# Source code for qiskit.circuit.library.standard_gates.r

# This code is part of Qiskit.
#
# (C) Copyright IBM 2017, 2019
#
# obtain a copy of this license in the LICENSE.txt file in the root directory
#
# 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

[docs]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{\th}{\frac{\theta}{2}}

R(\theta, \phi) = e^{-i \th \left(\cos{\phi} x + \sin{\phi} y\right)} =
\begin{pmatrix}
\cos\left(\th\right) & -i e^{-i \phi} \sin\left(\th\right) \\
-i e^{i \phi} \sin\left(\th\right) & \cos\left(\th\right)
\end{pmatrix}
"""

def __init__(
self, theta: ParameterValueType, phi: ParameterValueType, label: Optional[str] = None
):
"""Create new r single-qubit gate."""
super().__init__("r", 1, [theta, phi], label=label)

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

[docs]    def inverse(self):
"""Invert this gate.

r(θ, φ)^dagger = r(-θ, φ)
"""
return RGate(-self.params[0], self.params[1])

def __array__(self, dtype=None):
"""Return a numpy.array for the R gate."""
theta, phi = float(self.params[0]), float(self.params[1])
cos = math.cos(theta / 2)
sin = math.sin(theta / 2)
exp_m = exp(-1j * phi)
exp_p = exp(1j * phi)
return numpy.array([[cos, -1j * exp_m * sin], [-1j * exp_p * sin, cos]], dtype=dtype)

[docs]    def power(self, exponent: float):
"""Raise gate to a power."""
theta, phi = self.params
return RGate(exponent * theta, phi)