Source code for qiskit.circuit.library.generalized_gates.rv

# 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


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{\rotationangle}{|\vec{v}|}
        \newcommand{\sinc}{\text{sinc}}
            R(\vec{v}) = e^{-i \vec{v}\cdot\vec{\sigma}} =
                \begin{pmatrix}
                    \cos\left(\rotationangle\right) -i v_z \sinc\left(\rotationangle\right)
                    & -(i v_x + v_y) \sinc\left(\rotationangle\right) \\
                    -(i v_x - v_y) \sinc\left(\rotationangle\right)
                    & \cos\left(\rotationangle\right) + i v_z \sinc\left(\rotationangle\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

    def inverse(self):
        """Invert this gate."""
        vx, vy, vz = self.params
        return RVGate(-vx, -vy, -vz)

    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],
            ]
        )