Quantum Cellular Automata

2 Acknowledgments Writing a master's thesis can sometimes be a lonesome activity, I therefore feel privileged to be able to thank the following people. First of all I want to thank Kees Koster and Paul Vitt anyi for their experienced guidance and interest during the writing of this thesis. I also thank Andr e Berthiaume for giving me a ``rst hand' introduction in quantum computing, his knowledge of this eld prevented me from making a lot of typical beginner's mistakes. Sjoerd Stallinga and Paul Bastiaansen should be mentioned for explaining me the essentials of quantum mechanics. The hospitality of Christoph D urr and Huong L^ e Thanh made an inspiring and enjoyable visit to Paris possible in the summer of '95. In 1996, the Institute for Scientiic Interchange Foundation enabled me to go to thèTorino workshop on Quantum Computing'. During this workshop I enjoyed the interesting discussions with