Realizability in the Unitary Sphere

Alejandro Díaz-Caro (1, 2, 3) , Mauricio Guillermo (4) , Alexandre Miquel (4) , Benoît Valiron (5, 6)

1 UNQ - Universidad Nacional de Quilmes
2 UBA - Universidad de Buenos Aires [Buenos Aires]
3 CONICET - Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires]
4 IMERL - Instituto de Matemática y Estadística Rafael Laguardia [Montevideo]
5 CentraleSupélec
6 VALS - LRI - Vérification d'Algorithmes, Langages et Systèmes (LRI)

In this paper we present a semantics for a linear algebraic lambda-calculus based on realizability. This semantics characterizes a notion of unitarity in the system, answering a long standing issue. We derive from the semantics a set of typing rules for a simply-typed linear algebraic lambda-calculus, and show how it extends both to classical and quantum lambda-calculi.

Domaines: Logique en informatique [cs.LO]; Informatique et langage [cs.CL]; Physique Quantique [quant-ph]

Alejandro Díaz-Caro, Mauricio Guillermo, Alexandre Miquel, Benoît Valiron. Realizability in the Unitary Sphere. 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2019), Jun 2019, Vancouver, Canada. ⟨hal-02175168⟩