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By J. C. Jaeger

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NORDHOLT, J. , AND PETERSON, C. G. 1999. Practical Quantum Cryptography for Secure Free-Space Communications. gov/abs/ quant-ph/9905009. HUGHES, R. , BUTTLER, W. , KWIAT, P. , LUTHER, G. , MORGAN, G. , NORDHOLT, J. , PETERSON, C. , AND SIMMONS, C. M. 1997. Secure communications using quantum cryptography. In S. P. HOTALING AND A. R. , Photonic Quantum Computing, Vol. 3076, 2–11. HUNGERFORD, T. A. 1974. Algebra. Springer Verlag, New York, Heidelberg, Berlin. JONES, J. A. AND MOSCA, M. 1998. Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer.

An Introduction to the Theory of Numbers. Oxford University Press. HOGG, T. 1996. Quantum computing and phase transitions in combinatorial search. Journal of Artificial Intelligence Research 4, 91– 128. gov/abs/quant-ph/ 9508012. HOGG, T. 1998. Highly structured searches with quantum computers. Physical Review Letters 80, 2473–2473. HUGHES, R. , BUTTLER, W. , KWIAT, P. , LAMOREAUX, S. , MORGAN, G. , NORDHOLT, J. , AND PETERSON, C. G. 1999. Practical Quantum Cryptography for Secure Free-Space Communications.

ACKNOWLEDGMENTS The authors would like to thank Tad Hogg and Carlos Mochon for many enjoyable conversations about quantum computing and for their feedback on an earlier draft of this paper. We are also grateful to Lee Corbin, David Goldberg, Lov Grover, Norman Hardy, Vaughan Pratt, Marc Rieffel, and the anonymous referees for detailed comments on earlier drafts of this paper. Finally, we would like to thank FXPAL for enthusiastically supporting this work. REFERENCES ABRAMS, D. S. AND LLOYD, S. 1998.

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