quantum gate directory
SWAP Gate
Symbol
$\mathrm{SWAP}$
Description:
The SWAP gate exchanges the states of two qubits. It is commonly used in quantum circuits to reorder qubits or facilitate interactions between qubits that are not directly connected.
| Notation(s) | $\mathrm{SWAP}$ |
| Matrix | $\begin{bmatrix}1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$ |
| Arity | 2 |
| Group | $\mathsf{U}(4)$ |
Properties
- Reversible: The SWAP gate is its own inverse, i.e., $\mathrm{SWAP} \cdot \mathrm{SWAP} = I$. Or put differently, the gate is self-adjoint.
- Decomposition: The SWAP gate can be decomposed into three CNOT gates: $\mathrm{SWAP} = \mathrm{CNOT}_{12} \cdot \mathrm{CNOT}_{21} \cdot \mathrm{CNOT}_{12}$
Applications
- Reordering qubits in a circuit.
- Facilitating interactions between qubits in hardware with limited connectivity.
Groups
This gate is contained in the following groups:
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