From Fermat's last theorem to the quantum computer

Alexander Yu. Vlasov

Published 2003-07-03Version 1

Despite of an active work of many researchers in the theory of quantum computations, this area still saves some mysterious charm. It is already an almost common idea, that maybe many fashionable current projects will fade in future, but some absolutely unpredictable applications appear instead. Why such optimistic predictions are legal here, despite of an extreme difficulty to suggest each one new promising quantum algorithm or realistic "industrial" application? One reason -- is very deep contents of this area. It maybe only an extremely unlucky occasion, if such a fundamental thing won't supply us with some bright insights and serious new applications. A sign of such nontrivial contents of a theory -- are unexpected links between different branches of our knowledge. In the present paper is mentioned one such link -- between application of Weyl quantization in the theory of quantum computations and abstract mathematical constructions born in mid of XIX century due to unsuccessful tries to prove Fermat's last theorem.