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.

Representation

The SWAP gate is represented by the 4x4 unitary matrix:

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

Operation

The application of quantum gates to qubits corresponds to matrix multiplication. Hence, the application of SWAP to a two-qubit quantum register $|\psi \rangle$ is denoted by the matrix multiplaction SWAP$|\psi \rangle$. For example, on the computational basis states $|00\rangle$, $|01\rangle$, $|10\rangle$, and $|11\rangle$.

See also

• Quantum computing
• Quantum logic gate
• Quantum circuit