Quantum Cryptography and Quantum Computing

Abstract

In these lecture notes we will examine the possible contributions of quantum mechanics to the fields of cryptography as well as to machine computation in general. These topics are very much under development but can already boast of initial successes, especially in cryptography. With regard to quantum computing, the realization of the necessary components still presents some major technical problems, whereas the theoretical basis has made considerable advances. One can say, however, that there are no obstacles of a fundamental nature to the construction of a quantum computer. The future will show if and when quantum computing can surpass the power of conventional computers in the performance of specific tasks. In order to be able to follow the essential parts of the text, the reader will require a minimum knowledge of quantum mechanics. For most outsiders this is a book with seven seals. But in fact the basic principle is very simple, if a little unusual and counter-intuitive. I will try to make the most important aspects clear with the aid of examples. A minimum of familiarity with mathematics on the part of the reader will be assumed – mathematics is of course the fundamental language of physics. The central concept in quantum mechanics is the probaility amplitude, or simply amplitude, a concept which doesn’t exist in classical physics. Experience shows that this concept is essential for the understanding of such phenomena as interference and entanglement, phenomena which play a fundamental role in quantum cryptography and, above all, in quantum computing. The notes consist of three main sections: