z i`fSrSSKJr SSKrSSKJr SSKJr SSKJ r J r SSK J r "SS \5r g) zTwo-qubit ZX-rotation gate.) annotationsN)Optional)Gate)ParameterValueTypeParameterExpression) StandardGatec^\rSrSrSr\R rS S U4SjjjrSr S SU4Sjjjr SSSjjr SSjr SSSjjr S rS rU=r$)RZXGateu! A parametric 2-qubit :math:`Z \otimes X` interaction (rotation about ZX). This gate is maximally entangling at :math:`\theta = \pi/2`. The cross-resonance gate (CR) for superconducting qubits implements a ZX interaction (however other terms are also present in an experiment). Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.rzx` method. Circuit symbol: .. code-block:: text ┌─────────┐ q_0: ┤0 ├ │ Rzx(θ) │ q_1: ┤1 ├ └─────────┘ Matrix representation: .. math:: \newcommand{\rotationangle}{\frac{\theta}{2}} R_{ZX}(\theta)\ q_0, q_1 = \exp\left(-i \frac{\theta}{2} X{\otimes}Z\right) = \begin{pmatrix} \cos\left(\rotationangle\right) & 0 & -i\sin\left(\rotationangle\right) & 0 \\ 0 & \cos\left(\rotationangle\right) & 0 & i\sin\left(\rotationangle\right) \\ -i\sin\left(\rotationangle\right) & 0 & \cos\left(\rotationangle\right) & 0 \\ 0 & i\sin\left(\rotationangle\right) & 0 & \cos\left(\rotationangle\right) \end{pmatrix} .. note:: In Qiskit's convention, higher qubit indices are more significant (little endian convention). In the above example we apply the gate on (q_0, q_1) which results in the :math:`X \otimes Z` tensor order. Instead, if we apply it on (q_1, q_0), the matrix will be :math:`Z \otimes X`: .. code-block:: text ┌─────────┐ q_0: ┤1 ├ │ Rzx(θ) │ q_1: ┤0 ├ └─────────┘ .. math:: \newcommand{\rotationangle}{\frac{\theta}{2}} R_{ZX}(\theta)\ q_1, q_0 = exp(-i \frac{\theta}{2} Z{\otimes}X) = \begin{pmatrix} \cos(\rotationangle) & -i\sin(\rotationangle) & 0 & 0 \\ -i\sin(\rotationangle) & \cos(\rotationangle) & 0 & 0 \\ 0 & 0 & \cos(\rotationangle) & i\sin(\rotationangle) \\ 0 & 0 & i\sin(\rotationangle) & \cos(\rotationangle) \end{pmatrix} This is a direct sum of RX rotations, so this gate is equivalent to a uniformly controlled (multiplexed) RX gate: .. math:: R_{ZX}(\theta)\ q_1, q_0 = \begin{pmatrix} RX(\theta) & 0 \\ 0 & RX(-\theta) \end{pmatrix} Examples: .. math:: R_{ZX}(\theta = 0)\ q_0, q_1 = I .. math:: R_{ZX}(\theta = 2\pi)\ q_0, q_1 = -I .. math:: R_{ZX}(\theta = \pi)\ q_0, q_1 = -i X \otimes Z .. math:: R_{ZX}(\theta = \frac{\pi}{2})\ q_0, q_1 = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & 0 & -i & 0 \\ 0 & 1 & 0 & i \\ -i & 0 & 1 & 0 \\ 0 & i & 0 & 1 \end{pmatrix} c(>[TU]SSU/US9 g)zQ Args: theta: The rotation angle. label: An optional label for the gate. rzx)labelN)super__init__)selfthetar __class__s c/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/circuit/library/standard_gates/rzx.pyrRZXGate.__init__}s E7%8cSSKJn UR[RR UR 5SURS9Ulg)zDefault definitionr)QuantumCircuitT) legacy_qubitsnameN) qiskit.circuitr_from_circuit_datarRZX_get_definitionparamsr definition)rrs r_defineRZXGate._definesC 2);;    , ,T[[ 9TXT]T]< rcf>Uc[SUR55n[TU] UUUUS9nU$)aCReturn a (multi-)controlled-RZX 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 "RZXGate.control..sT 1Jq*=>> s)num_ctrl_qubitsr ctrl_state annotated)anyr rcontrol)rr,rr-r.gaters rr0RZXGate.controlsE,  T TTIw+!    rc4[URS*5$)aReturn inverse RZX gate (i.e. with the negative rotation angle). Args: annotated: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as the inverse of this gate is always a :class:`.RZXGate` with an inverted parameter value. Returns: RZXGate: inverse gate. r)r r )rr.s rinverseRZXGate.inverses A''rc  SSKnUSLa [S5e[URS5S- n[R "U5nS[R "U5-nURUSU*S/SUSU/U*SUS/SUSU//US9$)z&Return a numpy.array for the RZX gate.rNFz9unable to avoid copy while creating an array as requestedry?)dtype)numpy ValueErrorfloatr mathcossinarray)rr7copyr8 half_thetar<isins r __array__RZXGate.__array__s 5=XY Y4;;q>*Q. hhz"DHHZ(({{1teQ !S!T!2dUAsA4FDRSUXHY Z  rc8URun[X-5$r&)r r )rexponentr.rs rpower RZXGate.powers;;x'((rcP[U[5(aURU5$g)NF)r'r _compare_parameters)rothers r__eq__RZXGate.__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)rEr:r.rO)__name__ __module__ __qualname____firstlineno____doc__rr_standard_gaterr"r0r4rBrFrK__static_attributes__ __classcell__)rs@rr r s~`D"%%N99  ! 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