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qiskit.circuit.library.standard_gates.u2의 소스 코드

# 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.

"""One-pulse single-qubit gate."""
from math import sqrt, pi
from cmath import exp
from typing import Optional
import numpy
from qiskit.circuit.gate import Gate
from qiskit.circuit.parameterexpression import ParameterValueType
from qiskit.circuit.quantumregister import QuantumRegister

[문서]class U2Gate(Gate):
r"""Single-qubit rotation about the X+Z axis.

Implemented using one X90 pulse on IBM Quantum systems:

.. warning::

This gate is deprecated. Instead, the following replacements should be used

.. math::

U2(\phi, \lambda) = U\left(\frac{\pi}{2}, \phi, \lambda\right)

.. code-block:: python

circuit = QuantumCircuit(1)
circuit.u(pi/2, phi, lambda)

**Circuit symbol:**

.. parsed-literal::

┌─────────┐
q_0: ┤ U2(φ,λ) ├
└─────────┘

**Matrix Representation:**

.. math::

U2(\phi, \lambda) = \frac{1}{\sqrt{2}}
\begin{pmatrix}
1          & -e^{i\lambda} \\
e^{i\phi} & e^{i(\phi+\lambda)}
\end{pmatrix}

**Examples:**

.. math::

U2(\phi,\lambda) = e^{i \frac{\phi + \lambda}{2}}RZ(\phi)
RY\left(\frac{\pi}{2}\right) RZ(\lambda)
= e^{- i\frac{\pi}{4}} P\left(\frac{\pi}{2} + \phi\right)
\sqrt{X} P\left(\lambda- \frac{\pi}{2}\right)

.. math::

U2(0, \pi) = H

.. math::

U2(0, 0) = RY(\pi/2)

.. math::

U2(-\pi/2, \pi/2) = RX(\pi/2)

.. seealso::

:class:~qiskit.circuit.library.standard_gates.U3Gate:
U3 is a generalization of U2 that covers all single-qubit rotations,
using two X90 pulses.
"""

def __init__(
self, phi: ParameterValueType, lam: ParameterValueType, label: Optional[str] = None
):
"""Create new U2 gate."""
super().__init__("u2", 1, [phi, lam], label=label)

def _define(self):
# pylint: disable=cyclic-import
from qiskit.circuit.quantumcircuit import QuantumCircuit
from .u3 import U3Gate

q = QuantumRegister(1, "q")
qc = QuantumCircuit(q, name=self.name)
rules = [(U3Gate(pi / 2, self.params[0], self.params[1]), [q[0]], [])]
for instr, qargs, cargs in rules:
qc._append(instr, qargs, cargs)

self.definition = qc

[문서]    def inverse(self):
r"""Return inverted U2 gate.

:math:U2(\phi, \lambda)^{\dagger} =U2(-\lambda-\pi, -\phi+\pi))
"""
return U2Gate(-self.params[1] - pi, -self.params[0] + pi)

def __array__(self, dtype=complex):
"""Return a Numpy.array for the U2 gate."""
isqrt2 = 1 / sqrt(2)
phi, lam = self.params
phi, lam = float(phi), float(lam)
return numpy.array(
[
[isqrt2, -exp(1j * lam) * isqrt2],
[exp(1j * phi) * isqrt2, exp(1j * (phi + lam)) * isqrt2],
],
dtype=dtype,
)