Quantum networks for elementary arithmetic operations

Abstract

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 factorizing 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 factorized. \textcopyright{} 1996 The American Physical Society.