quantum gate directory
Square Root SWAP
Symbol
$\sqrt{\mathrm{SWAP}}$
Description:
Applies half of a SWAP interaction, creating maximal entanglement from a product state.
SDK Support
| SDK | Name |
|---|---|
| Qiskit | — |
| PennyLane | — |
| Cirq |
cirq.SwapPowGate
ⓘ
|
| Q# | — |
| PyQuil | — |
| Braket | — |
| BQSKit | — |
The $\sqrt{\mathrm{SWAP}}$ gate is the canonical maximally entangling two-qubit gate: a single application takes a product state to a maximally entangled state, and two applications recover the full SWAP.
$$ \sqrt{\mathrm{SWAP}} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & \frac{1+i}{2} & \frac{1-i}{2} & 0 \\ 0 & \frac{1-i}{2} & \frac{1+i}{2} & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} $$
Properties
- Maximally entangling: maps $|01\rangle \mapsto \tfrac{1+i}{2}|01\rangle + \tfrac{1-i}{2}|10\rangle$, a state with concurrence 1.
- Symmetric under exchange of qubits.
- Together with single-qubit rotations, forms a universal gate set.
- Weyl coordinates $(\frac{\pi}{8}, \frac{\pi}{8}, \frac{\pi}{8})$.
- Native gate on some spin-based and exchange-coupled hardware platforms.
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