arXiv subjects
Publications and source records attributed to P. H. Potgieter.
The paper considers the halting scheme for quantum Turing machines. The scheme originally proposed by Deutsch appears to be correct, but not exactly as originally intended. We discuss the result of Ozawa as well as the objections raised by Myers, Kieu and Danos and others. Finally, the relationship of the halting scheme to the quest for a universal quantum Turing machine is considered.
There has been no lack of coverage in the past few years in scientific journals of the topic of quantum computation. Rightly so, as this is a novel idea with--so far--at least one very important practical application (prime factorisation) as soon as the technology can accommodate reasonably sized computations. Interest in quantum computing has been sparked by both the realization that increasing miniaturisation will eventually bring computer scientists face-to-face with quantum effects, and by the grasping of the potential for massive parallelism inherent in the Hilbert space representation of quantum systems and in the special effects of quantum entanglement.
The main ideas behind developments in the theory and technology of quantum computation were formulated in the late 1970s and early 1980s by two physicists in the West and a mathematician in the former Soviet Union. It is not generally known in the West that the subject has roots in the Russian technical literature. The author hopes to present as impartial a synthesis as possible of the early history of thought on this subject. The role of reversible and irreversible computational processes is examined briefly as it relates to the origins of quantum computing and the so-called Information Paradox in physics.
We study partitions of Fra\"ıssé limits of classes of finite relational structures where the partitions are encoded by infinite binary sequences which are random in the sense of Kolmogorov, Chaitin and Solomonoff. It is shown that partition by a random sequence of a Fra\"ıssé limit preserves the limit property of the object.