## Cryptology ePrint Archive: Report 2014/828

Remarks on Quantum Modular Exponentiation and Some Experimental Demonstrations of Shor's Algorithm

Zhengjun Cao and Zhenfu Cao and Lihua Liu

Abstract: 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 $q=2^s$, where $s$ is the number of qubits used in the first register, must satisfy $n^2 \leq q < 2n^2$, where $n$ is the large number to be factored.

Category / Keywords: foundations / Shor's factoring algorithm; quantum modular exponentiation; superposition; continued fraction expansion.