z iGrSrSSKJrJr SSKJr SSKJr SSKrSSK J r SSK J r SSK Jr "S S \ 5rg) zOne-pulse single-qubit gate.)sqrtpi)exp)OptionalN)Gate)ParameterValueType) StandardGatec^\rSrSrSr\R rS S\S\S\ \ 4U4Sjjjr Sr SS\ 4S jjrSS jrS rS rU=r$)U2GateuSingle-qubit rotation about the X+Z axis. Implemented using one X90 pulse on IBM Quantum systems: .. warning:: This gate is deprecated. Instead, the following replacements should be used .. math:: U2(\phi, \lambda) = U\left(\frac{\pi}{2}, \phi, \lambda\right) .. code-block:: python circuit = QuantumCircuit(1) circuit.u(pi/2, phi, lambda) Circuit symbol: .. code-block:: text ┌─────────┐ q_0: ┤ U2(φ,λ) ├ └─────────┘ Matrix representation: .. math:: U2(\phi, \lambda) = \frac{1}{\sqrt{2}} \begin{pmatrix} 1 & -e^{i\lambda} \\ e^{i\phi} & e^{i(\phi+\lambda)} \end{pmatrix} Examples: .. math:: U2(\phi,\lambda) = e^{i \frac{\phi + \lambda}{2}}RZ(\phi) RY\left(\frac{\pi}{2}\right) RZ(\lambda) = e^{- i\frac{\pi}{4}} P\left(\frac{\pi}{2} + \phi\right) \sqrt{X} P\left(\lambda- \frac{\pi}{2}\right) .. math:: U2(0, \pi) = H .. math:: U2(0, 0) = RY(\pi/2) .. math:: U2(-\pi/2, \pi/2) = RX(\pi/2) .. seealso:: :class:`~qiskit.circuit.library.standard_gates.U3Gate`: U3 is a generalization of U2 that covers all single-qubit rotations, using two X90 pulses. philamlabelc(>[TU]SSX/US9 g)z Args: phi: The rotation angle :math:`\phi`. lam: The rotation angle :math:`\lambda`. label: An optional label for the gate. u2)rN)super__init__)selfr rr __class__s b/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/circuit/library/standard_gates/u2.pyrU2Gate.__init__Ys q3*E:cSSKJn UR[RR UR 5SURS9Ulg)zDefault definitionr)QuantumCircuitT) legacy_qubitsnameN) qiskit.circuitr_from_circuit_datar U2_get_definitionparamsr definition)rrs r_defineU2Gate._definegsA 2 );; OO + +DKK 8SWS\S\< r annotatedcn[URS*[- URS*[-5$)aReturn inverted U2 gate. :math:`U2(\phi, \lambda)^{\dagger} =U2(-\lambda-\pi, -\phi+\pi))` 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:`.U2Gate` with inverse parameter values. Returns: U2Gate: inverse gate. rr)r r"r)rr&s rinverseU2Gate.inversets/t{{1~o*T[[^Ob,@AArc 4USLa [S5eS[S5- nURupE[U5[U5pT[R "U[ SU-5*U-/[ SU-5U-[ SXE--5U-//U=(d [S9$)z%Return a Numpy.array for the U2 gate.Fz9unable to avoid copy while creating an array as requestedry?)dtype) ValueErrorrr"floatnumpyarrayrcomplex)rr,copyisqrt2r rs r __array__U2Gate.__array__s 5=XY YT!W;;:uSzS{{#b3h-&01R#X'R39-=)>)GH "7   rcR[U[5=(a URU5$N) isinstancer _compare_parameters)rothers r__eq__ U2Gate.__eq__s%(LT-E-Ee-LLr)r#r7)F)NN)__name__ __module__ __qualname____firstlineno____doc__r r _standard_gaterrstrrr$boolr(r4r;__static_attributes__ __classcell__)rs@rr r sg=~"__N $ ;  ;  ;} ; ;  BB  MMrr )rAmathrrcmathrtypingrr/qiskit.circuit.gater"qiskit.circuit.parameterexpressionrqiskit._accelerate.circuitr r rrrNs/# $A3}MT}Mr