Mathematics, Physics and Technological Sciences
Organisation / Company University CEU Cardenal Herrera Department Mathematics, Physics and Technological Sciences Laboratory The XQBO research group (Computational Methods for the Modelling of Physical Processes) Is the Hosting related to staff position within a Research Infrastructure? No
UCH‑CEU is seeking excellent postdoctoral researchers interested in applying for the MSCA Postdoctoral Fellowships (MSCA‑PF 2026) .
Hosting Research Group
The XQBO research group (Computational Methods for the Modelling of Physical Processes) at CEU Cardenal Herrera University, founded in 1995 and led by Prof. Antonio Falcó Montesinos, offers a strong interdisciplinary environment for frontier research in computational mathematics, mathematical modelling, AI, and quantum computing. The group focuses on the development of new mathematical structures, algorithms, and computational methods to analyse and simulate complex systems, combining rigorous theoretical foundations with implementation-oriented research. This makes it a particularly suitable host for MSCA projects addressing the mathematical foundations of quantum machine learning and its applications. The environment supports high-level training, interdisciplinary interaction, and international collaboration. In addition, the group has access to a 3-qubit NMR quantum computer, enabling experimental benchmarking, validation of quantum algorithms, and proof-of-concept developments in quantum information and computation.
Scientific keywords
Quantum machine learning;
mathematical foundations;
quantum algorithms;
scientific computing;
quantum computing
Relevant publications and projects
1.A Rigorous and Self-Contained Proof of the Grover–Rudolph State Preparation Algorithm (A.



Falcó, D. Falcó-Pomares, H. G. Matthies, 2025). as a rigorous mathematical framework for universal digital quantum computation, with explicit links to probability encoding, quantum algorithms, and potential applications to quantum machine learning.
Relevant to the theoretical foundations of quantum dynamics and continuous-variable quantum systems, providing mathematical background of interest for future QML formulations.
3.A Quantum Hybrid Digital Twin model for the study of the influence of erosion damage on wind turbine performance COMCUANTICA/007 (project, 2022–2025).
A quantum-oriented applied project showing the group’s capacity to connect mathematical and quantum methods with real industrial problems.
4. ESI-CEU International Chair (ongoing research structure supporting advanced work in mathematical modelling, computational simulation, and emerging quantum-computing directions). not a quantum paper per se, it is highly relevant to the mathematical foundations side of the proposal, especially for representation, approximation, and high-dimensional learning models connected to quantum machine learning.
Research Project Description
The project, tentatively entitled “Mathematical Foundations of Quantum Machine Learning and Its Applications”, aims to develop a rigorous mathematical framework for quantum machine learning (QML), bridging advanced mathematics,



quantum computing, and data-driven applications. Its main objective is to investigate the theoretical principles that govern quantum learning models, with particular attention to representation, approximation, optimisation, trainability, and computational complexity.
The research will combine methods from functional analysis, operator theory, approximation theory, optimisation, scientific computing, and quantum information in order to establish mathematically sound foundations for hybrid quantum-classical learning architectures and quantum-enhanced algorithms. In parallel, the project will explore concrete proof-of-concept applications in areas such as scientific machine learning, modelling of complex systems, and quantum-assisted data analysis.
A distinctive feature of the project is its combination of theoretical development and experimental validation. In addition to deriving new mathematical results, the researcher will be able to test selected algorithms and state-preparation strategies on a 3-qubit NMR-based quantum computer available at the host institution. This will enable the assessment of feasibility, robustness, and implementation constraints in realistic small-scale quantum settings.
The project is expected to contribute to the emerging field of QML by clarifying its mathematical structure, identifying domains where quantum methods may provide meaningful advantages, and opening new connections between rigorous mathematics and quantum technologies. It will also provide strong interdisciplinary training for the fellow at the interface of mathematics, artificial intelligence, and quantum computation, while strengthening international collaboration and the

📌 Msca Postdoctoral Position In Foundations Of Quantum Machine Learning For Scientific And Industrial (Madrid)
🏢 University CEU Cardenal Herrera
📍 Madrid