20 December 2001. Thanks to SD.
Related news reports:
http://www.nytimes.com/2001/12/20/science/20QUAN.html
See also Lov Grover's excellent description of quantum computing:
http://cryptome.org/qc-grover.htm
Nature magazine has published today:
by Lieven M. K. Vandersypen*†, Matthias Steffen*†, Gregory Breyta*, Costantino S. Yannoni*, Mark H. Sherwood* & Isaac L. Chuang*†
* IBM Almaden Research Center, San Jose, California 95120, USA
† Solid State and Photonics Laboratory, Stanford University, Stanford,
California 94305-4075, USA
[Abstract]
The number of steps any classical computer requires in order to find the prime factors of an l-digit integer N increases exponentially with l, at least using algorithms known at present1. Factoring large integers is therefore conjectured to be intractable classically, an observation underlying the security of widely used cryptographic codes1, 2. Quantum computers3, however, could factor integers in only polynomial time, using Shor's quantum factoring algorithm4-6. Although important for the study of quantum computers7, experimental demonstration of this algorithm has proved elusive8-10. Here we report an implementation of the simplest instance of Shor's algorithm: factorization of N = 15 (whose prime factors are 3 and 5). We use seven spin-1/2 nuclei in a molecule as quantum bits11, 12, which can be manipulated with room temperature liquid-state nuclear magnetic resonance techniques. This method of using nuclei to store quantum information is in principle scalable to systems containing many quantum bits13, but such scalability is not implied by the present work. The significance of our work lies in the demonstration of experimental and theoretical techniques for precise control and modelling of complex quantum computers. In particular, we present a simple, parameter-free but predictive model of decoherence effects14 in our system.
References
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| 2. | Koblitz, N. A Course in Number Theory and Cryptography (Springer, New York, 1994). |
| 3. | Bennett, C. H. & DiVincenzo, D. P. Quantum information and computation. Nature 404, 247-255 (2000). | Article | PubMed | ISI | |
| 4. | Shor, P. in Proc. 35th Annu. Symp. on the Foundations of Computer Science (ed. Goldwasser, S.) 124-134 (IEEE Computer Society Press, Los Alamitos, California, 1994). |
| 5. | Shor, P. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484-1509 (1997). | ISI | |
| 6. | Ekert, A. & Jozsa, R. Quantum computation and Shor's factoring algorithm. Rev. Mod. Phys. 68(3), 733-753 (1996). | ISI | |
| 7. | Beckman, D., Chari, A. N., Devabhaktuni, S. & Preskill, J. Efficient networks for quantum factoring. Phys. Rev. A 54, 1034-1063 (1996). | Article | PubMed | ISI | |
| 8. | Jones, J. A. NMR quantum computation. Prog. NMR Spectrosc. 38, 325-360 (2001). | ISI | |
| 9. | Vandersypen, L. M. K. et al. Experimental realization of an order-finding algorithm with an NMR quantum computer. Phys. Rev. Lett. 85, 5452-5455 (2000). | Article | PubMed | ISI | |
| 10. | Knill, E., Laflamme, R., Martinez, R. & Tseng, C.-H. An algorithmic benchmark for quantum information processing. Nature 404, 368-370 (2000). | Article | PubMed | ISI | |
| 11. | Gershenfeld, N. & Chuang, I. L. Bulk spin-resonance quantum computation. Science 275, 350-356 (1997). | Article | PubMed | ISI | |
| 12. | Cory, D. G., Fahmy, A. F. & Havel, T. F. Ensemble quantum computing by NMR spectroscopy. Proc. Natl Acad. Sci. 94, 1634-1639 (1997). | PubMed | ISI | |
| 13. | Schulman, L. & Vazirani, U. in Proc. 31st ACM Symp. on Theory of Computing 322-329 (Association for Computing Machinery, New York, 1999). |
| 14. | Chuang, I. L., Laflamme, R., Shor, P. & Zurek, W. H. Quantum computers, factoring, and decoherence. Science 270, 1633-1635 (1995). | ISI | |
Acknowledgements. We thank X. Zhou and J. Preskill for discussions, J. Smolin for the use of his IBM workstation, D. Miller for help with spectral analysis, A. Schwartz and his team for their technical assistance, and J. Harris, W. Risk and H. Coufal for their support. L.V. acknowledges a Yansouni Family Stanford graduate fellowship. This work was supported in part by the QuARC project under a DARPA Quantum Information Science and Technology grant.
Cryptome has purchased a copy of the 5-page article for $15.00 and makes it available to those who cannot afford to buy it -- but only until Nature, a most distinguished public interest journal, politely asks to stop doing it.
http://cryptome.org/shor-nature.pdf (390KB)