gw~dZddlmZddlmZddlmZddlmZddl m Z ddl m Z m Z ddlmZGd d eZd S) zTwo-qubit ZZ-rotation gate.) annotations)exp)Optional)Gate)QuantumRegister)ParameterValueTypeParameterExpression) StandardGatec|eZdZdZejZ dddddfd Zd Z ddfd Z d d!dZ d"dZ d d#dZ dZ xZS)$RZZGateu A 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} Ndt)durationunitthetarlabel Optional[str]cXtdd|g|||dS)zCreate new RZZ gate.rzz)rrrN)super__init__)selfrrrr __class__s _/granary/edev/quantum/lib/python3.11/site-packages/qiskit/circuit/library/standard_gates/rzz.pyrzRZZGate.__init__]s3 E7%(QUVVVVVcjddlm}ddlm}ddlm}t dd}|jd}|||j}||d|dggf|||dggf||d|dggfg}|D]\}} } | || | ||_ d S) zI gate rzz(theta) a, b { cx a, b; u1(theta) b; cx a, b; } r)QuantumCircuit)CXGate)RZGaterq)nameN) qiskit.circuit.quantumcircuitrxrrzr rparamsr"_append definition) rrrr r!rqcrulesinstrqargscargss r_definezRZZGate._definecs A@@@@@ As # # A ^ADI . . . VXX!ad|R ( VE]]QqTFB ' VXX!ad|R (  $) , , E5% JJueU + + + +rrnum_ctrl_qubitsint str | None ctrl_statestr | int | None annotated bool | Nonec|td|jD}t||||}|S)aReturn 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. Nc3@K|]}t|tVdSN) isinstancer ).0ps r z"RZZGate.control..s-TT1Jq*=>>TTTTTTr)r/rr2r4)anyr&rcontrol)rr/rr2r4gaters rr>zRZZGate.control}sX,  TT TTTTTIww+!     rFboolc8t|jd S)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&)rr4s rinversezRZZGate.inverses A'''rc 2ddl}|durtddt|jdzdz }|t | dddgdt |ddgddt |dgdddt | gg|S)z&Return a numpy.array for the RZZ gate.rNFz9unable to avoid copy while creating an array as requestedy?r)dtype)numpy ValueErrorfloatr&arrayr)rrDcopyrEitheta2s r __array__zRZZGate.__array__s 5==XYY YuT[^,,,q0{{gX1a(CLL!Q'As7||Q'Aq#wh--(      rexponentrGc8|j\}t||zSr8)r&r )rrLr4rs rpowerz RZZGate.powers;x%'(((rcZt|tr||SdS)NF)r9r _compare_parameters)rothers r__eq__zRZZGate.__eq__s- eW % % 3++E22 2urr8)rrrr)rNNN)r/r0rr1r2r3r4r5)F)r4r@)NN)rLrGr4r@)__name__ __module__ __qualname____doc__r r _standard_gaterr.r>rBrKrNrR __classcell__)rs@rr r s ??B")NAEWRV]aWWWWWWWW 8 ! '+!% B ( ( ( ( (    ")))))rr N)rV __future__rcmathrtypingrqiskit.circuit.gaterqiskit.circuit.quantumregisterr"qiskit.circuit.parameterexpressionrr qiskit._accelerate.circuitr r rrras"!""""""$$$$$$::::::VVVVVVVV333333kkkkkdkkkkkr