quantum gate directory

Qubits: $2$ Parameters: $1$

SDK Support

SDK	Name
Qiskit	qiskit.circuit.library.RYYGate
PennyLane	pennylane.IsingYY
Cirq	cirq.YYPowGate ⓘ
Q#	Std.Intrinsic.Ryy
PyQuil	pyquil.simulation.matrices.RYY ⓘ
Braket	braket.circuits.gates.YY
BQSKit	bqskit.ir.gates.RYYGate
Qibo	qibo.gates.RYY
pytket	pytket.circuit.OpType.YYPhase ⓘ
Stim	SQRT_YY ⓘ
OpenQASM	—

Groups

This gate is contained in the following groups:

• matchgate

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.