# 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} }

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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