z ijSrSSKJr SSKJr SSKJr SSKJr SSK J r J r SSK J r "SS \5rg ) zTwo-qubit ZZ-rotation gate.) annotations)exp)Optional)Gate)ParameterValueTypeParameterExpression) StandardGatec^\rSrSrSr\R rS S U4SjjjrSr S SU4Sjjjr SSSjjr SSjr SSSjjr S rS rU=r$)RZZGateuA parametric 2-qubit :math:`Z \otimes Z` interaction (rotation about ZZ). This gate is symmetric, and is maximally entangling at :math:`\theta = \pi/2`. Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.rzz` method. Circuit symbol: .. code-block:: text q_0: ───■──── │zz(θ) q_1: ───■──── Matrix representation: .. math:: \newcommand{\rotationangle}{\frac{\theta}{2}} R_{ZZ}(\theta) = \exp\left(-i \rotationangle Z{\otimes}Z\right) = \begin{pmatrix} e^{-i \rotationangle} & 0 & 0 & 0 \\ 0 & e^{i \rotationangle} & 0 & 0 \\ 0 & 0 & e^{i \rotationangle} & 0 \\ 0 & 0 & 0 & e^{-i \rotationangle} \end{pmatrix} This is a direct sum of RZ rotations, so this gate is equivalent to a uniformly controlled (multiplexed) RZ gate: .. math:: R_{ZZ}(\theta) = \begin{pmatrix} RZ(\theta) & 0 \\ 0 & RZ(-\theta) \end{pmatrix} Examples: .. math:: R_{ZZ}(\theta = 0) = I .. math:: R_{ZZ}(\theta = 2\pi) = -I .. math:: R_{ZZ}(\theta = \pi) = - i Z \otimes Z .. math:: R_{ZZ}\left(\theta = \frac{\pi}{2}\right) = \frac{1}{\sqrt{2}} \begin{pmatrix} 1-i & 0 & 0 & 0 \\ 0 & 1+i & 0 & 0 \\ 0 & 0 & 1+i & 0 \\ 0 & 0 & 0 & 1-i \end{pmatrix} c(>[TU]SSU/US9 g)zQ Args: theta: The rotation angle. label: An optional label for the gate. rzz)labelN)super__init__)selfthetar __class__s c/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/circuit/library/standard_gates/rzz.pyrRZZGate.__init__\s E7%8cSSKJn UR[RR UR 5SURS9Ulg)zDefault definitionr)QuantumCircuitT) legacy_qubitsnameN) qiskit.circuitr_from_circuit_datar RZZ_get_definitionparamsr definition)rrs r_defineRZZGate._definedsC 2);;    , ,T[[ 9TXT]T]< rcf>Uc[SUR55n[TU] UUUUS9nU$)aCReturn a (multi-)controlled-RZZ gate. Args: num_ctrl_qubits: number of control qubits. label: An optional label for the gate [Default: ``None``] ctrl_state: control state expressed as integer, string (e.g.``'110'``), or ``None``. If ``None``, use all 1s. annotated: indicates whether the controlled gate should be implemented as an annotated gate. If ``None``, this is set to ``True`` if the gate contains free parameters, in which case it cannot yet be synthesized. Returns: ControlledGate: controlled version of this gate. c3B# UHn[U[5v M g7fN) isinstancer).0ps r "RZZGate.control..sT 1Jq*=>> s)num_ctrl_qubitsr ctrl_state annotated)anyr!rcontrol)rr-rr.r/gaters rr1RZZGate.controlrsE,  T TTIw+!    rc4[URS*5$)aReturn inverse RZZ gate (i.e. with the negative rotation angle). Args: annotated: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as the inverse of this gate is always a :class:`.RZZGate` with an inverted parameter value. Returns: RZZGate: inverse gate. r)r r!)rr/s rinverseRZZGate.inverses A''rc SSKnUSLa [S5eS[URS5-S- nUR [ U*5SSS/S[ U5SS/SS[ U5S/SSS[ U*5//US9$)z&Return a numpy.array for the RZZ gate.rNFz9unable to avoid copy while creating an array as requestedy?r)dtype)numpy ValueErrorfloatr!arrayr)rr8copyr9itheta2s r __array__RZZGate.__array__s 5=XY YuT[[^,,q0{{gX1a(CL!Q'As7|Q'Aq#wh-(     rc8URun[X-5$r')r!r )rexponentr/rs rpower RZZGate.powers;;x'((rcP[U[5(aURU5$g)NF)r(r _compare_parameters)rothers r__eq__RZZGate.__eq__s# eW % %++E2 2r)r"r')rrrz Optional[str])NNN)r-intrz str | Noner.zstr | int | Noner/z bool | None)F)r/bool)NN)rBr;r/rL)__name__ __module__ __qualname____firstlineno____doc__r r_standard_gaterr#r1r5r?rCrH__static_attributes__ __classcell__)rs@rr r s}?B"%%N99  ! '+!% %   B ( ")rr N)rQ __future__rcmathrtypingrqiskit.circuit.gater"qiskit.circuit.parameterexpressionrrqiskit._accelerate.circuitr r rrr\s*""$V3adar