# This code is part of Qiskit.
#
# (C) Copyright IBM 2017, 2020
#
# This code is licensed under the Apache License, Version 2.0. You may
# 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.
"""Rotation around an arbitrary axis on the Bloch sphere."""
import numpy
from qiskit.circuit.gate import Gate
from qiskit.circuit.exceptions import CircuitError
[Doku]class RVGate(Gate):
r"""Rotation around arbitrary rotation axis :math:`v` where :math:`|v|` is
angle of rotation in radians.
Can be applied to a :class:`~qiskit.circuit.QuantumCircuit`
with the :meth:`~qiskit.circuit.QuantumCircuit.rv` method.
**Circuit symbol:**
.. parsed-literal::
┌─────────────────┐
q_0: ┤ RV(v_x,v_y,v_z) ├
└─────────────────┘
**Matrix Representation:**
.. math::
\newcommand{\th}{|\vec{v}|}
\newcommand{\sinc}{\text{sinc}}
R(\vec{v}) = e^{-i \vec{v}\cdot\vec{\sigma}} =
\begin{pmatrix}
\cos\left(\th\right) -i v_z \sinc\left(\th\right)
& -(i v_x + v_y) \sinc\left(\th\right) \\
-(i v_x - v_y) \sinc\left(\th\right)
& \cos\left(\th\right) + i v_z \sinc\left(\th\right)
\end{pmatrix}
"""
def __init__(self, v_x, v_y, v_z, basis="U"):
"""Create new rv single-qubit gate.
Args:
v_x (float): x-component
v_y (float): y-component
v_z (float): z-component
basis (str, optional): basis (see
:class:`~qiskit.quantum_info.synthesis.one_qubit_decompose.OneQubitEulerDecomposer`)
"""
# pylint: disable=cyclic-import
from qiskit.quantum_info.synthesis.one_qubit_decompose import OneQubitEulerDecomposer
super().__init__("rv", 1, [v_x, v_y, v_z])
self._decomposer = OneQubitEulerDecomposer(basis=basis)
def _define(self):
try:
self.definition = self._decomposer(self.to_matrix())
except TypeError as ex:
raise CircuitError(
f"The {self.name} gate cannot be decomposed with unbound parameters"
) from ex
[Doku] def inverse(self):
"""Invert this gate."""
vx, vy, vz = self.params
return RVGate(-vx, -vy, -vz)
[Doku] def to_matrix(self):
"""Return a numpy.array for the R(v) gate."""
v = numpy.asarray(self.params, dtype=float)
angle = numpy.sqrt(v.dot(v))
if angle == 0:
return numpy.array([[1, 0], [0, 1]])
nx, ny, nz = v / angle
sin = numpy.sin(angle / 2)
cos = numpy.cos(angle / 2)
return numpy.array(
[
[cos - 1j * nz * sin, (-ny - 1j * nx) * sin],
[(ny - 1j * nx) * sin, cos + 1j * nz * sin],
]
)