7 papers
Two Problems on Quantum Computing in Finite Abelian Groups
Ulises Pastor-Díaz, José M. Tornero
In the context of finite Abelian groups two problems are presented and solved using quantum computing techniques. The first is the well--known Hidden Subgroup Problem, originally s…
On the torsion growth in quadratic number fields for elliptic curves defined over the rationals
Sara Arias-de-Reyna, Miguel Pineda-Martín, José M. Tornero
Given an elliptic curve defined over the field of rational numbers, it is known how its torsion subgroup may grow when we make a base change to a quadratic number field. In this pa…
Onthe computation of the MED closure of a numerical semigroup
Jorge Jiménez Urroz, José M. Tornero
Maximally embedding dimension (MED) numerical semigroups are a wide and interesting family, with some remarkable algebraic and combinatorial properties. Associated to any numerical…
Further Applications of the Generalised Phase Kick-Back
Joaquín Ossorio-Castillo, Ulises Pastor-Díaz, José M. Tornero
In our previous work, we defined a quantum algorithmic technique known as the Generalised Phase Kick-Back, or , and analysed its applications in generalising some classical qu…
Quantum algorithms for the Sylvester denumerant and the numerical semigroup membership problem
J. Ossorio-Castillo, José M. Tornero
Two quantum algorithms are presented, which tackle well--known problems in the context of numerical semigroups: the numerical semigroup membership problem (NSMP) and the Sylvester…
On the Walsh and Fourier-Hadamard Supports of Boolean Functions From a Quantum Viewpoint
Claude Carlet, Ulises Pastor-Díaz, José María Tornero
In this paper, we focus on the links between Boolean function theory and quantum computing. In particular, we study the notion of what we call fully-balanced functions and analyse…
Hironaka's characteristic polygon and effective resolution of surfaces
R. Piedra, J. M. Tornero
Hironaka's concept of characteristic polyhedron of a singularity has been one of the most powerful and fruitful ideas of the last decades in singularity theory. In fact, since then…