN using only transpiled circuit information, along with five regression models. In the overall-model setting, the transpiled GNN achieves the strongest performance among the graph-based representations at all four optimization levels, obtaining $R^2$ values of 0.974, 0.713, 0.745, and 0.605 for optimization levels 0 through 3, respectively. However, under backend-specific evaluation, the advantage of GNN decreases, with conventional regression models matching or outperforming the GNNs in several settings. These results indicate that post-transpilation information is useful, while the value of explicit graph modeling depends on the backend and optimization level.

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Predicting the runtime of noisy quantum circuit simulations is important for scheduling, resource allocation, and performance optimization. However, accurate prediction is challenging because backend-aware transpilation can substantially alter the original circuit structure, while the backend-derived noise model and simulator execution behavior can introduce additional runtime variation. We study the effectiveness of graph neural networks (GNNs) and conventional regression methods in predicting Qiskit Aer simulation runtime measured after transpilation. We construct a dataset from a benchmark pool of 1,402 unique circuits spanning 22 circuit families, two Qiskit fake-backend configurations, and four transpiler optimization levels. Specifically, we compare a source GNN using original circuit information, hybrid GNN combining source-level graph with post-transpilation features, and transpiled GNN using only transpiled circuit information, along with five regression models. In the overall-model setting, the transpiled GNN achieves the strongest performance among the graph-based representations at all four optimization levels, obtaining R2R^2R2 values of 0.974, 0.713, 0.745, and 0.605 for optimization levels 0 through 3, respectively. However, under backend-specific evaluation, the advantage of GNN decreases, with conventional regression models matching or outperforming the GNNs in several settings. These results indicate that post-transpilation information is useful, while the value of explicit graph modeling depends on the backend and optimization level.
The output prediction of quantum circuits is a formidably challenging task imperative in developing quantum devices. Motivated by the natural graph representation of quantum circuits, this paper proposes a Graph Neural Networks (GNNs)-based framework to predict the output expectation values of quantum circuits under noisy and noiseless conditions and compare the performance of different parameterized quantum circuits (PQCs). We construct datasets under noisy and noiseless conditions using a non-parameterized quantum gate set to predict circuit expectation values. The node feature vectors for GNNs are specifically designed to include noise information. In our simulations, we compare the prediction performance of GNNs in both noisy and noiseless conditions against Convolutional Neural Networks (CNNs) on the same dataset and their qubit scalability. GNNs demonstrate superior prediction accuracy across diverse conditions. Subsequently, we utilize the parameterized quantum gate set to construct noisy PQCs and compute the ground state energy of hydrogen molecules using the Variational Quantum Eigensolver (VQE). We propose two schemes: the Indirect Comparison scheme, which involves directly predicting the ground state energy and subsequently comparing circuit performances, and the Direct Comparison scheme, which directly predicts the relative performance of the two circuits. Simulation results indicate that the Direct Comparison scheme significantly outperforms the Indirect Comparison scheme by an average of 36.2% on the same dataset, providing a new and effective perspective for using GNNs to predict the overall properties of PQCs, specifically by focusing on their performance differences.
The growing variety of quantum hardware technologies, each with unique peculiarities such as connectivity and native gate sets, creates challenges when selecting the best platform for executing a specific quantum circuit. This selection process usually involves a brute-force approach: compiling the circuit on various devices and evaluating performance based on factors such as circuit depth and gate fidelity. However, this method is computationally expensive and does not scale well as the number of available quantum processors increases. In this work, we propose a Graph Neural Network (GNN)based predictor that automates hardware selection by analyzing the Directed Acyclic Graph (DAG) representation of a quantum circuit. Our study evaluates 498 quantum circuits (up to 27 qubits) from the MQT Bench dataset, compiled using Qiskit on four devices: three superconducting quantum processors (IBM-Kyiv, IBM-Brisbane, IBM-Sherbrooke) and one trappedion processor (IONQ-Forte). Performance is estimated using a metric that integrates circuit depth and gate fidelity, resulting in a dataset where 93 circuits are optimally compiled on the trappedion device, while the remaining circuits prefer superconducting platforms. By exploiting graph-based machine learning, our approach avoids extracting the circuit features for the model evaluation but directly embeds it as a graph, significantly accelerating the optimal target decision-making process and maintaining all the information. Experimental results prove94.4%\mathbf{9 4. 4 \%}94.4%accuracy and an85.5%\mathbf{8 5. 5 \%}85.5%F1 score for the minority class, effectively predicting the best compilation target. The developed code is publicly available on GitHub (https://github.com/antotu/GNN-Model-Quantum-Predictor).
Parameterized quantum circuits (PQCs) are fundamental to quantum machine learning (QML), quantum optimization, and variational quantum algorithms (VQAs). The expressibility of PQCs is a measure that determines their capability to harness the full potential of the quantum state space. It is thus a crucial guidepost to know when selecting a particular PQC ansatz. However, the existing technique for expressibility computation through statistical estimation requires a large number of samples, which poses significant challenges due to time and computational resource constraints. This paper introduces a novel approach for expressibility estimation of PQCs using Graph Neural Networks (GNNs). We demonstrate the predictive power of our GNN model with a dataset consisting of 25,000 samples from the noiseless IBM QASM Simulator and 12,000 samples from three distinct noisy quantum backends. The model accurately estimates expressibility, with root mean square errors (RMSE) of 0.05 and 0.06 for the noiseless and noisy backends, respectively. We compare our model's predictions with reference circuits from Sim et al. and IBM Qiskit's hardware-efficient ansatz sets to further evaluate our model's performance. Our experimental evaluation in noiseless and noisy scenarios reveals a close alignment with ground truth expressibility values, highlighting the model's efficacy. Moreover, our model exhibits promising extrapolation capabilities, predicting expressibility values with low RMSE for out-of-range qubit circuits trained solely on only up to 5-qubit circuit sets. This work thus provides a reliable means of efficiently evaluating the expressibility of diverse PQCs on noiseless simulators and hardware.
Quantum software engineering is an emerging research field focusing on efficiently embedding the quantum programming paradigm into existing software ecosystems. A key aspect of this field is the realization of quantum algorithms using gate-based programming and the subsequent low-level optimization of the resulting quantum circuits, a process that is commonly performed by so-called transpilation pipelines. One significant challenge in these pipelines is determining which optimizations to apply to a given circuit. This decision is usually based on fixed default configurations that are uniformly applied to all circuits, frequently resulting in missed opportunities for more aggressive circuit optimization. In this work, we tackle this challenge by applying autotuning with supervised machine learning to develop an automated method for selection of transpiler passes. To train our machine-learning models, we employ feature-model based sampling to generate a representative dataset that examines how different combinations of Qiskit transpiler passes perform across thousands of circuits drawn from the state-of-the-art benchmarking suite MQT Bench. Using these data, we build a predictive model extension for the Qiskit transpilation pipeline that uses a machine learning model to automatically select combinations of transpiler passes aiming to achieve a maximum reduction in two-qubit gates. Our empirical evaluation shows that the combinations selected by our model are never outperformed by Qiskit's optimization levels, achieve on average an additional 19.1%\%% - 32.4%\%% reduction in two-qubit gates, and for some circuits finds reductions of up to 95.8%95.8\%95.8% in cases where Qiskit achieves no reduction at all.
Modern High-Performance Computing (HPC) infrastructures are increasingly integrating multiple Quantum Processing Units (QPUs) of different types alongside classical resources. Unlike traditional accelerator scheduling, quantum device selection affects not only performance but also the quality of the computed result because current quantum hardware exhibits device-dependent noise characteristics. This makes efficient and fidelity-based device selection a key challenge in multi-QPU environments. In this work, we propose a Graph Neural Network (GNN) model that exploits the structural representation of quantum circuits to predict their execution fidelity across different QPUs. By operating on uncompiled circuits, the approach supports earlystage device selection and enables making informed scheduling decisions. We evaluate the model on a diverse set of benchmark circuits compiled for superconducting and trapped-ion devices. The results show that the proposed approach outperforms existing baseline models, achieving 30% Mean Squared Error (MSE) and 20% Mean Absolute Error (MAE) reduction, and provides an effective basis for fidelity-based scheduling in heterogeneous HPC-quantum systems.
This article proposes a Graph Neural Network (GNN) approach to estimate nonstabilizerness in quantum circuits, measured by the stabilizer Rényi entropy (SRE). Nonstabilizerness is a fundamental resource for quantum advantage, and efficient SRE estimations are highly beneficial in practical applications. We address the nonstabilizerness estimation problem through three supervised learning formulations starting from easier classification tasks to the more challenging regression task. Experimental results show that the proposed GNN manages to capture meaningful features from the graph-based circuit representation, resulting in robust generalization performances achieved across diverse scenarios. In classification tasks, the GNN is trained on product states and generalizes on circuits evolved under Clifford operations, entangled states, and circuits with higher number of qubits. In the regression task, the GNN significantly improves the SRE estimation on out-of-distribution circuits with higher number of qubits and gate counts compared to previous work, for both unstructured random quantum circuits and structured circuits derived from the transverse-field Ising model. Moreover, the graph representation of quantum circuits naturally integrates hardware-specific information. Simulations on noisy quantum hardware highlight the potential of the proposed GNN to predict the SRE measured on quantum devices.