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Oversimplifying quantum factoring


Shor’s quantum factoring algorithm exponentially outperforms known classical methods. Previous experimental implementations have used simplifications dependent on knowing the factors in advance. However, as we show here, all composite numbers admit simplification of the algorithm to a circuit equivalent to flipping coins. The difficulty of a particular experiment therefore depends on the level of simplification chosen, not the size of the number factored. Valid implementations should not make use of the answer sought.

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Figure 1: Circuit for Shor’s algorithm using the semi-classical quantum Fourier transform.
Figure 2: The circuit for the fully compiled Shor’s algorithm.
Figure 3: Experimental data from unbiased coins.


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We acknowledge support from IARPA (contract no. W911NF-10-1-0324) and from the DARPA QUEST programme (contract no. HR0011-09-C-0047). All statements of fact, opinion or conclusions contained herein are those of the authors and should not be construed as representing the official views or policies of the US Government.

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J.A.S., G.S. and A.V. designed and carried out the research. G.S. performed the experiments, J.A.S. analysed the data, and A.V. carried out the number theory. J.A.S., G.S. and A.V. wrote the paper.

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Correspondence to John A. Smolin.

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The authors declare no competing financial interests.

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Supplementary Information

This file contains N-20000, a 20,000-bit number of our own creation. (PDF 96 kb)

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Smolin, J., Smith, G. & Vargo, A. Oversimplifying quantum factoring. Nature 499, 163–165 (2013).

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