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Remarks on Quantum Modular Exponentiation and Some Experimental Demonstrations of Shor's Algorithm
An efficient quantum modular exponentiation method is indispensible for
Shor's factoring algorithm. But we find that all descriptions presented by
Shor, Nielsen and Chuang, Markov and Saeedi, et al., are flawed. We also remark
that some experimental demonstrations of Shor's algorithm are misleading,
because they violate the necessary condition that the selected number ,
where is the number of qubits used in the first register, must satisfy , where is the large number to be factored.Comment: 12 pages,5 figures. The original version has 6 pages. It did not
point out the reason that some researchers took for granted that quantum
modlar exponentiation is in polynomial time. In the new version, we indicate
the reason and analyze some experimental demonstrations of Shor's algorithm.
Besides, the author Zhenfu Cao is added to the version for his contribution.
arXiv admin note: text overlap with arXiv:1409.735
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