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Quantum Adder for Superposition States

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Abstract

Quantum superposition is one of the essential features that make quantum computation surpass classical computation in space complexity and time complexity. However, it is a double-edged sword. For example, it is troublesome to add all the numbers stored in a superposition state. The usual solution is taking out and adding the numbers one by one. If there are \(2^{n}\) numbers, the complexity of this scheme is \(O(2^{n})\) which is the same as the complexity of the classical scheme \(O(2^{n})\). Moreover, taking account to the current physical computing speed, quantum computers will have no advantage. In order to solve this problem, a new method for summing all numbers in a quantum superposition state is proposed in this paper, whose main idea is that circularly shifting the superposition state and summing the new one with the original superposition state. Our scheme can effectively reduce the time complexity to \(O(n)\).

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Acknowledgments

This work is supported by the National Natural Science Foundation of China under Grants No. 61502016, and the Joint Open Fund of Information Engineering Team in Intelligent Logistics under Grants No. LDXX2017KF152.

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Authors and Affiliations

  1. Faculty of Information Technology, Beijing University of Technology, Beijing, 100124, China

    Xiaowei Lu, Nan Jiang, Hao Hu & Zhuoxiao Ji

  2. School of Information Science and Technology, Linyi University, Linyi, 276000, China

    Nan Jiang

  3. Beijing Key Laboratory of Trusted Computing, Beijing, 100124, China

    Nan Jiang

  4. National Engineering Laboratory for Critical Technologies of Information Security Classified Protection, Beijing, 100124, China

    Nan Jiang

Authors
  1. Xiaowei Lu
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  2. Nan Jiang
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  3. Hao Hu
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  4. Zhuoxiao Ji
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Corresponding author

Correspondence to Nan Jiang.

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Lu, X., Jiang, N., Hu, H. et al. Quantum Adder for Superposition States. Int J Theor Phys 57, 2575–2584 (2018). https://doi.org/10.1007/s10773-018-3779-2

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  • DOI: https://doi.org/10.1007/s10773-018-3779-2

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