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Entanglement in Phase Estimation Algorithm and Quantum Counting Algorithm

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Abstract

For some certain problems, quantum algorithms are theoretically able to solve them quickly than classical algorithms. But the role of entanglement in achieving the quantum computational speedup is not fully understood. By theoretical analysis and numerical calculation of four practical use cases, we investigate the entanglement features of the quantum states employed in quantum phase estimation algorithm and quantum counting algorithm. The results show that whether these two algorithms generate entanglement depend on whether the input quantum state of the second register is a superposition state of the eigenstates.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 61170321,61502101,61871120,61802002), Natural Science Foundation of Jiangsu Province, China (Grant No. BK20140651), Natural Science Foundation of Anhui Province, China (Grant No. 1608085MF129), Research Fund for the Doctoral Program of Higher Education (Grant No. 20110092110024), Foundation for Natural Science Major Program of Education Bureau of Anhui Province (Grant No. KJ2015ZD09) and the open fund of Key Laboratory of Computer Network and Information Integration in Southeast University, Ministry of Education, China (Grant No. K93-9-2015-10C).

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Authors and Affiliations

  1. School of Computer Science and Engineering, Southeast University, Nanjing, 210096, China

    Jianing Tan, Zhihao Liu & Hanwu Chen

  2. Key Laboratory of Computer Network and Information Integration In Southeast University, Ministry of Education, Nanjing, 210096, China

    Zhihao Liu & Hanwu Chen

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  1. Jianing Tan
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  2. Zhihao Liu
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  3. Hanwu Chen
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Correspondence to Zhihao Liu or Hanwu Chen.

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Tan, J., Liu, Z. & Chen, H. Entanglement in Phase Estimation Algorithm and Quantum Counting Algorithm. Int J Theor Phys 59, 1372–1381 (2020). https://doi.org/10.1007/s10773-019-04341-y

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