User:Jaydavidmartin/Swap gate

Circuit representation of SWAP gate

The SWAP gate is a two-qubit quantum logic gate that swaps the states of two qubits.

Operation

The SWAP gate operates on a quantum register of two qubits. The SWAP gates swaps the states of the two qubits. For example, on the computational basis states $|00\rangle$, $|01\rangle$, $|10\rangle$, and $|11\rangle$:

SWAP$|00\rangle$=$|00\rangle$

SWAP$|01\rangle$=$|10\rangle$

SWAP$|10\rangle$=$|01\rangle$

SWAP$|11\rangle$=$|11\rangle$

In permutation matrix form, the SWAP gate is represented by the 4x4 unitary matrix:

${\mbox{SWAP}}:={\begin{bmatrix}1&0&0&0\\0&0&1&0\\0&1&0&0\\0&0&0&1\end{bmatrix}}$.

Hence, on a more general arbitrary superposition $a|00\rangle +b|01\rangle +c|10\rangle +d|11\rangle$,

SWAP$a|00\rangle +b|01\rangle +c|10\rangle +d|11\rangle$ =

See also

• Quantum computing
• Quantum logic gate
• Quantum circuit