text: # This code is part of Qiskit.
  #
  # (C) Copyright IBM 2017.
  #
  # 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 the Y axis."""
  
  import math
  import numpy
  from qiskit.qasm import pi
  from qiskit.circuit.controlledgate import ControlledGate
  from qiskit.circuit.gate import Gate
  from qiskit.circuit.quantumregister import QuantumRegister
  
  
  class RYGate(Gate):
      r"""Single-qubit rotation about the Y axis.
  
      **Circuit symbol:**
  
      .. parsed-literal::
  
               ┌───────┐
          q_0: ┤ Ry(ϴ) ├
               └───────┘
  
      **Matrix Representation:**
  
      .. math::
  
          \newcommand{\th}{\frac{\theta}{2}}
  
          RY(\theta) = exp(-i \th Y) =
              \begin{pmatrix}
                  \cos{\th} & -\sin{\th} \\
                  \sin{\th} & \cos{\th}
              \end{pmatrix}
      """
  
      def __init__(self, theta, label=None):
          """Create new RY gate."""
          super().__init__('ry', 1, [theta], label=label)
  
      def _define(self):
          """
          gate ry(theta) a { r(theta, pi/2) a; }
          """
          # pylint: disable=cyclic-import
          from qiskit.circuit.quantumcircuit import QuantumCircuit
          from .r import RGate
          q = QuantumRegister(1, 'q')
          qc = QuantumCircuit(q, name=self.name)
          rules = [
              (RGate(self.params[0], pi / 2), [q[0]], [])
          ]
          for instr, qargs, cargs in rules:
              qc._append(instr, qargs, cargs)
  
          self.definition = qc
  
      def control(self, num_ctrl_qubits=1, label=None, ctrl_state=None):
          """Return a (mutli-)controlled-RY gate.
  
          Args:
              num_ctrl_qubits (int): number of control qubits.
              label (str or None): An optional label for the gate [Default: None]
              ctrl_state (int or str or None): control state expressed as integer,
                  string (e.g. '110'), or None. If None, use all 1s.
  
          Returns:
              ControlledGate: controlled version of this gate.
          """
          if num_ctrl_qubits == 1:
              gate = CRYGate(self.params[0], label=label, ctrl_state=ctrl_state)
              gate.base_gate.label = self.label
              return gate
          return super().control(num_ctrl_qubits=num_ctrl_qubits, label=label, ctrl_state=ctrl_state)
  
      def inverse(self):
          r"""Return inverted RY gate.
  
          :math:`RY(\lambda){\dagger} = RY(-\lambda)`
          """
          return RYGate(-self.params[0])
  
      def __array__(self, dtype=None):
          """Return a numpy.array for the RY gate."""
          cos = math.cos(self.params[0] / 2)
          sin = math.sin(self.params[0] / 2)
          return numpy.array([[cos, -sin],
                              [sin, cos]], dtype=dtype)
  
  
  class CRYGate(ControlledGate):
      r"""Controlled-RY gate.
  
      **Circuit symbol:**
  
      .. parsed-literal::
  
          q_0: ────■────
               ┌───┴───┐
          q_1: ┤ Ry(ϴ) ├
               └───────┘
  
      **Matrix representation:**
  
      .. math::
  
          \newcommand{\th}{\frac{\theta}{2}}
  
          CRY(\theta)\ q_0, q_1 =
              I \otimes |0\rangle\langle 0| + RY(\theta) \otimes |1\rangle\langle 1| =
              \begin{pmatrix}
                  1 & 0         & 0 & 0 \\
                  0 & \cos{\th} & 0 & -\sin{\th} \\
                  0 & 0         & 1 & 0 \\
                  0 & \sin{\th} & 0 & \cos{\th}
              \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:
  
          .. parsed-literal::
                   ┌───────┐
              q_0: ┤ Ry(ϴ) ├
                   └───┬───┘
              q_1: ────■────
  
          .. math::
  
              \newcommand{\th}{\frac{\theta}{2}}
  
              CRY(\theta)\ q_1, q_0 =
              |0\rangle\langle 0| \otimes I + |1\rangle\langle 1| \otimes RY(\theta) =
                  \begin{pmatrix}
                      1 & 0 & 0 & 0 \\
                      0 & 1 & 0 & 0 \\
                      0 & 0 & \cos{\th} & -\sin{\th} \\
                      0 & 0 & \sin{\th} & \cos{\th}
                  \end{pmatrix}
      """
  
      def __init__(self, theta, label=None, ctrl_state=None):
          """Create new CRY gate."""
          super().__init__('cry', 2, [theta], num_ctrl_qubits=1, label=label,
                           ctrl_state=ctrl_state, base_gate=RYGate(theta))
  
      def _define(self):
          """
          gate cry(lambda) a,b
          { u3(lambda/2,0,0) b; cx a,b;
            u3(-lambda/2,0,0) b; cx a,b;
          }
          """
          # pylint: disable=cyclic-import
          from qiskit.circuit.quantumcircuit import QuantumCircuit
          from .u3 import U3Gate
          from .x import CXGate
          q = QuantumRegister(2, 'q')
          qc = QuantumCircuit(q, name=self.name)
          rules = [
              (U3Gate(self.params[0] / 2, 0, 0), [q[1]], []),
              (CXGate(), [q[0], q[1]], []),
              (U3Gate(-self.params[0] / 2, 0, 0), [q[1]], []),
              (CXGate(), [q[0], q[1]], [])
          ]
          for instr, qargs, cargs in rules:
              qc._append(instr, qargs, cargs)
  
          self.definition = qc
  
      def inverse(self):
          """Return inverse CRY gate (i.e. with the negative rotation angle)."""
          return CRYGate(-self.params[0], ctrl_state=self.ctrl_state)
  
      def __array__(self, dtype=None):
          """Return a numpy.array for the CRY gate."""
          half_theta = float(self.params[0]) / 2
          cos = numpy.cos(half_theta)
          sin = numpy.sin(half_theta)
          if self.ctrl_state:
              return numpy.array([[1, 0, 0, 0],
                                  [0, cos, 0, -sin],
                                  [0, 0, 1, 0],
                                  [0, sin, 0, cos]],
                                 dtype=dtype)
          else:
              return numpy.array([[cos, 0, -sin, 0],
                                  [0, 1, 0, 0],
                                  [sin, 0, cos, 0],
                                  [0, 0, 0, 1]],
                                 dtype=dtype)
  