SWAP Gate

Last updated Jun 24, 2022

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The SWAP gate simply swaps the two qubits: $$\begin{aligned}
SWAP\ket{00} &= \ket{00}, \
SWAP\ket{01} &= \ket{10}, \
SWAP\ket{10} &= \ket{01}, \
SWAP\ket{11} &= \ket{11}.
\end{aligned}$$
In other words, $$SWAP\ket a \ket b = \ket b \ket a.$$

• Chapter 4 - Multiple Quantum Bits > Two-Qubit Quantum Gates

• This gate cannot produce Entanglement because if the qubits are in a produce state, swapping the factors results in a product state.