g zdZddlmZddlZddlmZddlmZddlm Z ddl m Z m Z ddl mZGd d eZdS) zTwo-qubit ZX-rotation gate.) annotationsN)Optional)Gate)QuantumRegister)ParameterValueTypeParameterExpression) StandardGatec|eZdZdZejZ dddddfd Zd Z ddfd Z d d!dZ d"dZ d d#dZ dZ xZS)$RZXGateuq 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} Ndt)durationunitthetarlabel Optional[str]cXtdd|g|||dS)zCreate new RZX gate.rzx)rr rN)super__init__)selfrrr r __class__s _/granary/edev/quantum/lib/python3.11/site-packages/qiskit/circuit/library/standard_gates/rzx.pyrzRZXGate.__init__~s3 E7%(QUVVVVVcddlm}ddlm}ddlm}ddlm}|jd}tdd}|||j }||dggf||d|dggf|||dggf||d|dggf||dggfg}|D]\} } } | | | | ||_ d S) zR gate rzx(theta) a, b { h b; cx a, b; u1(theta) b; cx a, b; h b;} r)QuantumCircuit)HGate)CXGate)RZGaterq)nameN) qiskit.circuit.quantumcircuitrhrxrrzr paramsrr"_append definition) rrrrr rr!qcrulesinstrqargscargss r_definezRZXGate._defines> A@@@@@  A As # # ^ADI . . . UWWqtfb ! VXX!ad|R ( VE]]QqTFB ' VXX!ad|R ( UWWqtfb !  $) , , E5% JJueU + + + +rrnum_ctrl_qubitsint str | None ctrl_statestr | int | None annotated bool | Nonec|td|jD}t||||}|S)aReturn 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. Nc3@K|]}t|tVdSN) isinstancer).0ps r z"RZXGate.control..s-TT1Jq*=>>TTTTTTr)r0rr3r5)anyr'rcontrol)rr0rr3r5gaters rr?zRZXGate.controlsX,  TT TTTTTIww+!     rFboolc8t|jd S)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')rr5s rinversezRZXGate.inverses A'''rc ddl}|durtdt|jddz }t j|}dt j|z}||d| dgd|d|g| d|dgd|d|gg|S)z&Return a numpy.array for the RZX gate.rNFz9unable to avoid copy while creating an array as requestedry?)dtype)numpy ValueErrorfloatr'mathcossinarray)rrEcopyrF half_thetarJisins r __array__zRZXGate.__array__s 5==XYY Y4;q>**Q. hz""DHZ((({{1teQ !S!T!2dUAsA4FDRSUXHY Z   rexponentrHc8|j\}t||zSr9)r'r )rrQr5rs rpowerz RZXGate.powers;x%'(((rcZt|tr||SdS)NF)r:r _compare_parameters)rothers r__eq__zRZXGate.__eq__s- eW % % 3++E22 2urr9)rrrr)rNNN)r0r1rr2r3r4r5r6)F)r5rA)NN)rQrHr5rA)__name__ __module__ __qualname____doc__r r _standard_gaterr/r?rCrPrSrW __classcell__)rs@rr r s``D")NAEWRV]aWWWWWWWW > ! '+!% B ( ( ( ( (     )))))rr )r[ __future__rrItypingrqiskit.circuit.gaterqiskit.circuit.quantumregisterr"qiskit.circuit.parameterexpressionrrqiskit._accelerate.circuitr r rrres"!"""""" $$$$$$::::::VVVVVVVV333333LLLLLdLLLLLr