RYYGate

class RYYGate(theta)

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.
RYYGate.assemble()	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.
RYYGate.inverse()	Return inverse RYY gate (i.e.
RYYGate.is_parameterized()	Return True .IFF.
RYYGate.mirror()	For a composite instruction, reverse the order of sub-gates.
RYYGate.power(exponent)	Creates a unitary gate as gate^exponent.
RYYGate.qasm()	Return a default OpenQASM string for the instruction.
RYYGate.repeat(n)	Creates an instruction with gate repeated n amount of times.
RYYGate.to_matrix()	Return a Numpy.array for the gate unitary matrix.