Improved quantum ripple-carry addition circuit

Science China Information Sciences volume 59, Article number: 042406 (2016) Cite this article

Abstract

A serious obstacle to large-scale quantum algorithms is the large number of elementary gates, such as the controlled-NOT gate or Toffoli gate. Herein, we present an improved linear-depth ripple-carry quantum addition circuit, which is an elementary circuit used for quantum computations. Compared with previous addition circuits costing at least two Toffoli gates for each bit of output, the proposed adder uses only a single Toffoli gate. Moreover, our circuit may be used to construct reversible circuits for modular multiplication, C x mod M with x < M, arising as components of Shor’s algorithm. Our modular-multiplication circuits are simpler than previous constructions, and may be used as primitive circuits for quantum computations.

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Author information

Affiliations

  1. College of mathematical sciences, Dezhou University, Dezhou, 253023, China

    Feng Wang

  2. Information Security and National Computing Grid Laboratory, Southwest Jiaotong University, Chengdu, 610031, China

    Mingxing Luo & Huiran Li

  3. Jiangsu Engineering Center of Network Monitoring, Nanjing University of Information Science & Technology, Nanjing, 210044, China

    Zhiguo Qu

  4. School of Electronic Engineering, Dublin City University, Dublin 9, Ireland

    Xiaojun Wang

Authors
  1. Feng Wang
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  2. Mingxing Luo
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  3. Huiran Li
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  4. Zhiguo Qu
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  5. Xiaojun Wang
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Corresponding author

Correspondence to Zhiguo Qu.

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Wang, F., Luo, M., Li, H. et al. Improved quantum ripple-carry addition circuit. Sci. China Inf. Sci. 59, 042406 (2016). https://doi.org/10.1007/s11432-015-5411-x

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Keywords

  • quantum addition circuit
  • modular multiplication
  • CNOT gate
  • Toffoli gate
  • circuit complexity