Related papers: Classical Control, Quantum Circuits and Linear Log…
Building on our previous work on enriched universal algebra, we define a notion of enriched language consisting of function and relation symbols whose arities are objects of the base of enrichment. In this context, we construct atomic…
Modern quantum programming languages integrate quantum resources and classical control. They must, on the one hand, be linearly typed to reflect the no-cloning property of quantum resources. On the other hand, high-level and practical…
qPCF is a paradigmatic quantum programming language that ex- tends PCF with quantum circuits and a quantum co-processor. Quantum circuits are treated as classical data that can be duplicated and manipulated in flexible ways by means of a…
It is well-known that combinatorial circuits are modeled mathematically by string diagrams in a monoidal category. Given a gate set $\Sigma$, the circuits over $\Sigma$ can be thought of as string diagrams in the free monoidal category…
Quantum programs today are written at a low level of abstraction - quantum circuits akin to assembly languages - and the unitary parts of even advanced quantum programming languages essentially function as circuit description languages.…
Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the…
In this paper, a monad-based denotational model is introduced and shown adequate for the Proto-Quipper family of calculi, themselves being idealized versions of the Quipper programming language. The use of a monadic approach allows us to…
Building on our previous work on enriched regular logic, we introduce an enriched version of positive logic and relate it to enriched cone-injectivity classes and enriched accessible categories. To do this, we need a factorization system on…
Quantum computation constitutes a rapidly expanding subfield of computer science. Development quantum algorithms is facilitated by the availability of efficient quantum programming languages, and a plethora of approaches has been already…
Quantum based systems are a relatively new research area for that different modelling languages including process calculi are currently under development. Encodings are often used to compare process calculi. Quality criteria are used then…
Circuit description languages are a class of quantum programming languages in which programs are classical and produce a description of a quantum computation, in the form of a quantum circuit. Since these programs can leverage all the…
We describe an embedding of the QWIRE quantum circuit language in the Coq proof assistant. This allows programmers to write quantum circuits using high-level abstractions and to prove properties of those circuits using Coq's theorem proving…
The goal of this article is to emphasize the role of cubical sets in enriched categories theory and infinity-categories theory. We show in particular that categories enriched in cubical sets provide a convenient way to describe many…
We introduce the language QML, a functional language for quantum computations on finite types. Its design is guided by its categorical semantics: QML programs are interpreted by morphisms in the category FQC of finite quantum computations,…
This thesis introduces quantum natural language processing (QNLP) models based on a simple yet powerful analogy between computational linguistics and quantum mechanics: grammar as entanglement. The grammatical structure of text and…
Quantum assembly languages are machine-independent languages that traditionally describe quantum computation in the circuit model. Open quantum assembly language (OpenQASM 2) was proposed as an imperative programming language for quantum…
Selinger gave a superoperator model of a first-order quantum programming language and proved that it is fully definable and hence fully abstract. This paper proposes an extension of the superoperator model to higher-order programs based on…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
We introduce dependently typed Proto-Quipper, or Proto-Quipper-D for short, an experimental quantum circuit programming language with linear dependent types. We give several examples to illustrate how linear dependent types can help in the…
Linear type theories, of various types and kinds, are of fundamental importance in most programming language research nowadays. In this paper we describe an extension of Benton's Linear-Non-Linear type theory and model for which we can…