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Quantum Counting: Algorithm and Error Distribution

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Abstract

Counting is one of the most basic procedures in mathematics and statistics. In statistics literature it is usually done via the proportion estimation method. In this article we manifest a radically different counting procedure first proposed in the late 1990’s based on the techniques of quantum computation. It combines two major tools in quantum computation, quantum Fourier transform and quantum amplitude amplification, and shares similar structure to the quantum part of the celebrated Shor’s factoring algorithm. We present complete details of this quantum counting algorithm and the analysis of its error distribution. Comparing it with the conventional proportion estimation method, we demonstrate that this quantum approach achieves much faster convergence rate than the classical approach.

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Notes

  1. In [8], they are misdefined to be the other way around.

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Acknowledgements

The first author was supported by an Ohio University Faculty Research Activity Fund. The second author was supported by National Science Foundation Award DMS 0808993. The third author was partially supported by a grant from the Scientific Research Foundation for the Returned Overseas Chinese Scholars, Ministry of Education of China.

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Authors and Affiliations

  1. Ohio University Eastern Campus, 45425 National Road West, St Clairsville, OH, 43950, USA

    Zijian Diao

  2. Department of Statistics, Indiana University-Bloomington, Statistics House, 309 North Park Ave, Bloomington, IN, 47408, USA

    Chunfeng Huang

  3. Department of Statistics, Fudan University, 670 Guoshun Road, Yangpu District, Shanghai, 200633, P.R. China

    Ke Wang

Authors
  1. Zijian Diao
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  2. Chunfeng Huang
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  3. Ke Wang
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Corresponding author

Correspondence to Zijian Diao.

Additional information

To Prof. Goong Chen on the occasion of his 60th birthday.

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Diao, Z., Huang, C. & Wang, K. Quantum Counting: Algorithm and Error Distribution. Acta Appl Math 118, 147–159 (2012). https://doi.org/10.1007/s10440-012-9682-6

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  • DOI: https://doi.org/10.1007/s10440-012-9682-6

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