arXiv:2508.04048v2 Announce Type: replace 
Abstract: The \textit{Temporal Fusion Transformer} (TFT), proposed by Lim \textit{et al.}, published in \textit{International Journal of Forecasting} (2021), is a state-of-the-art attention-based deep neural network architecture specifically designed for multi-horizon time series forecasting. It has demonstrated significant performance improvements over existing benchmarks. In this work, we introduce the Quantum Temporal Fusion Transformer (QTFT), a quantum-enhanced hybrid quantum-classical architecture that extends the capabilities of the classical TFT framework. The core idea of this work is inspired by the foundation studies, \textit{The Power of Quantum Neural Networks} by Amira Abbas \textit{et al.} and \textit{Quantum Vision Transformers} by El Amine Cherrat \textit{et al.}, published in \textit{ Nature Computational Science} (2021) and \textit{Quantum} (2024), respectively. A key advantage of our approach lies in its foundation on a variational quantum algorithm, enabling implementation on current noisy intermediate-scale quantum (NISQ) devices without strict requirements on the number of qubits or circuit depth. Our results demonstrate that QTFT is successfully trained on the forecasting datasets and is capable of accurately predicting future values. In particular, our experimental results on two different datasets display that the model outperforms its classical counterpart in terms of both training and test loss. These results indicate the prospect of using quantum computing to boost deep learning architectures in complex machine learning tasks.

تقديم Quantum Temporal Fusion Transformer (QTFT) يمثل تقدمًا كبيرًا في مجال التنبؤ بسلاسل الزمن. بناءً على نجاح Temporal Fusion Transformer الأصلي، يستفيد هذا النموذج الجديد من الحوسبة الكمومية لتحسين الأداء بشكل أكبر. هذا مثير لأنه لا يظهر فقط إمكانيات التكنولوجيا الكمومية في التطبيقات العملية، بل يعد أيضًا بتحسين دقة التنبؤ عبر مختلف الصناعات، مما يجعله تطورًا ملحوظًا للباحثين والشركات على حد سواء.

La introducción del Quantum Temporal Fusion Transformer (QTFT) marca un avance significativo en el campo de la predicción de series temporales. Basándose en el éxito del Temporal Fusion Transformer original, este nuevo modelo aprovecha la computación cuántica para mejorar aún más el rendimiento. Esto es emocionante porque no solo muestra el potencial de la tecnología cuántica en aplicaciones prácticas, sino que también promete mejorar la precisión de las predicciones en diversas industrias, lo que lo convierte en un desarrollo notable para investigadores y empresas por igual.

L'introduction du Quantum Temporal Fusion Transformer (QTFT) représente une avancée significative dans le domaine de la prévision des séries temporelles. S'appuyant sur le succès de l'original Temporal Fusion Transformer, ce nouveau modèle exploite l'informatique quantique pour améliorer encore les performances. C'est passionnant car cela démontre non seulement le potentiel de la technologie quantique dans des applications pratiques, mais cela promet également d'améliorer la précision des prévisions dans divers secteurs, ce qui en fait un développement remarquable pour les chercheurs et les entreprises.

The introduction of the Quantum Temporal Fusion Transformer (QTFT) marks a significant advancement in the field of time series forecasting. Building on the success of the original Temporal Fusion Transformer, this new model leverages quantum computing to enhance performance even further. This is exciting because it not only showcases the potential of quantum technology in practical applications but also promises to improve forecasting accuracy across various industries, making it a noteworthy development for researchers and businesses alike.

Quantum Temporal Fusion Transformer

arXiv:2507.06038v3 Announce Type: replace-cross 
Abstract: Building on our previous work introducing Fredholm Neural Networks (Fredholm NNs/ FNNs) for solving integral equations, we extend the framework to tackle forward and inverse problems for linear and semi-linear elliptic partial differential equations. The proposed scheme consists of a deep neural network (DNN) which is designed to represent the iterative process of fixed-point iterations for the solution of elliptic PDEs using the boundary integral method within the framework of potential theory. The number of layers, weights, biases and hyperparameters are computed in an explainable manner based on the iterative scheme, and we therefore refer to this as the Potential Fredholm Neural Network (PFNN). We show that this approach ensures both accuracy and explainability, achieving small errors in the interior of the domain, and near machine-precision on the boundary. We provide a constructive proof for the consistency of the scheme and provide explicit error bounds for both the interior and boundary of the domain, reflected in the layers of the PFNN. These error bounds depend on the approximation of the boundary function and the integral discretization scheme, both of which directly correspond to components of the Fredholm NN architecture. In this way, we provide an explainable scheme that explicitly respects the boundary conditions. We assess the performance of the proposed scheme for the solution of both the forward and inverse problem for linear and semi-linear elliptic PDEs in two dimensions.

تم تقديم إطار عمل جديد يوسع الشبكات العصبية فريدولم (FNN) لمعالجة المشاكل الأمامية والعكسية في المعادلات التفاضلية الجزئية (PDE) البيضاوية الخطية وشبه الخطية. تستخدم هذه الطريقة شبكة عصبية عميقة مصممة لتمثيل عمليات التكرار الثابتة لحل PDE البيضاوية من خلال طريقة التكامل الحدودي، والتي تُسمى شبكة فريدولم العصبية المحتملة (PFNN).

Se ha introducido un nuevo marco que extiende las Redes Neuronales de Fredholm (FNN) para abordar problemas directos e inversos en ecuaciones diferenciales parciales (EDP) elípticas lineales y semilineales. Este enfoque utiliza una red neuronal profunda diseñada para representar iteraciones de punto fijo para resolver EDP elípticas mediante el método de integral de frontera, denominado Red Neuronal de Fredholm Potencial (PFNN).

Un nouveau cadre a été introduit, étendant les Réseaux de Neurones de Fredholm (FNN) pour traiter les problèmes directs et inverses dans les équations aux dérivées partielles (EDP) elliptiques linéaires et semi-linéaires. Cette approche utilise un réseau de neurones profond conçu pour représenter les itérations de point fixe pour résoudre les EDP elliptiques par la méthode d'intégrale de frontière, appelée Réseau de Neurones de Fredholm Potentiel (PFNN).

A new framework has been introduced that extends Fredholm Neural Networks (FNNs) to address forward and inverse problems in linear and semi-linear elliptic partial differential equations (PDEs). This approach utilizes a deep neural network designed to represent fixed-point iterations for solving elliptic PDEs through the boundary integral method, termed the Potential Fredholm Neural Network (PFNN).

Quantum Temporal Fusion Transformer

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