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Quantum partial search algorithm with smaller oracles for multiple target items

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Abstract

Quantum search is one kind of the most important quantum algorithms, which is the only threat to postquantum cryptography till now. In this paper, we consider the problem of partial searching, where we are interested in part of the information of the item being searched. Then, we present the quantum partial search algorithm with smaller oracles, which reduces the difficulty of designing oracles without errors. The time complexity of this algorithm is smaller than that of the Grover search algorithm in practical instances. Furthermore, we present a punctuated version of the quantum partial search algorithm with smaller oracles to make the algorithm more practical by decreasing the number of iterations further. The punctuated algorithm could be running on several quantum computers in parallel. Taking these factors into consideration, the quantum partial search algorithm with smaller oracles for multiple target items is practical for running on a quantum computer and solving many real problems, such as the Hamiltonian circuit problem and solving systems of nonlinear equations.

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Acknowledgements

This work is supported by NSFC (Grant Nos. 61701229, 61901218, 62071015), Natural Science Foundation of Jiangsu Province, China (Grant No. BK20190407), China Postdoctoral Science Foundation funded Project (Grant Nos. 2018M630557, 2018T110499), Jiangsu Planned Projects for Postdoctoral Research Funds (Grant No. 1701139B), the Beijing Natural Science Foundation (Grant No. 4162005) and the Open Fund of the State Key Laboratory of Cryptology (Grant No. MMKFKT201914).

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Authors and Affiliations

  1. College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Dan Li, Ling Qian & Yu-Qian Zhou

  2. State Key Laboratory of Cryptology, P.O.Box 5159, Beijing, 100878, China

    Yu-Qian Zhou

  3. Faculty of Information Technology, Beijing University of Technology, Beijing, China

    Yu-Guang Yang

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  1. Dan Li
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  2. Ling Qian
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  4. Yu-Guang Yang
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Correspondence to Dan Li or Yu-Qian Zhou.

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Li, D., Qian, L., Zhou, YQ. et al. Quantum partial search algorithm with smaller oracles for multiple target items. Quantum Inf Process 21, 160 (2022). https://doi.org/10.1007/s11128-022-03496-8

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