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Improved quantum ripple-carry addition circuit

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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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