Efficient unitary approximations in quantum computing: the Solovay-Kitaev theorem

Abstract

[en] Over the past few years, quantum computing has become more plausible due to the great advances in technology. While quantum computers are on their birth, the underlying mathematics have evolved to the point of proving that some quantum algorithms can solve problems that were unsolvable in classic computers. In order to implement these algorithms in a real machine, it is important to develop efficient ways to do it. The Solovay-Kitaev Theorem states that is possible. This work pretends to offer a complete review of the Solovay- Kitaev Theorem giving all the necessary tools to prove it. Moreover, we offer a brief introduction to the standard mathematical model of quantum computing, based on unitary operations.