last updated: 4/5/04

I have done/ am doing research in the following topics (for more specific details and downloading please consult the publications page):

PhD: Quantum Computation

When finishing my physics studies, I decided that I wanted to study something else first instead of starting a PhD in physics immediately, mainly because I wanted to do interdisciplinary research. Several reasons naturally directed me towards quantum computation (QC). First, quantum mechanics has always fascinated me. Next, I already had in mind to study computer science if ever I decided to continue studying, since this seems to be a bit of a family tradition, unintentionally. Above all, QC is a really interesting and flourishing research topic, and it bridges a gap between physics and computer science. So here I am.

Quantum computation is a field of research that is rapidly acquiring a place as a significant topic in computer science. Nevertheless, quantum algorithms are currently done at a very low level only. My PhD is situated in this nascent area of quantum programming methodology and the design and semantics of quantum programming languages. Concretely, I am developing a weakest precondition semantics for quantum computation. Next to constructing this theory in a quantum context, the idea is to use it as a basis to develop a formal semantics for measurement-based quantum computational models, such as for example the one-way quantum computer, a model in which the entire computation is carried out by one-qubit projective measurements on a large entangled state. Typical computational concepts from the quantum circuit model thus cease to be suitable for describing these models in every respect. With these developments in place we want to evolve a goal-directed (axiomatic) programming methodology for quantum computation. In a later stage, we plan to develop an associated denotational and operational semantics, with the aim of designing a full-fledged quantum programming language and, as a potential consequence, new quantum algorithms.

PHYSICS: Inflation theory

Inflation theory is an adaptation to standard big bang cosmology which solves the latter's most fundamental problems. It postulates the existence of a short period of exponential expansion in between the big bang and the era where standard cosmology holds. As a result, formation of the universe as we know it is a a generic process, and no longer extremely sensitive to initial conditions - a common aspect in all of standard cosmology's fundamental problems. While inflation as an idea is widely accepted throughout the scientific community, it is still rather ad hoc and specific implementations are as many as there are people working on it. My physics thesis consists partly of an overview of inflation as an idea and a classification of its different existing implementations. However, the main goal of the research group I was working with is to find a physical inflationary scenario. For example, one crucial ingredient that has to be taken into account (and often is not) is the interaction of inflation with gravity, or so-called inflation with non-minimal coupling. Therefore, I also brought together most results done within this context, and I investigated what the general expressions of de Sitter solutions - a generic class of inflationary scenarios - are with non-minimal coupling. Strangely enough, I found a link with Higgs potentials, which are often encountered in particle physics; this again points to the idea of inflation being associated with an elementary particle. Continuing the search for a physical inflationary model, we did some further work trying to describe inflation as being connected to two particles - where during the inflationary era one particle is converted into the other - as well as generalising inflation theory towards curved spaces. However, here my research path diverges from cosmology...

COMPUTER SCIENCE: Amorphous Computing

Amorphous computing was proposed as a new potential computational paradigm at MIT, in view of recent developments in microelectronics and cellular biology. These advances make it feasable to use a set of randomly placed, locally communicating and possibly mobile particles, each with limited computational power, as a basis for doing computation. However, at this stage nobody knows how to program such a medium - dubbed as an amorphous computer. Therefore, the main goal of amorphous computing is to investigate what programming methodologies and techniques are required in order to do amorphous computation, or, in other words, to find out how one obtains predefined global goals through local communication only. In my computer science thesis I investigated amorphous computing in all its present aspects, giving an overview of the as yet applied metaphors (borrowed, for obvious reasons, from other sciences such as physics and biology) as well as the developed media (either conceptually or physically). Relying on the biological metaphors of pheromones and tropisms, Daniel Coore developed the Growing Point Language (GPL), the first and only - albeit preliminary- amorphous programming language that exists. It specialises in the formation of patterns (such as microelectronical circuits), a global goal which is achieved through the local communication protocol typical of an amorphous computer. Hence it is an important first step towards the development of amorphous computing as a full-blown paradigm of its own. Next to this, GPL is useful as a tool for investigating the power of amorphous computation in general. For example, in my investigations on amorphous geometry, or how to incorporate computational geometry into amorphous computing, I used GPL to carry out concrete experiments. An amorphous computer's layout is directly geometrical, and thus amorphous computers are well-suited candidates for solving geometrical problems. Next to this, I learned a lot from the paradigm point-of-view by comparing 'normal' computational geometry with it's (preliminary) amorphous version. Which is great, since my motivation for doing amorphous computing and computer science in general was to learn about paradigms and their differences - as a preparation for my PhD research in quantum computation...