Project information
Lie theOretic and algebraic foundations for quantum computing, graph neural networks and Generative AI applicatiOnS (LOGOS)

LOGOS is an interdisciplinary research and networking program, aiming to establish a common theoretical and methodological foundation, exploiting pure mathematical themes as Lie theory and Graph Theory, and theoretical physical ones, towards quantum computing, (quantum) information geometry and machine learning applications, focusing on topological data analysis, physically informed neural networks and flow matching methods for generative AI. The project is structured around three tightly interconnected research areas: (i) foundational developments in representation and graph theory, (ii) geometric approaches to quantum information and quantum computing, and (iii) geometry and physics driven methods for machine learning, including
topological data analysis, graph and sheaf neural networks, and generative AI on symmetric spaces. LOGOS strong intersectoral dimension will integrate the theoretical advances with the real-world applications stemming from the collaboration between academic and non-academic beneficiaries in key domains as biomedical data analysis with novel AI techniques towards the quantum computing advantage. LOGOS structured programme of interdisciplinary, intersectoral and international secondments will ensure effective knowledge transfer across the domains of the project. Together with an effective training programme, LOGOS will foster the
development of a new generation of researchers equipped with interdisciplinary and transferable skills. By creating a common language across mathematics, physics, quantum computing and machine learning, LOGOS will contribute to strengthening Europe’s leadership in AI and quantum technologies, in line with Horizon Europe priorities. The high-impact scientific results, open-access algorithms, and long-lasting collaborations, will deliver lasting benefits for research, industry, and society.