SWAP¶
The SWAP gate exchanges the states of two qubits - whatever q[0] held, q[1] now holds, and vice versa.
| Qubits | 2 |
| Parameters | None |
| Inverse | Itself (SWAP² = I) |
| Also called | SWAP |
What it does¶
SWAP leaves \( |00\rangle \) and \( |11\rangle \) unchanged (swapping identical values does nothing) and exchanges \( |01\rangle \) and \( |10\rangle \). It works the same way on superpositions and entangled states, not just definite basis states.
Matrix¶
\[
\text{SWAP} = \begin{pmatrix}
1&0&0&0\\
0&0&1&0\\
0&1&0&0\\
0&0&0&1
\end{pmatrix}
\]
Action on basis states¶
- \( |00\rangle \rightarrow |00\rangle \)
- \( |01\rangle \rightarrow |10\rangle \)
- \( |10\rangle \rightarrow |01\rangle \)
- \( |11\rangle \rightarrow |11\rangle \)
Example¶
On the circuit canvas, SWAP is drawn as an ✕ mark on each of the two wires it connects - see Multi-qubit gate symbols.
Other notations¶
Naming conventions across ecosystems; exact syntax can vary by library version, and this does not claim to be Qompile's generated output unless otherwise noted.
| Language | Typical form |
|---|---|
| OpenQASM 2.0 | swap q[0], q[1]; |
| Qiskit | circuit.swap[q[0], q[1]] |
| Cirq | cirq.SWAP(q[0], q[1]) |
| Q# | SWAP(q[0], q[1]); |