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Five Two-Qubit Gates Are Necessary for Implementing Toffoli Gate

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arxiv 1301.3372 v1 pith:L5UYZTMA submitted 2013-01-15 quant-ph

Nengkun Yu , Runyao Duan , Mingsheng Ying This is my paper · ORCID
classification quant-ph
keywords gatesfivenecessarytwo-qubitgateintroducedproblemtoffoli
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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.

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  1. Witnessing the architecture of quantum circuits

    quant-ph 2026-08 conditional novelty 6.0 of 10

    A witness framework certifies when a unitary cannot be realized by a prescribed quantum circuit architecture, with SDP and LP relaxations and analytical Clifford bounds.

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