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Initializing the Amplitude Distribution of a Quantum State

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Foundations of Physics Letters

Abstract

To date, quantum computational algorithms have operated on a superposition of all basis states of a quantum system. Typically, this is because it is assumed that some function f is known and implementable as a unitary evolution. However, what if only some points of the function f are known? It then becomes important to be able to encode only the knowledge that we have about f. This paper presents an algorithm that requires a polynomial number of elementary operations for initializing a quantum system to represent only the m known points of a function f.

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References

  1. P. Shor, SIAM J. Compt. 26, 1484, (1997).

    Article  MathSciNet  Google Scholar 

  2. L. Grover, in Proceedings, 28th ACM Symposium on the Theory of Computing (Philadelphia), Gary L. Miller, ed. (ACM Press, 1996).

    Google Scholar 

  3. D. Simon, SIAM J. Comput. 26, 1474 (1997).

    Article  MathSciNet  Google Scholar 

  4. D. Deutsch and R. Jozsa, Proc. Roy. Soc. London Ser. A 439, 553 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  5. T. Hogg, J. Artificial Intelligence Research 4, 91 (1996).

    Google Scholar 

  6. B. M. Terhal and J. A. Smolin, Phys. Rev. A 58, 1822 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  7. E. Kushilevitz and Y. Mansour, SIAM J. Comput. 22, 1331 (1993).

    Article  MathSciNet  Google Scholar 

  8. J. Jackson, J. Computer and System Sciences 55, 414 (1997).

    Article  Google Scholar 

  9. N. H. Bshouty and J. Jackson, in Proceedings, 8th Annual Conference on Computational Learning Theory (Santa Cruz), Wolfgang Maass, ed. (ACM Press, 1995).

    Google Scholar 

  10. E. Fredkin and T. Toffoli, Internat. J. Theoret. Phys. 21, 219 (1982).

    Article  ADS  MathSciNet  Google Scholar 

  11. E. Bernstein and U. Vazirani, SIAM J. Comput. 26, 1411 (1997).

    Article  MathSciNet  Google Scholar 

  12. D. Deutsch, Proc. Roy. Soc. London Ser. A 425, 73 (1989).

    Article  ADS  MathSciNet  Google Scholar 

  13. D. Biron et al., in Proceedings, 1st NASA International Conference on Quantum Computing and Quantum Communications (Palm Springs), C.P. Williams, ed. (Lecture Notes in Computer Science 1509) (Springer, 1998).

    Google Scholar 

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Authors and Affiliations

  1. Neural Networks and Machine Learning Laboratory, Department of Computer Science, Brigham Young University, Provo, Utah, 84602

    Dan Ventura & Tony Martinez

Authors
  1. Dan Ventura
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  2. Tony Martinez
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Ventura, D., Martinez, T. Initializing the Amplitude Distribution of a Quantum State. Found Phys Lett 12, 547–559 (1999). https://doi.org/10.1023/A:1021695125245

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  • DOI: https://doi.org/10.1023/A:1021695125245

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