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This code is part of Qiskit.","#","# (C) Copyright IBM 2017, 2019","#","# This code is licensed under the Apache License, Version 2.0. You may","# obtain a copy of this license in the LICENSE.txt file in the root directory","# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.","#","# Any modifications or derivative works of this code must retain this","# copyright notice, and modified files need to carry a notice indicating","# that they have been altered from the originals.","","\"\"\"Rotation around an axis in x-y plane.\"\"\"","","import math","from cmath import exp","from math import pi","from typing import Optional","import numpy","from qiskit.circuit.gate import Gate","from qiskit.circuit.quantumregister import QuantumRegister","from qiskit.circuit.parameterexpression import ParameterValueType","","","class RGate(Gate):"," r\"\"\"Rotation θ around the cos(φ)x + sin(φ)y axis.",""," Can be applied to a :class:`~qiskit.circuit.QuantumCircuit`"," with the :meth:`~qiskit.circuit.QuantumCircuit.r` method.",""," **Circuit symbol:**",""," .. parsed-literal::",""," ┌──────┐"," q_0: ┤ R(ϴ) ├"," └──────┘",""," **Matrix Representation:**",""," .. math::",""," \\newcommand{\\rotationangle}{\\frac{\\theta}{2}}",""," R(\\theta, \\phi) = e^{-i \\rotationangle \\left(\\cos{\\phi} x + \\sin{\\phi} y\\right)} ="," \\begin{pmatrix}"," \\cos\\left(\\rotationangle\\right) & -i e^{-i \\phi} \\sin\\left(\\rotationangle\\right) \\\\"," -i e^{i \\phi} \\sin\\left(\\rotationangle\\right) & \\cos\\left(\\rotationangle\\right)"," \\end{pmatrix}"," \"\"\"",""," def __init__("," self,"," theta: ParameterValueType,"," phi: ParameterValueType,"," label: Optional[str] = None,"," *,"," duration=None,"," unit=\"dt\","," ):"," \"\"\"Create new r single-qubit gate.\"\"\""," super().__init__(\"r\", 1, [theta, phi], label=label, duration=duration, unit=unit)",""," def _define(self):"," \"\"\""," gate r(θ, φ) a {u3(θ, φ - π/2, -φ + π/2) a;}"," \"\"\""," # pylint: disable=cyclic-import"," from qiskit.circuit.quantumcircuit import QuantumCircuit"," from .u3 import U3Gate",""," q = QuantumRegister(1, \"q\")"," qc = QuantumCircuit(q, name=self.name)"," theta = self.params[0]"," phi = self.params[1]"," rules = [(U3Gate(theta, phi - pi / 2, -phi + pi / 2), [q[0]], [])]"," for instr, qargs, cargs in rules:"," qc._append(instr, qargs, cargs)",""," self.definition = qc",""," def inverse(self, annotated: bool = False):"," \"\"\"Invert this gate as: :math:`r(θ, φ)^dagger = r(-θ, φ)`",""," 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`. 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