7 papers
Resolution-Consistent Greedy Neural Approximation on Infinite-Dimensional Spaces
Pablo M. Berná, Antonio Falcó, Diego Mondéjar
We develop constructive approximation and learning guarantees for shallow neural models with infinite-dimensional inputs observed through finitely many coordinates. The analysis is…
Universal optimality of the double-centred matrix under unitarily invariant norms for dissimilarity data
M. Nuria de las Heras Santos, Antonio Falcó, Francisco Javier Muñoz Almaraz
The classical identity relating squared distances to inner products determines every off-diagonal entry of a symmetric matrix associated with a set of pairwise dissimilarities, whi…
Dictionary-Restricted First-Order Descent Methods: Bounds and Convergence Rates
Miguel Berasategui, Pablo M. Berná, Antonio Falcó
This paper develops a general theory for first-order descent methods whose search directions are restricted to a prescribed dictionary in a reflexive Banach space. Instead of assum…
Density-Matrix Spectral Embeddings for Categorical Data: Operator Structure and Stability
Raquel Bosch-Romeu, Antonio Falcó, osé-Antonio Rodríguez-Gallego
We introduce a supervised dimensionality reduction methodology for categorical (and discretized mixed-type) data based on a density-matrix construction induced by class-conditional…
Vistas of Algebraic Probability: Quantum Computation and Information
Antonio Falcó, Hermann G. Matthies
Kolmogorov's foundation of probability takes measure spaces, -algebras, and probability measures as basic objects. It is, however, widely recognized that this classical framewor…
Geometric Complexity of Quantum Channels via Unitary Dilations
Alberto Acevedo, Antonio Falcó
Nielsen's geometric approach to quantum circuit complexity provides a Riemannian framework for quantifying the cost of implementing unitary closed-system dynamics. For open evoluti…
A mathematical model for a universal digital quantum computer with an application to the Grover-Rudolph algorithm
Antonio Falcó, Daniela Falcó--Pomares, Hermann G. Matthies
In this work, we develop a novel mathematical framework for universal digital quantum computation using algebraic probability theory. We rigorously define quantum circuits as finit…