User:Jaydavidmartin/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:

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

The quantum circuit symbol for the SWAP gate is:

SWAP gate symbol

Operation

The application of quantum gates to qubits corresponds to matrix multiplication. Hence, the application of SWAP to the state $|\psi \rangle$ of a two-qubit quantum register is represented by the matrix multiplaction SWAP$|\psi \rangle$. 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$|11\rangle$=$|11\rangle$

See also

• Quantum computing
• Quantum logic gate
• Quantum circuit