On the CNOT-cost of TOFFOLI gates

@article{Shende2009OnTC,
  title={On the CNOT-cost of TOFFOLI gates},
  author={Vivek V. Shende and Igor L. Markov},
  journal={Quantum Inf. Comput.},
  year={2009},
  volume={9},
  pages={461-486}
}
The three-input TOFFOLI gate is the workhorse of circuit synthesis for classical logic oper-ations on quantum data, e.g., reversible arithmetic circuits. In physical implementations,however, TOFFOLI gates are decomposed into six CNOT gates and several one-qubit gates.Though this decomposition has been known for at least 10 years, we provide here thefirst demonstration of its CNOT-optimality. We study three-qubit circuits which containless than six CNOT gates and implement a block-diagonal… 

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