Mathys Rennela

Mathys Rennela
Leiden University | LEI · Quantum group

PhD

About

16
Publications
887
Reads
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102
Citations
Additional affiliations
January 2018 - present
Centrum Wiskunde & Informatica
Position
  • Researcher
March 2013 - September 2017
Radboud University
Position
  • Research Assistant

Publications

Publications (16)
Preprint
Full-text available
Reversible computing is a computational paradigm in which computations are deterministic in both the forward and backward direction, so that programs have well-defined forward and backward semantics. We investigate the formal semantics of the reversible functional programming language Rfun. For this purpose, we introduce join inverse rig categories...
Chapter
Inductive datatypes in programming languages allow users to define useful data structures such as natural numbers, lists, trees, and others. In this paper we show how inductive datatypes may be added to the quantum programming language QPL. We construct a sound categorical model for the language and by doing so we provide the first detailed semanti...
Preprint
Inductive datatypes in programming languages allow users to define useful data structures such as natural numbers, lists, trees, and others. In this paper we show how inductive datatypes may be added to the quantum programming language QPL. We construct a sound categorical model for the language and by doing so we provide the first detailed semanti...
Thesis
Full-text available
The organizing framework of this thesis is category theory, which allows for compositional thinking in terms of mathematical objects and structure-preserving arrows between them. This thesis has been organised around two themes. The first theme is the use of operator algebras in the categorical study of quantum foundations. The second theme focuses...
Article
Full-text available
We describe categorical models of a circuit-based (quantum) functional programming language. We show that enriched categories play a crucial role. Following earlier work on QWire by Paykin et al., we consider both a simple first-order linear language for circuits, and a more powerful host language, such that the circuit language is embedded inside...
Article
Full-text available
We describe categorical models of a circuit-based (quantum) functional programming language. We show that enriched categories play a crucial role. Following earlier work on QWire by Paykin et al., we consider both a simple first-order linear language for circuits, and a more powerful host language, such that the circuit language is embedded inside...
Article
Full-text available
In this paper, W*-algebras are presented as canonical colimits of diagrams of matrix algebras and completely positive maps. In other words, matrix algebras are dense in W*-algebras.
Conference Paper
Full-text available
We describe categorical models of a circuit-based (quantum) functional programming language. We show that enriched categories play a crucial role. Following earlier work on QWire by Paykin et al., we consider both a simple first-order linear language for circuits, and a more powerful host language, such that the circuit language is embedded inside...
Article
Full-text available
In the present paper, Kegelspitzen, which can be seen dcpos associated with a compatible convex structure, will be shown to be models of the order-enriched Lawvere theory of subconvex sets and later used to adequately interpret PFPC, a probabilistic version of the well-known functional programming language FPC (Fixed Point Calculus) which involves...
Article
Full-text available
In two-party quantum communication complexity, Alice and Bob receive some classical inputs and wish to compute some function that depends on both these inputs, while minimizing the communication. This model has found numerous applications in many areas of computer science. One notion that has received a lot of attention recently is the information...
Article
Full-text available
We propose a new 'quantum domain theory' in which Scott-continuous functions are replaced by Scott-continuous natural transformations.
Article
Full-text available
We discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science. From a computer scientist point of view, we explain some fundamental results of operator theory and their relevance in the context of domain theory. In particular, we consider the category W* of W*-algebras together with normal s...
Article
Full-text available
In two-party quantum communication complexity, Alice and Bob receive some classical inputs and wish to compute some function that depends on both these inputs, while minimizing the communication. This model has found numerous applications in many areas of computer science. One question that has received a lot of attention recently is whether it is...
Article
Full-text available
In this master thesis, I discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science.

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Projects

Projects (3)
Project
The goal is to study the semantics of quantum circuits, using operator algebras and enriched category theory.