"Quantum computing involves a new computational paradigm based on thelaws of quantum mechanics. It uses qubits, which are superpositions ofordinary bits, and exploits the `strange' quantum phenomena likeentanglement of qubits. It promises new forms of very fast,distributed computation. First applications are now appearing incomputer security, based on the manipulation of individual qubits. Therealization of large scale quantum computing, involving multitudes ofqubits is still a technological challenge, beyond the scope of thisproposal.Quantum computing originated, understandably, in physics. Thisproject abstracts from this physical level and will transform anddevelop the relevant phenomena at a mathematical level so that theycan be integrated in computational models, logics and formal methodsused in computer science. The project will use the unifying languageand tools of category theory, which are working as a ``Rosetta Stone''in the multi-disciplinary area of computer science, mathematics andphysics. The project will clarify the subtle but fundamentaldifference between quantum computation/logic on the one hand andprobabilistic and non-deterministic computation/logic on theother. This should result in (programming) logics and models that areclear and usable for computer scientists, in particular in the area of(formal methods for) computer security. Overall, the proposal aims toensure that the discipline of computer science is well-prepared forthe (approaching) moment when quantum computing becomes a reality."