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# Implementation of a quantum search algorithm on a quantum computer

## Abstract

In 1982 Feynman1 observed that quantum-mechanical systems have an information-processing capability much greater than that of corresponding classical systems, and could thus potentially be used to implement a new type of powerful computer. Three years later Deutsch2 described a quantum-mechanical Turing machine, showing that quantum computers could indeed be constructed. Since then there has been extensive research in this field, but although the theory is fairly well understood, actually building a quantum computer has proved extremely difficult. Only two methods have been used to demonstrate quantum logic gates: ion traps3,4 and nuclear magnetic resonance (NMR)5,6. NMR quantum computers have recently been used to solve a simple quantum algorithm—the two-bit Deutsch problem7,8. Here we show experimentally that such a computer can be used to implement a non-trivial fast quantum search algorithm initially developed by Grover9,10, which can be conducted faster than a comparable search on a classical computer.

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## References

1. Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982).

2. Deutsch, D. Quantum-theory, the Church–Turing principle and the universal quantum computer. Proc. R. Soc. Lond. A 400, 97–117 (1985).

3. Cirac, J. I. & Zoller, P. Quantum computations with cold trapped ions. Phys. Rev. Lett. 74, 4091–4094 (1995).

4. Monroe, C., Meekhof, D. M., King, B. E., Itano, W. M. & Wineland, D. J. Demonstration of a fundamental quantum logic gate. Phys. Rev. Lett. 75, 4714–4715 (1995).

5. Cory, D. G., Fahmy, A. F. & Havel, T. F. Ensemble quantum computing by NMR spectroscopy. Proc. Natl Acad. Sci. USA 94, 1634–1639 (1997).

6. Gershenfeld, N. A. & Chuang, I. L. Bulk spin-resonance quantum computation. Science 275, 350–356 (1997).

7. Jones, J. A. & Mosca, M. Implementation of a quantum algorithm to solve Deutsch's problem on a nuclear magnetic resonance quantum computer. J. Chem. Phys. (in the press); also LANL preprint quant-ph/9801027.

8. Chuang, I. L., Vandersypen, L. M. K., Zhou, X., Leung, D. W. & Lloyd, S. Experimental realization of a quantum algorithm. Nature 393, 143–146 (1998); also LANL preprint quant-ph/9801037.

9. Grover, L. K. in Proc. 28th Annual ACM Symp. on Theory of Computation 212–218 (ACM, New York, (1996)).

10. Grover, L. K. Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79, 325–328 (1997).

11. Boyer, M., Brassard, G., Høyer, P. & Tapp, A. in Proc. 4th Workshop on Physics and Computation—PhysComp '96 (eds Toffoli, T., Biafore, M. & Leão, J.) 36–41 (New England Complex Systems Institute, Boston, MA, (1996)).

12. Chuang, I. L., Gershenfeld, N. & Kubinec, M. Experimental implementation of fast quantum searching. Phys. Rev. Lett. 80, 3408–3411 (1998).

13. Laflamme, R., Knill, E., Zurek, W. H., Catasti, P. & Mariappan, S. V. S. NMR GHZ Proc. R. Soc. Lond. A (in the press).

## Acknowledgements

We thank A. Ekert for discussions; J.A.J. thanks C. M. Dobson for encouragement. This is a contribution from the Oxford Centre for Molecular Sciences, which is supported by the UK EPSRC, BBSRC and MRC. M.M. thanks CESG (UK) for their support. R.H.H. thanks the Danish Research Academy for financial assistance.

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Correspondence to Jonathan A. Jones.

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Jones, J., Mosca, M. & Hansen, R. Implementation of a quantum search algorithm on a quantum computer. Nature 393, 344–346 (1998). https://doi.org/10.1038/30687

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• DOI: https://doi.org/10.1038/30687

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