Editing Quantum logic gate (section)

=== Swap gate ===
{{Further|List of quantum logic gates#Non-Clifford swap gates}}
[[Image:Swap gate.svg|upright=0.6|thumb|Circuit representation of SWAP gate]]
The swap gate swaps two qubits. With respect to the basis <math>|00\rangle</math>, <math>|01\rangle</math>, <math>|10\rangle</math>, <math>|11\rangle</math>, it is represented by the matrix

:<math> \mbox{SWAP} = \begin{bmatrix} 1&0&0&0\\0&0&1&0\\0&1&0&0\\0&0&0&1\end{bmatrix} . </math>
The swap gate can be decomposed into summation form:

:<math>\mbox{SWAP}=\frac{I\otimes I +X\otimes X+Y\otimes Y+Z\otimes Z}{2}</math>

{{Anchor|Toffoli gate|Toffoli|CCNOT}}