I get occasional mail from people asking me about quantum arithmetic. I usually point them to the Qwiki page on arithmetic I created a couple of years ago, which is a list of useful papers, rather than an actual technical description.
Most of the papers there are about specific arithmetic circuits, building from binary integer addition to modular exponentiation, and include some examples of actual experimental implementations.
This morning, I ran across some lecture notes by Ekert, Hayden, and Inamori on "Basic concepts in quantum computation," at Quantiki. The notes contain a nice intro to the theory behind reversible, binary, modular arithmetic.
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