# Toffoli gate a gate that uses 2 control qubits and one input qubit. It flips the input iff both control qubits are ones:$|a,b,c\rangle\rightarrow |a,b,c\oplus ab\rangle$ Properties: - $\text{Toffoli}\ket{a,b,0}=\ket{a,b,ab}$ i.e., it is multiplication function - $T=T^\dagger$ - $T$ permutes computational basis (convince yourself by checking its truth table) - It does not belong to [[Clifford group (quantum gates)]] ``` a: ───●─── │ b: ───●─── │ c: ───⊕─── ``` ## Created 2026-02-22 12:45