arXiv subjects

Nicolas Blanco

Publications and source records attributed to Nicolas Blanco.

2 recordsLinked to original sources

arXiv2026

Hybrid Path-Sums for Hybrid Quantum Programs

As quantum computing becomes an emerging reality, designing efficient quantum programming capabilities is becoming more and more important. Particularly, the debugging and validation of quantum programs is of paramount importance, as these programs are by definition hard to test. Static analysis and formal verification methods for quantum programs started to emerge a few years now, yet they often miss hybrid quantum/classical reasoning facilities with, e.g., generic quantum control, classical control and classical computation instructions. In this paper, we lay out the foundations of a framework for the automated formal verification of (full) hybrid quantum programs featuring both classical and quantum control, measurement and hybrid data structures. In particular, we propose: (1) a novel symbolic representation for describing and manipulating sets of hybrid quantum/classical states called Hybrid Path-Sums (HPS); (2) a set of rewriting rules providing a rich mechanism for simplifying and reasoning on these symbolic hybrid states, and (3) a core assertion language to specify equivalence of hybrid quantum programs, the satisfaction of properties on (parts of) hybrid states, and the extraction of probabilistic statements about the program behavior. We prove the correctness of the novel symbolic representation, of its rewriting system and of the specification system. Finally, we propose a full implementation of this framework as a dedicated symbolic execution engine for hybrid programs. We present an evaluation of a set of representative hybrid case-studies from the literature, showcasing the advantage of our approach and its efficiency compared to state-of-the-art solutions.

cs.PL↗

arXiv2023

Bifibrations of polycategories and classical multiplicative linear logic

In this thesis, we develop the theory of bifibrations of polycategories. We start by studying how to express certain categorical structures as universal properties by generalising the shape of morphism. We call this phenomenon representability and look at different variations, namely the correspondence between representable multicategories and monoidal categories, birepresentable polycategories and $\ast$-autonomous categories, and representable virtual double categories and double categories. We then move to introduce (bi)fibrations for these structures. We show that it generalises representability in the sense that these structures are (bi)representable when they are (bi)fibred over the terminal one. We show how to use this theory to lift models of logic to more refined ones. In particular, we illustrate it by lifting the compact closed structure of the category of finite dimensional vector spaces and linear maps to the (non-compact) $\ast$-autonomous structure of the category of finite dimensional Banach spaces and contractive maps by passing to their respective polycategories. We also give an operational reading of this example, where polylinear maps correspond to operations between systems that can act on their inputs and whose outputs can be measured/probed and where norms correspond to properties of the systems that are preserved by the operations. Finally, we recall the B\'enabou-Grothendieck correspondence linking fibrations to indexed categories. We show how the B-G construction can be defined as a pullback of virtual double categories and we make use of fibrational properties of vdcs to get properties of this pullback. Then we provide a polycategorical version of the B-G correspondence.

math.CT↗