Quantum Networks for Elementary Arithmetic Operations

Physics – Quantum Physics

Scientific paper

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7 pages, LaTeX, + 6 PS figures in a tar compressed file. See also http://eve.physics.ox.ac.uk/QChome.html

Scientific paper

10.1103/PhysRevA.54.147

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.

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