# qiskit.circuit.library.standard_gates.xx_plus_yy のソースコード

# 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.

"""Two-qubit XX+YY gate."""
import math
from cmath import exp
from math import pi
from typing import Optional
from qiskit.circuit.gate import Gate
from qiskit.circuit.quantumregister import QuantumRegister
from qiskit.circuit.parameterexpression import ParameterValueType

[ドキュメント]class XXPlusYYGate(Gate):
r"""XX+YY interaction gate.

A 2-qubit parameterized XX+YY interaction, also known as an XY gate. Its action is to induce
a coherent rotation by some angle between :math:|01\rangle and :math:|10\rangle.

**Circuit Symbol:**

.. parsed-literal::

┌───────────────┐
q_0: ┤0              ├
│  (XX+YY)(θ,β) │
q_1: ┤1              ├
└───────────────┘

**Matrix Representation:**

.. math::

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

R_{XX+YY}(\theta, \beta)\ q_0, q_1 =
RZ_0(-\beta) \cdot \exp\left(-i \frac{\theta}{2} \frac{XX+YY}{2}\right) \cdot RZ_0(\beta) =
\begin{pmatrix}
1 & 0                     & 0                    & 0  \\
0 & \cos\left(\th\right)             & -i\sin\left(\th\right)e^{-i\beta} & 0  \\
0 & -i\sin\left(\th\right)e^{i\beta} & \cos\left(\th\right)            & 0  \\
0 & 0                     & 0                    & 1
\end{pmatrix}

.. note::

In Qiskit's convention, higher qubit indices are more significant
(little endian convention). In the above example we apply the gate
on (q_0, q_1) which results in adding the (optional) phase defined
by :math:beta on q_0. Instead, if we apply it on (q_1, q_0), the
phase is added on q_1. If :math:beta is set to its default value
of :math:0, the gate is equivalent in big and little endian.

.. parsed-literal::

┌───────────────┐
q_0: ┤1              ├
│  (XX+YY)(θ,β) │
q_1: ┤0              ├
└───────────────┘

.. math::

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

R_{XX+YY}(\theta, \beta)\ q_0, q_1 =
RZ_1(-\beta) \cdot \exp\left(-i \frac{\theta}{2} \frac{XX+YY}{2}\right) \cdot RZ_1(\beta) =
\begin{pmatrix}
1 & 0                     & 0                    & 0  \\
0 & \cos\left(\th\right)             & -i\sin\left(\th\right)e^{i\beta} & 0  \\
0 & -i\sin\left(\th\right)e^{-i\beta} & \cos\left(\th\right)            & 0  \\
0 & 0                     & 0                    & 1
\end{pmatrix}
"""

def __init__(
self,
theta: ParameterValueType,
beta: ParameterValueType = 0,
label: Optional[str] = "(XX+YY)",
):
"""Create new XX+YY gate.

Args:
theta: The rotation angle.
beta: The phase angle.
label: The label of the gate.
"""
super().__init__("xx_plus_yy", 2, [theta, beta], label=label)

def _define(self):
"""
gate xx_plus_yy(theta, beta) a, b {
rz(beta) b;
rz(-pi/2) a;
sx a;
rz(pi/2) a;
s b;
cx a, b;
ry(theta/2) a;
ry(theta/2) b;
cx a, b;
sdg b;
rz(-pi/2) a;
sxdg a;
rz(pi/2) a;
rz(-beta) b;
}
"""
# pylint: disable=cyclic-import
from qiskit.circuit.quantumcircuit import QuantumCircuit
from .x import CXGate
from .s import SGate, SdgGate
from .sx import SXGate, SXdgGate
from .rz import RZGate
from .ry import RYGate

theta = self.params[0]
beta = self.params[1]
q = QuantumRegister(2, "q")
qc = QuantumCircuit(q, name=self.name)
rules = [
(RZGate(beta), [q[0]], []),
(RZGate(-pi / 2), [q[1]], []),
(SXGate(), [q[1]], []),
(RZGate(pi / 2), [q[1]], []),
(SGate(), [q[0]], []),
(CXGate(), [q[1], q[0]], []),
(RYGate(-theta / 2), [q[1]], []),
(RYGate(-theta / 2), [q[0]], []),
(CXGate(), [q[1], q[0]], []),
(SdgGate(), [q[0]], []),
(RZGate(-pi / 2), [q[1]], []),
(SXdgGate(), [q[1]], []),
(RZGate(pi / 2), [q[1]], []),
(RZGate(-beta), [q[0]], []),
]
for instr, qargs, cargs in rules:
qc._append(instr, qargs, cargs)

self.definition = qc

[ドキュメント]    def inverse(self):
"""Return inverse XX+YY gate (i.e. with the negative rotation angle and same phase angle)."""
return XXPlusYYGate(-self.params[0], self.params[1])

def __array__(self, dtype=complex):
"""Return a numpy.array for the XX+YY gate."""
import numpy

half_theta = float(self.params[0]) / 2
beta = float(self.params[1])
cos = math.cos(half_theta)
sin = math.sin(half_theta)
return numpy.array(
[
[1, 0, 0, 0],
[0, cos, -1j * sin * exp(-1j * beta), 0],
[0, -1j * sin * exp(1j * beta), cos, 0],
[0, 0, 0, 1],
],
dtype=dtype,
)

[ドキュメント]    def power(self, exponent: float):
"""Raise gate to a power."""
theta, beta = self.params
return XXPlusYYGate(exponent * theta, beta)