English

Five Two-Qubit Gates Are Necessary for Implementing Toffoli Gate

Quantum Physics 2013-09-24 v1

Abstract

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 1989.

Keywords

Cite

@article{arxiv.1301.3372,
  title  = {Five Two-Qubit Gates Are Necessary for Implementing Toffoli Gate},
  author = {Nengkun Yu and Runyao Duan and Mingsheng Ying},
  journal= {arXiv preprint arXiv:1301.3372},
  year   = {2013}
}

Comments

5 Pages, comments welcome

R2 v1 2026-06-21T23:09:43.534Z