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# Quellcode für qiskit.circuit.library.standard_gates.rx

# This code is part of Qiskit.
#
#
# 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 the X axis."""

import math
from math import pi
from typing import Optional, Union
import numpy

from qiskit.circuit.controlledgate import ControlledGate
from qiskit.circuit.gate import Gate
from qiskit.circuit.quantumregister import QuantumRegister
from qiskit.circuit.parameterexpression import ParameterValueType

[Doku]class RXGate(Gate):
r"""Single-qubit rotation about the X axis.

Can be applied to a :class:~qiskit.circuit.QuantumCircuit
with the :meth:~qiskit.circuit.QuantumCircuit.rx method.

**Circuit symbol:**

.. parsed-literal::

┌───────┐
q_0: ┤ Rx(ϴ) ├
└───────┘

**Matrix Representation:**

.. math::

\newcommand{\th}{\frac{\theta}{2}}

RX(\theta) = \exp\left(-i \th X\right) =
\begin{pmatrix}
\cos\left(\th\right)   & -i\sin\left(\th\right) \\
-i\sin\left(\th\right) & \cos\left(\th\right)
\end{pmatrix}
"""

def __init__(self, theta: ParameterValueType, label: Optional[str] = None):
"""Create new RX gate."""
super().__init__("rx", 1, [theta], label=label)

def _define(self):
"""
gate rx(theta) a {r(theta, 0) 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], 0), [q[0]], [])]
for instr, qargs, cargs in rules:
qc._append(instr, qargs, cargs)

self.definition = qc

[Doku]    def control(
self,
num_ctrl_qubits: int = 1,
label: Optional[str] = None,
ctrl_state: Optional[Union[str, int]] = None,
):
"""Return a (multi-)controlled-RX 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 = CRXGate(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)

[Doku]    def inverse(self):
r"""Return inverted RX gate.

:math:RX(\lambda)^{\dagger} = RX(-\lambda)
"""
return RXGate(-self.params[0])

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

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

[Doku]class CRXGate(ControlledGate):
r"""Controlled-RX gate.

Can be applied to a :class:~qiskit.circuit.QuantumCircuit
with the :meth:~qiskit.circuit.QuantumCircuit.crx method.

**Circuit symbol:**

.. parsed-literal::

q_0: ────■────
┌───┴───┐
q_1: ┤ Rx(ϴ) ├
└───────┘

**Matrix representation:**

.. math::

\newcommand{\th}{\frac{\theta}{2}}

CRX(\theta)\ q_0, q_1 =
I \otimes |0\rangle\langle 0| + RX(\theta) \otimes |1\rangle\langle 1| =
\begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & \cos\left(\th\right) & 0 & -i\sin\left(\th\right) \\
0 & 0 & 1 & 0 \\
0 & -i\sin\left(\th\right) & 0 & \cos\left(\th\right)
\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: ┤ Rx(ϴ) ├
└───┬───┘
q_1: ────■────

.. math::

\newcommand{\th}{\frac{\theta}{2}}

CRX(\theta)\ q_1, q_0 =
|0\rangle\langle0| \otimes I + |1\rangle\langle1| \otimes RX(\theta) =
\begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & \cos\left(\th\right)   & -i\sin\left(\th\right) \\
0 & 0 & -i\sin\left(\th\right) & \cos\left(\th\right)
\end{pmatrix}
"""

def __init__(
self,
theta: ParameterValueType,
label: Optional[str] = None,
ctrl_state: Optional[Union[str, int]] = None,
):
"""Create new CRX gate."""
super().__init__(
"crx",
2,
[theta],
num_ctrl_qubits=1,
label=label,
ctrl_state=ctrl_state,
base_gate=RXGate(theta),
)

def _define(self):
"""
gate cu3(theta,phi,lambda) c, t
{ u1(pi/2) t;
cx c,t;
u3(-theta/2,0,0) t;
cx c,t;
u3(theta/2,-pi/2,0) t;
}
"""
# pylint: disable=cyclic-import
from qiskit.circuit.quantumcircuit import QuantumCircuit
from .u1 import U1Gate
from .u3 import U3Gate
from .x import CXGate

# q_0: ─────────────■───────────────────■────────────────────
#      ┌─────────┐┌─┴─┐┌─────────────┐┌─┴─┐┌────────────────┐
# q_1: ┤ U1(π/2) ├┤ X ├┤ U3(0/2,0,0) ├┤ X ├┤ U3(0/2,-π/2,0) ├
#      └─────────┘└───┘└─────────────┘└───┘└────────────────┘
q = QuantumRegister(2, "q")
qc = QuantumCircuit(q, name=self.name)
rules = [
(U1Gate(pi / 2), [q[1]], []),
(CXGate(), [q[0], q[1]], []),
(U3Gate(-self.params[0] / 2, 0, 0), [q[1]], []),
(CXGate(), [q[0], q[1]], []),
(U3Gate(self.params[0] / 2, -pi / 2, 0), [q[1]], []),
]
for instr, qargs, cargs in rules:
qc._append(instr, qargs, cargs)

self.definition = qc

[Doku]    def inverse(self):
"""Return inverse CRX gate (i.e. with the negative rotation angle)."""
return CRXGate(-self.params[0], ctrl_state=self.ctrl_state)

def __array__(self, dtype=None):
"""Return a numpy.array for the CRX gate."""
half_theta = float(self.params[0]) / 2
cos = math.cos(half_theta)
isin = 1j * math.sin(half_theta)
if self.ctrl_state:
return numpy.array(
[[1, 0, 0, 0], [0, cos, 0, -isin], [0, 0, 1, 0], [0, -isin, 0, cos]], dtype=dtype
)
else:
return numpy.array(
[[cos, 0, -isin, 0], [0, 1, 0, 0], [-isin, 0, cos, 0], [0, 0, 0, 1]], dtype=dtype
)