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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


[docs]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{\th} -i v_z \sinc(\th) & -(i v_x + v_y) \sinc(\th) \\ -(i v_x - v_y) \sinc(\th) & \cos(\th) + i v_z \sinc(\th) \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
[docs] def inverse(self): """Invert this gate.""" vx, vy, vz = self.params return RVGate(-vx, -vy, -vz)
[docs] 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], ] )