z i'SrSSKJr SSKJr SSKJrJr SSKJ r SSK J r SSK J r SSKJr "S S \ 5r"S S \ 5rg )zRotation around the Z axis.) annotations)exp)OptionalUnion)Gate)ControlledGate)ParameterValueType) StandardGatec^\rSrSrSr\R rS S U4SjjjrSr S SU4Sjjjr SSSjjr SSjr SSSjjr S rS rU=r$)RZGateuSingle-qubit rotation about the Z axis. This is a diagonal gate. It can be implemented virtually in hardware via framechanges (i.e. at zero error and duration). Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.rz` method. Circuit symbol: .. code-block:: text ┌───────┐ q_0: ┤ Rz(φ) ├ └───────┘ Matrix representation: .. math:: RZ(\phi) = \exp\left(-i\frac{\phi}{2}Z\right) = \begin{pmatrix} e^{-i\frac{\phi}{2}} & 0 \\ 0 & e^{i\frac{\phi}{2}} \end{pmatrix} .. seealso:: :class:`~qiskit.circuit.library.standard_gates.U1Gate` This gate is equivalent to U1 up to a phase factor. .. math:: U1(\theta=\phi) = e^{i{\phi}/2}RZ(\phi) Reference for virtual Z gate implementation: `1612.00858 `_ c(>[TU]SSU/US9 g)zQ Args: theta: The rotation angle. label: An optional label for the gate. rzlabelN)super__init__)selfphir __class__s b/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/circuit/library/standard_gates/rz.pyrRZGate.__init__Cs q3%u5cSSKJn UR[RR UR 5SURS9UlgzDefault definitionr)QuantumCircuitT) legacy_qubitsnameN) qiskit.circuitr_from_circuit_datar RZ_get_definitionparamsr definitionrrs r_defineRZGate._defineKsA 2);; OO + +DKK 8SWS\S\< rc>U(d:US:Xa4[URSX#S9nURURlU$[TU]UUUUS9nU$)aReturn a (multi-)controlled-RZ gate. Args: num_ctrl_qubits: number of control qubits. label: An optional label for the gate [Default: ``None``] ctrl_state: control state expressed as integer, string (e.g.``'110'``), or ``None``. If ``None``, use all 1s. annotated: indicates whether the controlled gate should be implemented as an annotated gate. If ``None``, this is set to ``True`` if the gate contains free parameters and more than one control qubit, in which case it cannot yet be synthesized. Otherwise it is set to ``False``. Returns: ControlledGate: controlled version of this gate. rr)r ctrl_state)num_ctrl_qubitsrr* annotated)CRZGater$r base_gatercontrol)rr+rr*r,gaters rr/RZGate.controlYsb._14;;q>ND#'::DNN  7? /%# #D  rc4[URS*5$)aReturn inverted RZ gate :math:`RZ(\lambda)^{\dagger} = RZ(-\lambda)` Args: annotated: when set to ``True``, this is typically used to return an :class:`.AnnotatedOperation` with an inverse modifier set instead of a concrete :class:`.Gate`. However, for this class this argument is ignored as the inverse of this gate is always a :class:`.RZGate` with an inverted parameter value. Returns: RZGate: inverse gate. r)r r$rr,s rinverseRZGate.inverse|st{{1~o&&rcSSKnUSLa [S5eS[URS5-nUR [ U*5S/S[ U5//US9$)z%Return a numpy.array for the RZ gate.rNF9unable to avoid copy while creating an array as requestedy?dtype)numpy ValueErrorfloatr$arrayr)rr9copynpilam2s r __array__RZGate.__array__sZ 5=XY YuT[[^,,xx#uf+q)As5z?;5xIIrc8URun[X-5$N)r$r )rexponentr,thetas rpower RZGate.powers;;h&''rcP[U[5(aURU5$gNF) isinstancer _compare_parametersrothers r__eq__ RZGate.__eq__s# eV $ $++E2 2rr%rD)rr r Optional[str])rNNN)r+intrz str | Noner*zstr | int | Noner,z bool | NoneFr,boolNN)rEr<r,rV)__name__ __module__ __qualname____firstlineno____doc__r r"_standard_gaterr'r/r4rArGrO__static_attributes__ __classcell__rs@rr r s|%N"__N66  ! '+!% !!!% !  !!F' J(rr c^\rSrSrSr\R rS SS.S U4SjjjjrSr S SSjjr S Sjr S r S r U=r$)r-uQControlled-RZ gate. This is a diagonal but non-symmetric gate that induces a phase on the state of the target qubit, depending on the control state. Can be applied to a :class:`~qiskit.circuit.QuantumCircuit` with the :meth:`~qiskit.circuit.QuantumCircuit.crz` method. Circuit symbol: .. code-block:: text q_0: ────■──── ┌───┴───┐ q_1: ┤ Rz(θ) ├ └───────┘ Matrix representation: .. math:: CRZ(\theta)\ q_0, q_1 = I \otimes |0\rangle\langle 0| + RZ(\phi=\theta) \otimes |1\rangle\langle 1| = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & e^{-i\frac{\theta}{2}} & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & e^{i\frac{\theta}{2}} \end{pmatrix} .. note:: In Qiskit's convention, higher qubit indices are more significant (little endian convention). In many textbooks, controlled gates are presented with the assumption of more significant qubits as control, which in our case would be q_1. Thus a textbook matrix for this gate will be: .. code-block:: text ┌───────┐ q_0: ┤ Rz(θ) ├ └───┬───┘ q_1: ────■──── .. math:: CRZ(\theta)\ q_1, q_0 = |0\rangle\langle 0| \otimes I + |1\rangle\langle 1| \otimes RZ(\theta) = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & e^{-i\frac{\theta}{2}} & 0 \\ 0 & 0 & 0 & e^{i\frac{\theta}{2}} \end{pmatrix} .. seealso:: :class:`~qiskit.circuit.library.standard_gates.CU1Gate`: Due to the global phase difference in the matrix definitions of U1 and RZ, CU1 and CRZ are different gates with a relative phase difference. N) _base_labelc <>[TU]SSU/SUU[XS9S9 g)zCreate new CRZ gate.crzrr)r+rr*r.N)rrr )rrFrr*rcrs rrCRZGate.__init__s3   G!U6  rcSSKJn UR[RR UR 5SURS9Ulgr) r rr!r CRZr#r$rr%r&s rr'CRZGate._definesC 2);;    , ,T[[ 9TXT]T]< rcF[URS*URS9$)aReturn inverse CRZ 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:`.CRZGate` with an inverted parameter value. Returns: CRZGate: inverse gate. r)r*)r-r$r*r3s rr4CRZGate.inverses A4??CCrc TSSKnUSLa [S5eS[URS5-S- nUR(a3UR /SQS[ U*5SS//SQSSS[ U5//US 9$UR [ U*5SSS//S QSS[ U5S//S Q/US 9$) z&Return a numpy.array for the CRZ gate.rNFr7y?rf)rrrr)rrrrr8)rrrr)rrrr)r:r;r<r$r*r=r)rr9r>r:args rrACRZGate.__array__s 5=XY Y5Q((1, ??;;3t9a3\Aq!SQTXCVW  ;;sd)Q1%|aCHa5H,W rc[U[5(a1URU5=(a URUR:H$grJ)rKr-rLr*rMs rrOCRZGate.__eq__#s7 eW % %++E2Zt%JZJZ7Z ZrrQrW)rFr rrRr*zOptional[Union[str, int]]rTrU)rXrYrZr[r\r rir]rr'r4rArOr^r_r`s@rr-r-sh>@"%%N $04    !  .   &   D$rr-N)r\ __future__rcmathrtypingrrqiskit.circuit.gaterqiskit.circuit.controlledgater"qiskit.circuit.parameterexpressionr qiskit._accelerate.circuitr r r-rrrzs<"""$8A3CTCLGnGr