Abstract
Computation has long been deriving force in the development of mathematics in general and in number theory in particular. Many of the great theorems such as the Prime Number Theorem and conjectures such as the Riemann hypothesis and the BSD (Birch and Swinnerton-Dyer) conjecture, are rooted and motivated from the computational experiments. So computation is the main ingredient and component of both computational number theory and quantum computational number theory. In this chapter, we shall give an account of the basic concepts and results in both classical and quantum computation theories, that will be used in the rest of the book.
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