Abstract Graph neural networks (GNNs) are effective for processing graph-structured data but face challenges with large graphs due to high memory requirements and inefficient sparse matrix operations on GPUs. Quantum computing offers a promising avenue to address these issues and inspires new algorithmic approaches. In particular, quantum GNNs (QGNNs) have been explored in recent literature. However, current quantum hardware limits the dimension of the data that can be effectively encoded. Existing approaches either simplify datasets manually or use artificial graph datasets. This work introduces the guided graph compression (GGC) framework, which uses a graph autoencoder to reduce both the number of nodes and the dimensionality of node features. The compression is guided to enhance the performance of a downstream classification task, which can be applied either with a quantum or a classical classifier. The framework is evaluated on the Jet Tagging task, a classification problem of fundamental importance in high energy physics that involves distinguishing particle jets initiated by quarks from those by gluons. We compare GGC to a model that uses the autoencoder as a preprocessing step and to a baseline classical GNN classifier. Our numerical results demonstrate that GGC outperforms both alternatives, while also facilitating the testing of novel QGNN ansatzes on realistic datasets.
Abstract Graph neural networks (GNNs) are effective for processing graph-structured data but face challenges with large graphs due to high memory requirements and inefficient sparse matrix operations on GPUs. Quantum computing offers a promising avenue to address these issues and inspires new algorithmic approaches. In particular, quantum GNNs (QGNNs) have been explored in recent literature. However, current quantum hardware limits the dimension of the data that can be effectively encoded. Existing approaches either simplify datasets manually or use artificial graph datasets. This work introduces the guided graph compression (GGC) framework, which uses a graph autoencoder to reduce both the number of nodes and the dimensionality of node features. The compression is guided to enhance the performance of a downstream classification task, which can be applied either with a quantum or a classical classifier. The framework is evaluated on the Jet Tagging task, a classification problem of fundamental importance in high energy physics that involves distinguishing particle jets initiated by quarks from those by gluons. We compare GGC to a model that uses the autoencoder as a preprocessing step and to a baseline classical GNN classifier. Our numerical results demonstrate that GGC outperforms both alternatives, while also facilitating the testing of novel QGNN ansatzes on realistic datasets.
Graph Neural Networks (GNNs) are effective for analyzing graph-structured data but face challenges with large graphs due to high memory requirements and inefficient sparse matrix operations on GPUs. Quantum Computing (QC) may be used to overcome these problems. For instance, Quantum Graph Neural Networks (QGNNs) have already been implemented in the literature. However, current quantum hardware limits the dimensionality of the datasets that can be encoded. For this reason, previous works simplify graph datasets manually or use small synthetic datasets. This work introduces the Guided Graph Compression (GGC) framework. It uses a graph autoencoder to reduce the size of graphs in terms of number of nodes and node feature dimensionality. The compression is guided towards enhancing the performance of a classification task by coupling the loss functions of the autoencoder and the classifier. The framework is applied to the Jet Tagging task that is relevant at CERN's LHC. It involves classifying jets as being originated from quarks or gluons. It is tested on three different training paradigms. First, a classical GNN is trained using the uncompressed data. Then, graph autoencoders are trained as a separate preprocessing step and used for classical and quantum classifiers. Lastly, the GGC framework is applied to both types of classifiers. Results show that the GGC framework outperforms the other two paradigms. Moreover, the classical and quantum classifiers achieve competitive performance in terms of ROC-AUC score.
Quantum computing has been a prominent research area for decades, inspiring transformative fields such as quantum simulation, quantum teleportation, and quantum machine learning (QML), which are undergoing rapid development. Within QML, hybrid classical-quantum algorithms like Quantum Neural Networks (QNNs) and Variational Quantum Classifiers (VQCs) have shown promise in leveraging quantum circuits and classical optimizers to classify classical data efficiently. Simultaneously, classical machine learning has made significant strides in graph classification, employing Graph Neural Networks (GNNs) to analyze systems ranging from large-scale structures like the Large Hadron Collider to molecular and biological systems like proteins and DNA. Combining the advancements in quantum computing and graph classification presents a unique opportunity to develop quantum algorithms capable of extracting features from graphs and performing their classification effectively. In this paper, we propose a novel quantum encoding framework for graph classification using VQCs. Unlike existing approaches such as PCA-VQC, which rely on dimensionality reduction techniques like Principal Component Analysis (PCA) and may lead to information loss, our method preserves the integrity of graph data. Furthermore, our encoding approach is optimized for Noise-Intermediate Scale Quantum (NISQ) devices, requiring a limited number of qubits while achieving comparable or superior classification performance to PCA-VQC. By constructing slightly more complex circuits tailored for graph encoding, we demonstrate that VQCs can effectively classify graphs within the constraints of current quantum hardware.
Graph Neural Networks (GNNs) achieve state-of-the-art performance on graph-structured data, but training and inference on large graphs are often bottlenecked by memory constraints and sparse linear-algebra workloads. Quantum computing offers an alternative set of primitives that may improve scalability for graph learning. Building on the quantum graph neural network (QGNN) framework of Liao \textit{et al.}, this work implements two representative architectures --- the Simplified Graph Convolution (SGC) and Linear Graph Convolution (LGC) models --- and evaluates them on open benchmark graph datasets and semi-supervised learning tasks using quantum simulation. We compare predictive performance and optimization behavior against classical baselines, showing that the quantum models achieve competitive performance with fewer parameters. Finally, we present a cost gradient analysis that identifies the tasks for which the models showcased are trainable. This is followed by a classical simulability study to find regimes in which the proposed circuits remain robust during training.
We present a quantum enhanced tagger to identify jets with large Lorentz boost at colliders. For the first time, a convolutional quantum graph neural network (QGNN) is designed to discriminate boosted jets arising from hadronic decays of the Z boson, against those produced from gluons with large momentum. The network receives data without any physics-driven refinement, relying solely on the dimensionality reduction. The reduction is performed using a convolutional autoencoder whose performance is improved in the presence of added noise. The latent data are put into a graph format and fed to the QGNN of ten qubits. The autoencoder and the QGNN are trained separately, and simultaneously, and the resulting performances are compared with a classic algorithm based on graph networks. The findings indicate a strong potential of quantum graph networks to reproduce the performance of classical methods.
Jets are central to the physics programs of both current and future colliders, from precision Standard Model measurements and searches for new physics at the Large Hadron Collider to studies of nucleon structure at the future Electron-Ion Collider. Motivated by these applications, we explore quantum machine learning for jet classification and present a permutation-invariant Quantum Graph Neural Network (QGNN) applied to particle-cloud representations of jets. We apply the model to two such discrimination tasks: quark vs. gluon and up vs. down quark flavor tagging, with the latter being, to our knowledge, the first application of a quantum model to this problem. In the ideal simulation, the QGNN performs competitively against the Particle Flow Network and traditional QCD observables. We further deploy scaled-down models to IBM and IonQ quantum processing units (QPUs), where we train and evaluate them, obtaining promising results. Finally, we perform an interpretability analysis to characterize the observables learned by the quantum model, relating them to generalized angularities for the quark-gluon study and to jet charge for the flavor study.
Quantum computing offers a promising avenue to reduce growing machine learning model complexity as required in large language models and simulation models for weather forecasts, financial forecasts, or engineering. Graph neural networks are a particular class of machine learning models that have garnered much attention for their ability to deal well with structured data. We investigate how to enhance existing GNNs and find through the inductive bias that quantum circuits are used best to encode node features. The proposed Quantum Feature Embeddings (QFEs) turn raw input features into quantum states, enabling non-linear and entangled representations. In particular, QFEs provide normalized, non-redundant weight matrices in an exponentially larger feature space and require much fewer qubits than fully quantum graph neural networks. On standard graph benchmark datasets, we showcase that for the same parameter count QFEs perform better than their classical counterpart, and are able to match the performance of an exponentially larger model. Finally, we study the potential benefit of using a hybrid quantum graph neural network over a classic alternative on a concrete use case, laser cutting. We find that the proposed model has the performance and thus the near-term potential to uplift these business applications.