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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Shor, P. W. in Proc. 35th IEEE Symp. on the Foundations of Computer Science (FOCS) 124–134 (IEEE Computer Society, 1994)
Shor, P. W. in Proc. 37th IEEE Symp. on the Foundations of Computing (FOCS) 56–65 (IEEE Computer Society, 1996)
Aliferis, P., Gottesman, D. & Preskill, J. Accuracy threshold for postselected quantum computation. Quant. Inform. Comput. 8, 181–244 (2008)
Zurek, W. H. Pointer basis of quantum apparatus: into what mixture does the wave packet collapse? Phys. Rev. D 24, 1516–1525 (1981)
Vandersypen, L. M. K. et al. Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance. Nature 414, 883–887 (2001)
Lanyon, B. P. et al. Experimental demonstration of a compiled version of Shor’s algorithm with quantum entanglement. Phys. Rev. Lett. 99, 250505 (2007)
Lu, C.-Y., Browne, D. E., Yang, T. & Pan, J.-W. Demonstration of a compiled version of Shor’s quantum factoring algorithm using photonic qubits. Phys. Rev. Lett. 99, 250504 (2007)
Politi, A., Matthews, J. C. F. & O’Brien, J. L. Shor’s quantum factoring algorithm on a photonic chip. Science 325, 1221 (2009)
Martín-López, E., Laing, A., Lawson, T., Zhou, X.-Q. & O’Brien, J. L. Experimental realization of Shor’s quantum factoring algorithm using qubit recycling. Nature Photon. 6, 773–776 (2012)
Lucero, E. Computing prime factors with a Josephson phase qubit quantum processor. Nature Phys. 8, 719–723 (2012)
Lenstra, A. K., Lenstra, H. W., Jr, Manasse, M. S. & Pollard, J. M. in Proc. 22nd Annual ACM Symp. on Theory of Computing (STOC) 564–572 (ACM Press, New York, 1990)
Zalka, C. Shor’s algorithm with fewer (pure) qubits. Preprint at http://arXiv.org/abs/quant-ph/0601097 (2006)
Mosca, M. & Ekert, A. in Quantum Computing and Quantum Communications (ed. Williams, C. P. ) 174–188 (Vol. 1509, Lecture Notes in Computer Science, Springer, 1999)
Parker, S. & Plenio, M. B. Efficient factorization with a single pure qubit and logN mixed qubits. Phys. Rev. Lett. 85, 3049–3052 (2000)
Griffiths, R. B. & Niu, C. S. Semiclassical Fourier transform for quantum computation. Phys. Rev. Lett. 76, 3228–3231 (1996)
Zhou, Z. & Geller, M. R. Factoring 51 and 85 with 8 qubits. Preprint at http://arXiv.org/abs/1304.0128 (2013)
Zi, S. The mathematical classic of Sun Zi. In Yong, L.-L. & Se, A.-T. Fleeting Footsteps: Tracing the Conception of Arithmetic and Algebra in Ancient China (World Scientific, 2004)
Heath, T. (ed) The Thirteen Books of Euclid's Elements (Dover, 1956)
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.
The authors declare no competing financial interests.
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Smolin, J., Smith, G. & Vargo, A. Oversimplifying quantum factoring. Nature 499, 163–165 (2013). https://doi.org/10.1038/nature12290
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