Toffoli gate

In logic circuits, the Toffoli gate, also known as the CCNOT gate (“controlled-controlled-not”), invented by Tommaso Toffoli, is a CNOT gate with two control qubits and one target qubit. That is, the target qubit (third qubit) will be inverted if the first and second qubits are both 1. It is a universal reversible logic gate, which means that any classical reversible circuit can be constructed from Toffoli gates.

The truth table and matrix are as follows:

Truth table

Permutation matrix form

Input			Output
0	0	0	0	0	0
0	0	1	0	0	1
0	1	0	0	1	0
0	1	1	0	1	1
1	0	0	1	0	0
1	0	1	1	0	1
1	1	0	1	1	1
1	1	1	1	1	0

${\begin{bmatrix}1&0&0&0&0&0&0&0\\0&1&0&0&0&0&0&0\\0&0&1&0&0&0&0&0\\0&0&0&1&0&0&0&0\\0&0&0&0&1&0&0&0\\0&0&0&0&0&1&0&0\\0&0&0&0&0&0&0&1\\0&0&0&0&0&0&1&0\\\end{bmatrix}}$