quantum gate directory
$yy$ Rotation
Symbol
$R_{yy}$
Description:
Two-qubit rotation generated by $Y \otimes Y$.
Alternate notations:
- $R_{yy}(\theta)$
- $\mathrm{RYY}(\theta)$
- $YY(\theta)$
SDK Support
| SDK | Name |
|---|---|
| Qiskit |
qiskit.circuit.library.RYYGate
|
| PennyLane |
pennylane.IsingYY
|
| Cirq |
cirq.YYPowGate
ⓘ
|
| Q# | — |
| PyQuil | — |
| Braket | — |
| BQSKit | — |
The $R_{yy}$ gate rotates in the $YY$ interaction basis by angle $\theta$.
$$ \begin{align*} R_{yy}(\theta) & = \exp\left(-i\frac{\theta}{2}Y\otimes Y\right) \\ & = \begin{bmatrix} \cos\frac{\theta}{2} & 0 & 0 & i\sin\frac{\theta}{2} \\ 0 & \cos\frac{\theta}{2} & -i\sin\frac{\theta}{2} & 0 \\ 0 & -i\sin\frac{\theta}{2} & \cos\frac{\theta}{2} & 0 \\ i\sin\frac{\theta}{2} & 0 & 0 & \cos\frac{\theta}{2} \end{bmatrix} \end{align*} $$
Properties
- Entangling for $\theta$ that are not an integer multiple of $\pi$.
- Related to $R_{xx}$ by single-qubit phase rotations: $R_{yy}(\theta) = (S \otimes S),R_{xx}(\theta),(S^\dagger \otimes S^\dagger)$.
- Generated by a $YY$ interaction Hamiltonian.
Usage
- Entangling layers in variational algorithms.
- Basis-changed implementations of $XX$ or $ZZ$ couplings.
Back to home