ABSTRACT
The use of light as a physical medium to perform complex mathematical transformations has a long history. The possibility to efficiently implement quantum algorithms using this purely electromagnetic “material”, however, has only recently been recognized [39]. Our goal in this chapter is to make the non-specialist familiar both with the basic methods and with the particular language used in this context. Although we have tried to compile a more or less comprehensive and updated bibliographical list, this collection is mainly aimed to help readers rapidly acquire most of the pertinent literature in an efficient way. This chapter is not a review, but rather an introduction to the subject. Instead of presenting the most recent and elaborate ideas, here we will provide a basic introduction for the newcomer. It will contain most of the ingredients necessary for a deeper study of the literature and for the development of new ideas. Simple situations are better suited for the comprehension of fundamental concepts, and it is in this spirit that our choice of illustrative examples has been made. Special attention has also been paid to clarify the oftentimes confusing, heterogeneous use of notational conventions and terminology by different authors.
