# RYYGate¶

class RYYGate(theta)[source]

A parameteric 2-qubit $$Y \otimes Y$$ interaction (rotation about YY).

This gate is symmetric, and is maximally entangling at $$\theta = \pi/2$$.

Circuit Symbol:

     ┌─────────┐
q_0: ┤1        ├
│  Ryy(ϴ) │
q_1: ┤0        ├
└─────────┘


Matrix Representation:

\begin{align}\begin{aligned}\newcommand{\th}{\frac{\theta}{2}}\\\begin{split}R_{YY}(\theta) = exp(-i \th Y{\otimes}Y) = \begin{pmatrix} \cos(\th) & 0 & 0 & i\sin(\th) \\ 0 & \cos(\th) & -i\sin(\th) & 0 \\ 0 & -i\sin(\th) & \cos(\th) & 0 \\ i\sin(\th) & 0 & 0 & \cos(\th) \end{pmatrix}\end{split}\end{aligned}\end{align}

Examples:

$R_{YY}(\theta = 0) = I$
$R_{YY}(\theta = \pi) = i Y \otimes Y$
$\begin{split}R_{YY}(\theta = \frac{\pi}{2}) = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & 0 & 0 & i \\ 0 & 1 & -i & 0 \\ 0 & -i & 1 & 0 \\ i & 0 & 0 & 1 \end{pmatrix}\end{split}$

Create new RYY gate.

Attributes

 RYYGate.decompositions Get the decompositions of the instruction from the SessionEquivalenceLibrary. RYYGate.definition Return definition in terms of other basic gates. RYYGate.label Return gate label RYYGate.params return instruction params.

Methods

 RYYGate.add_decomposition(decomposition) Add a decomposition of the instruction to the SessionEquivalenceLibrary. Assemble a QasmQobjInstruction RYYGate.broadcast_arguments(qargs, cargs) Validation and handling of the arguments and its relationship. RYYGate.c_if(classical, val) Add classical condition on register classical and value val. RYYGate.control([num_ctrl_qubits, label, …]) Return controlled version of gate. RYYGate.copy([name]) Copy of the instruction. Return inverse RYY gate (i.e. Return True .IFF. DEPRECATED: use instruction.reverse_ops(). RYYGate.power(exponent) Creates a unitary gate as gate^exponent. Return a default OpenQASM string for the instruction. Creates an instruction with gate repeated n amount of times. For a composite instruction, reverse the order of sub-instructions. Return a numpy.array for the RYY gate.