Omar Gamel, Daniel F. V. James
Periodic functions are of special importance in quantum computing, particularly in applications of Shor's algorithm. We explore methods of creating circuits for periodic functions to better understand their properties. We introduce a method for constructing the circuit for the simplest periodic function, that is one-to-one within a single period, of a given period p. We conjecture that to create the simplest periodic function of period p, where p is an n-bit number, one needs at most n To?ffoli gates.
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http://arxiv.org/abs/1305.3642
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