# Quellcode fΓΌr qiskit.circuit.library.standard_gates.rxx

# 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
# 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.

"""Two-qubit XX-rotation gate."""
import math
from typing import Optional
import numpy
from qiskit.circuit.gate import Gate
from qiskit.circuit.quantumregister import QuantumRegister
from qiskit.circuit.parameterexpression import ParameterValueType

[Doku]class RXXGate(Gate):
r"""A parametric 2-qubit :math:X \otimes X interaction (rotation about XX).

This gate is symmetric, and is maximally entangling at :math:\theta = \pi/2.

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

**Circuit Symbol:**

.. parsed-literal::

βββββββββββ
q_0: β€1        β
β  Rxx(Ο΄) β
q_1: β€0        β
βββββββββββ

**Matrix Representation:**

.. math::

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

R_{XX}(\theta) = \exp\left(-i \th X{\otimes}X\right) =
\begin{pmatrix}
\cos\left(\th\right)   & 0           & 0           & -i\sin\left(\th\right) \\
0           & \cos\left(\th\right)   & -i\sin\left(\th\right) & 0 \\
0           & -i\sin\left(\th\right) & \cos\left(\th\right)   & 0 \\
-i\sin\left(\th\right) & 0           & 0           & \cos\left(\th\right)
\end{pmatrix}

**Examples:**

.. math::

R_{XX}(\theta = 0) = I

.. math::

R_{XX}(\theta = \pi) = i X \otimes X

.. math::

R_{XX}\left(\theta = \frac{\pi}{2}\right) = \frac{1}{\sqrt{2}}
\begin{pmatrix}
1  & 0  & 0  & -i \\
0  & 1  & -i & 0 \\
0  & -i & 1  & 0 \\
-i & 0  & 0  & 1
\end{pmatrix}
"""

def __init__(self, theta: ParameterValueType, label: Optional[str] = None):
"""Create new RXX gate."""
super().__init__("rxx", 2, [theta], label=label)

def _define(self):
"""Calculate a subcircuit that implements this unitary."""
# pylint: disable=cyclic-import
from qiskit.circuit.quantumcircuit import QuantumCircuit
from .x import CXGate
from .h import HGate
from .rz import RZGate

#      βββββ                   βββββ
# q_0: β€ H ββββ ββββββββββββββ βββ€ H β
#      βββββ€βββ΄ββββββββββββββ΄βββββββ€
# q_1: β€ H ββ€ X ββ€ Rz(0) ββ€ X ββ€ H β
#      βββββββββββββββββββββββββββββ
theta = self.params[0]
q = QuantumRegister(2, "q")
qc = QuantumCircuit(q, name=self.name)
rules = [
(HGate(), [q[0]], []),
(HGate(), [q[1]], []),
(CXGate(), [q[0], q[1]], []),
(RZGate(theta), [q[1]], []),
(CXGate(), [q[0], q[1]], []),
(HGate(), [q[1]], []),
(HGate(), [q[0]], []),
]
for instr, qargs, cargs in rules:
qc._append(instr, qargs, cargs)

self.definition = qc

[Doku]    def inverse(self):
"""Return inverse RXX gate (i.e. with the negative rotation angle)."""
return RXXGate(-self.params[0])

def __array__(self, dtype=None):
"""Return a Numpy.array for the RXX gate."""
theta2 = float(self.params[0]) / 2
cos = math.cos(theta2)
isin = 1j * math.sin(theta2)
return numpy.array(
[[cos, 0, 0, -isin], [0, cos, -isin, 0], [0, -isin, cos, 0], [-isin, 0, 0, cos]],
dtype=dtype,
)

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