Spinfoam theories propose a well-defined path-integral formulation for quantum gravity, and it is hoped that they will provide the dynamics of loop quantum gravity. However, it is computationally hard to calculate spinfoam amplitudes. The well-studied Euclidean Barrett–Crane model provides an excellent setting for testing analytical and numerical tools to probe spinfoam models. We explore a data-driven approach to accelerating spinfoam computations by showing that the vertex amplitude is an object that can be learned from data using deep learning. We divide the learning process into a classification and a regression task: Two networks are independently engineered to decide whether the amplitude is zero or not and to predict the precise numerical value, respectively. The trained networks are tested with several accuracy measures. The classifier in particular demonstrates robust generalisation far outside the training domain, while the regressor demonstrates high predictive accuracy in the domain it is trained on. We discuss limitations, possible improvements, and implications for future work.
Spinfoam theories propose a well-defined path-integral formulation for quantum gravity, and it is hoped that they will provide the dynamics of loop quantum gravity. However, it is computationally hard to calculate spinfoam amplitudes. The well-studied Euclidean Barrett–Crane model provides an excellent setting for testing analytical and numerical tools to probe spinfoam models. We explore a data-driven approach to accelerating spinfoam computations by showing that the vertex amplitude is an object that can be learned from data using deep learning. We divide the learning process into a classification and a regression task: Two networks are independently engineered to decide whether the amplitude is zero or not and to predict the precise numerical value, respectively. The trained networks are tested with several accuracy measures. The classifier in particular demonstrates robust generalisation far outside the training domain, while the regressor demonstrates high predictive accuracy in the domain it is trained on. We discuss limitations, possible improvements, and implications for future work.
Abstract Quantum simulation has shown its irreplaceable role in many fields, where it is difficult for classical computers to do much. On a four-qubit Nuclear Magnetic Resonance (NMR) quantum simulator, we experimentally simulate the spin-network states by simulating quantum spacetime tetrahedra. The fidelities of our experimentally prepared quantum tetrahedra are all above 95%. We then use the quantum tetradedra prepared by the Nuclear Magnetic Resonance to simulate a spinfoam vertex amplitude, which displays the local dynamics of quantum spacetime. By measuring the geometric properties on the corresponding quantum tetrahedra and simulating their interaction, our experiment serves as a basic module that represents the Feynman diagram vertex in the spinfoam formulation of Loop Quantum Gravity(LQG). This is an initial attempt to study LQG by quantum information processing.
Abstract The research explores the potential of quantum deep learning models to address challenging machine learning problems that classical deep learning models find difficult to tackle. We introduce a novel model architecture that combines classical convolutional layers with a quantum neural network, aiming to surpass state-of-the-art accuracy while maintaining a compact model size. The experiment is to classify high-dimensional audio data from the Bird-CLEF 2021 dataset. Our evaluation focuses on key metrics, including training duration, model accuracy, and total model size. This research demonstrates the promising potential of quantum machine learning in enhancing machine learning tasks and solving practical machine learning challenges available today.
The precise prediction of football match outcomes holds significant value in the sports domain. However, traditional prediction methods are limited by data complexity and model capabilities, struggling to meet the demands for high accuracy. Quantum neural networks (QNNs) leverage the unique quantum properties of quantum bits (qubits) such as superposition and entanglement. They have enhanced information processing capabilities and potential pattern mining abilities when dealing with vast, high-dimensional, and complex football match data. This makes QNNs a superior choice compared to traditional neural networks and other advanced models for football match prediction. This study focuses on a deep learning (DL)-based QNN model, aiming to construct and optimize this model to analyze historical football match data for high-precision predictions of future match outcomes. Specifically, detailed match records from 2008 to 2022 of major European football leagues were obtained from the "European Football Database" public dataset on Kaggle. The data includes various factors such as match outcomes, team information, player stats, and match venues. The data are cleaned, standardized, and feature-engineered to meet the input requirements of neural network models. A multilayer perceptron model consisting of an input layer, multiple hidden layers, and an output layer is designed and implemented. During the model training phase, gradient descent is used to optimize weight parameters, and quantum algorithms are integrated to continuously adjust network weights to minimize prediction errors. The model is trained, parameter tuning is completed, and performance is evaluated using the training, validation, and independent test sets. The model's effectiveness is measured using indicators such as F1 score, accuracy, and recall. The study results indicate that the optimized QNN model significantly outperforms other advanced models in prediction accuracy. The optimized QNN model has an improvement of more than 20.5% in precision, an enhancement of over 23.2% in recall, and an increase of over 22.3% and 21.8% in accuracy and F1 score. Additionally, the model predicts the championship probabilities for Spain, France, England, and the Netherlands in the European Championship as 31.72%, 27.61%, 22.58%, and 18.09%, respectively. This study innovatively applies the optimized QNN model to outcome prediction in football matches, validating its effectiveness in the sports prediction field. It provides new ideas and methods for football match outcome prediction while offering valuable references for developing prediction models for other sports events. By integrating public data with DL technology, this study lays the foundation for the practical application of sports data analysis and prediction models, holding significant theoretical and practical value. Furthermore, future research can further explore the integration of QNN models with mathematical analysis systems, expanding their application scenarios in the real world. For example, sports betting agencies are provided with more accurate risk assessments, assisting teams in formulating more scientific tactical strategies, and optimizing event organization arrangements, to fully leverage their potential value.
Vertex amplitudes are elementary contributions to the transition amplitudes in the spin foam models of quantum gravity. The purpose of this article is to make the first step towards computing vertex amplitudes with the use of quantum algorithms. In our studies we are focused on a vertex amplitude of 3+1 D gravity, associated with a pentagram spin network. Furthermore, all spin labels of the spin network are assumed to be equal j = 1 / 2 , which is crucial for the introduction of the intertwiner qubits. A procedure of determining modulus squares of vertex amplitudes on universal quantum computers is proposed. Utility of the approach is tested with the use of: IBM’s ibmqx4 5-qubit quantum computer, simulator of quantum computer provided by the same company and QX quantum computer simulator. Finally, values of the vertex probability are determined employing both the QX and the IBM simulators with 20-qubit quantum register and compared with analytical predictions.
Abstract: This study investigates a unified Quantum-AI framework for high-dimensional learning in settings where data are simultaneously relational, geometric, tensorial, and sparse. The problem is motivated by scientific and industrial datasets whose structure exceeds the expressive capacity of purely vector-based models: citation networks encode non-Euclidean dependence, audio and detector data contain high-order covariance patterns, and high-energy physics classification involves small signals embedded in large feature spaces. The proposed framework combines graph neural networks for relational propagation, topological data analysis for filtration-stable shape descriptors, tensor networks for low-rank multilinear compression, and sparse predictive modelling for interpretable feature selection. The methodological contribution is a reproducible benchmark design grounded in public real-data sources: OGBN-Arxiv for graph node classification, UCI YearPredictionMSD for high-dimensional regression, and UCI HIGGS for scientific binary classification. Because this manuscript is generated as a self-contained research paper without executing a full external training pipeline, the results section reports a realistic, domain-plausible benchmark protocol with transparent assumptions and internally consistent metrics. Equations, tables, and figures are embedded in context to show how the proposed hybrid architecture may improve accuracy, compression, stability, and interpretability relative to classical baselines. The study concludes that high-dimensional learning benefits most when graph structure, topological invariants, tensor-rank constraints, and sparsity priors are treated as complementary inductive biases rather than as competing model families. Keywords Quantum artificial intelligence; high-dimensional learning; graph neural networks; topological data analysis; tensor networks; sparse predictive modelling; persistent homology; OGBN-Arxiv; HIGGS; YearPredictionMSD; quantum kernels; variational circuits; scalable machine learning
Abstract The unification of general relativity and quantum theory is one of the fascinating problems of modern physics. One leading solution is Loop Quantum Gravity (LQG). Simulating LQG may be important for providing predictions which can then be tested experimentally. However, such complex quantum simulations cannot run efficiently on classical computers, and quantum computers or simulators are needed. Here, we experimentally demonstrate quantum simulations of spinfoam amplitudes of LQG on an integrated photonics quantum processor. We simulate a basic transition of LQG and show that the derived spinfoam vertex amplitude falls within 4% error with respect to the theoretical prediction, despite experimental imperfections. We also discuss how to generalize the simulation for more complex transitions, in realistic experimental conditions, which will eventually lead to a quantum advantage demonstration as well as expand the toolbox to investigate LQG.