Quantum Networks for Elementary Arithmetic Operations

Quantum computers require quantum arithmetic. We provide an explicit
construction of quantum networks effecting basic arithmetic operations: from
addition to modular exponentiation. Quantum modular exponentiation seems to be
the most difficult (time and space consuming) part of Shor's quantum
factorising algorithm. We show that the auxiliary memory required to perform
this operation in a reversible way grows linearly with the size of the number
to be factorised.