Related papers: Quantum Programming with Inductive Datatypes: Caus…
We develop a sound and complete equational theory for the functional quantum programming language QML. The soundness and completeness of the theory are with respect to the previously-developed denotational semantics of QML. The completeness…
This book is a graduate-level introduction to probabilistic programming. It not only provides a thorough background for anyone wishing to use a probabilistic programming system, but also introduces the techniques needed to design and build…
Quantum machine learning (QML) is an emerging field that investigates the capabilities of quantum computers for learning tasks. While QML models can theoretically offer advantages such as exponential speed-ups, challenges in data loading…
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…
Generalisation in machine learning often relies on the ability to encode structures present in data into an inductive bias of the model class. To understand the power of quantum machine learning, it is therefore crucial to identify the…
Domain theory has been developed as a mathematical theory of computation and to give a denotational semantics to programming languages. It helps us to fix the meaning of language concepts, to understand how programs behave and to reason…
The main goal of this master's thesis is to introduce Quantum Natural Language Processing (QNLP) in a way understandable by both the NLP engineer and the quantum computing practitioner. QNLP is a recent application of quantum computing that…
According to the statistical interpretation of quantum theory, quantum computers form a distinguished class of probabilistic machines (PMs) by encoding n qubits in 2n pbits (random binary variables). This raises the possibility of a…
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
In supervised learning, an inductive learning algorithm extracts general rules from observed training instances, then the rules are applied to test instances. We show that this splitting of training and application arises naturally, in the…
Large language models (LLMs) have displayed an impressive ability to harness natural language to perform complex tasks. In this work, we explore whether we can leverage this learned ability to find and explain patterns in data.…
Language models now provide an interface to express and often solve general problems in natural language, yet their ultimate computational capabilities remain a major topic of scientific debate. Unlike a formal computer, a language model is…
We derive the category-theoretic backbone of quantum theory from a process ontology. More specifically, we treat quantum theory as a theory of systems, processes and their interactions. In this first part of a three-part overview, we first…
Quantitative aspects of computation are related to the use of both physical and mathematical quantities, including time, performance metrics, probability, and measures for reliability and security. They are essential in characterizing the…
This paper gives an introduction to and overview of the functional quantum programming language QML. The syntax of this language is defined and explained, along with a new QML definition of the quantum teleport algorithm. The categorical…
A theory of data types based on category theory is presented. We organize data types under a new categorical notion of F,G-dialgebras which is an extension of the notion of adjunctions as well as that of T-algebras. T-algebras are also used…
The main contribution of this paper is the introduction of a dynamic logic formalism for reasoning about information flow in composite quantum systems. This builds on our previous work on a complete quantum dynamic logic for single systems.…
With the growing interest in quantum computing, the emergence of quantum supremacy has marked a pivotal milestone in the field. As a result, numerous quantum programming languages (QPLs) have been introduced to support the development of…
Quantum computers have leaped from the theoretical realm into a race to large-scale implementations. This is due to the promise of revolutionary speedups, where achieving such speedup requires designing an algorithm that harnesses the…
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum…