Five two-qubit gates are necessary for implementing the Toffoli gate

@article{Yu2013FiveTG,
  title={Five two-qubit gates are necessary for implementing the Toffoli gate},
  author={N. Yu and Runyao Duan and M. Ying},
  journal={Physical Review A},
  year={2013},
  volume={88},
  pages={010304}
}
  • N. Yu, Runyao Duan, M. Ying
  • Published 2013
  • Physics
  • Physical Review A
  • In this paper, we settle the long-standing open problem of the minimum cost of two-qubit gates for simulating a Toffoli gate. More precisely, we show that five two-qubit gates are necessary. Before our work, it is known that five gates are sufficient and only numerical evidences have been gathered, indicating that the five-gate implementation is necessary. The idea introduced here can also be used to solve the problem of optimal simulation of three-qubit control phase introduced by Deutsch in… CONTINUE READING
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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 27 REFERENCES
    Quantum computation and quantum information
    • T. Paul
    • Mathematics, Computer Science
    • 2007
    • 7,660
    Quantum information and quantum computation
    • 8,277
    • Highly Influential
    Proc
    • 1989
    26
    • 1997
    Commun
    • 2002
    Int
    • 1982
    J
    • 307,583
    • PDF
    Lett
    • 2003
    On σ-Automata
    • 75