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International Conference on AI-ML Systems (AIMLSystems)

A Transformer-GNN Framework for Learning Full Output Distributions of Quantum Circuits

Tourad Baba, Tianxiang Lu

Published Oct 8, 2025• 0 citations
Publisher

Abstract

Comprehensive knowledge of a quantum circuit's full output distribution-beyond mere summary statistics-is crucial for benchmarking and hybrid algorithm development in the noisy intermediate-scale quantum (NISQ) computing era. However, existing prediction methods typically focus on scalar observables. We introduce an attention-enhanced Graph Neural Network (GNN) that learns entire output distributions directly from directed acyclic graph (DAG) representations of parameterized quantum circuits, incorporating structural, parametric, and noise-aware features. Formulated as supervised multi-output regression over the exponentially large$(2^{n})$probability space, our model consistently outperforms a capacity-matched convolutional neural network (CNN) baseline on 2 to 5 qubit circuits, achieving near-perfect fidelity (0.993) and reducing KL divergence by an order of magnitude. Evaluations on unseen 6-qubit circuits under zero-shot and few-shot conditions reveal expected performance degradation due to the exponential scaling, highlighting the importance of size-specific training. These findings demonstrate the inductive advantages of attention-based GNNs as a structureaware approach for distribution-level prediction in NISQ computing.

DOI
10.1109/aimlsystems67835.2025.11331193

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Comprehensive knowledge of a quantum circuit's full output distribution-beyond mere summary statistics-is crucial for benchmarking and hybrid algorithm development in the noisy intermediate-scale quantum (NISQ) computing era. However, existing prediction methods typically focus on scalar observables. We introduce an attention-enhanced Graph Neural Network (GNN) that learns entire output distributions directly from directed acyclic graph (DAG) representations of parameterized quantum circuits, incorporating structural, parametric, and noise-aware features. Formulated as supervised multi-output regression over the exponentially large(2n)(2^{n})(2n)probability space, our model consistently outperforms a capacity-matched convolutional neural network (CNN) baseline on 2 to 5 qubit circuits, achieving near-perfect fidelity (0.993) and reducing KL divergence by an order of magnitude. Evaluations on unseen 6-qubit circuits under zero-shot and few-shot conditions reveal expected performance degradation due to the exponential scaling, highlighting the importance of size-specific training. These findings demonstrate the inductive advantages of attention-based GNNs as a structureaware approach for distribution-level prediction in NISQ computing.
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.
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The current advancement in quantum computers has been focusing on increasing the number of qubits and enhancing their fidelity. However, the available quantum devices, known as intermediate scale quantum (NISQ) computers, still suffer from different sources of noise that impact their reliability. Thus, practical noise modeling is of great importance in the development of quantum error mitigation approaches. In this article, we propose a machine learning (ML)-based scheme to predict the output fidelity of the quantum circuit executed on NISQ devices. We show the benefit of using graph neural network (GNN)-based models compared to traditional ML-based models in capturing the quantum circuit structure in addition to its gates’ features, which enable characterizing unpredicted quantum circuit errors. We use different metrics to measure the fidelity of the quantum circuit output. Our experimental results using different quantum algorithms executed on IBM Q Guadalupe quantum computer show the high prediction accuracy of our ML reliability models. Our results also show that our models can guide the single-qubit gate rescheduling to improve the output fidelity of the quantum circuit without the need for prior execution of dedicated calibration circuits.
Graph neural networks (GNNs) are a powerful framework for learning representations from graph-structured data, but their direct implementation on near-term quantum hardware remains challenging due to circuit depth, multi-qubit interactions, and qubit scalability constraints. In this work, we introduce a hybrid quantum graph learning architecture designed explicitly for unsupervised learning in the noisy intermediate-scale quantum (NISQ) regime. Our approach combines a variational quantum feature extraction layer with an edge-local and qubit-efficient quantum message-passing mechanism inspired by the Quantum Alternating Operator Ansatz (QAOA) framework. The message-passing operation is decomposed into pairwise interactions along graph edges using standard single- and two-qubit gates. For a graph with NNN nodes and nnn-qubit feature registers, this reduces the number of qubits required at one time from NnNnNn to at most 2n2n2n. We train the model using the Deep Graph Infomax objective to perform unsupervised node representation learning. The external class labels are not used during graph construction or training and are used only to evaluate the learned embeddings. Experiments on the Cora citation network and the Phase 3 release of the 1000 Genomes Project show that the quantum edge interaction contributes to the quality of the learned node representations.
Abstract Predicting the output of quantum circuits is a hard computational task that plays a pivotal role in the development of universal quantum computers. Here we investigate the supervised learning of output expectation values of random quantum circuits. Deep convolutional neural networks (CNNs) are trained to predict single-qubit and two-qubit expectation values using databases of classically simulated circuits. These circuits are built using either a universal gate set or a continuous set of rotations plus an entangling gate, and they are represented via properly designed encodings of these gates. The prediction accuracy for previously unseen circuits is analyzed, also making comparisons with small-scale quantum computers available from the free IBM Quantum program. The CNNs often outperform these quantum devices, depending on the circuit depth, on the network depth, and on the training set size. Notably, our CNNs are designed to be scalable. This allows us exploiting transfer learning and performing extrapolations to circuits larger than those included in the training set. These CNNs also demonstrate remarkable resilience against noise, namely, they remain accurate even when trained on (simulated) expectation values averaged over very few measurements.
We introduce Quantum Graph Attention Networks (QGATs) as trainable quantum encoders for inductive learning on graphs, extending the Quantum Graph Neural Networks (QGNN) framework. QGATs leverage parameterized quantum circuits to encode node features and neighborhood structures, with quantum attention mechanisms modulating the contribution of each neighbor via dynamically learned unitaries. This allows for expressive, locality-aware quantum representations that can generalize across unseen graph instances. We evaluate our approach on the QM9 dataset, targeting the prediction of various chemical properties. Our experiments compare classical and quantum graph neural networks-with and without attention layers-demonstrating that attention consistently improves performance in both paradigms. Notably, we observe that quantum attention yields increasing benefits as graph size grows, with QGATs significantly outperforming their non-attentive quantum counterparts on larger molecular graphs. Furthermore, for smaller graphs, QGATs achieve predictive accuracy comparable to classical GAT models, highlighting their viability as expressive quantum encoders. These results show the potential of quantum attention mechanisms to enhance the inductive capacity of QGNN in chemistry and beyond.