qiskit/circuit/library/generalized_gates/gr.py

# This code is part of Qiskit.
#
# (C) Copyright IBM 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.

"""Global R gates."""

import numpy as np
from qiskit.circuit.quantumcircuit import QuantumCircuit


class GR(QuantumCircuit):
    r"""Global R gate.

    Circuit symbol:

    .. code-block:: text

             ┌──────────┐
        q_0: ┤0         ├
             │          │
        q_1: ┤1 GR(ϴ,φ) ├
             │          │
        q_2: ┤2         ├
             └──────────┘

    The global R gate is native to atomic systems (ion traps, cold neutrals). The global R
    can be applied to multiple qubits simultaneously.

    In the one-qubit case, this is equivalent to an R(theta, phi) operation,
    and is thus reduced to the RGate. The global R gate is a direct sum of R
    operations on all individual qubits.

    .. math::

        GR(\theta, \phi) = \exp(-i \sum_{i=1}^{n} (\cos(\phi)X_i + \sin(\phi)Y_i) \theta/2)

    Expanded Circuit:

    .. plot::
       :alt: Diagram illustrating the previously described circuit.

       from qiskit.circuit.library import GR
       from qiskit.visualization.library import _generate_circuit_library_visualization
       import numpy as np
       circuit = GR(num_qubits=3, theta=np.pi/4, phi=np.pi/2)
       _generate_circuit_library_visualization(circuit)

    """

    def __init__(self, num_qubits: int, theta: float, phi: float) -> None:
        """
        Args:
            num_qubits: number of qubits.
            theta: rotation angle about axis determined by phi
            phi: angle of rotation axis in xy-plane
        """
        name = f"GR({theta:.2f}, {phi:.2f})"
        circuit = QuantumCircuit(num_qubits, name=name)
        circuit.r(theta, phi, circuit.qubits)

        super().__init__(num_qubits, name=name)
        self.append(circuit.to_gate(), self.qubits)


class GRX(GR):
    r"""Global RX gate.

    **Circuit symbol:**

    .. code-block:: text

             ┌──────────┐
        q_0: ┤0         ├
             │          │
        q_1: ┤1  GRX(ϴ) ├
             │          │
        q_2: ┤2         ├
             └──────────┘

    The global RX gate is native to atomic systems (ion traps, cold neutrals). The global RX
    can be applied to multiple qubits simultaneously.

    In the one-qubit case, this is equivalent to an RX(theta) operations,
    and is thus reduced to the RXGate. The global RX gate is a direct sum of RX
    operations on all individual qubits.

    .. math::

        GRX(\theta) = \exp(-i \sum_{i=1}^{n} X_i \theta/2)

    **Expanded Circuit:**

    .. plot::
       :alt: Diagram illustrating the previously described circuit.

        from qiskit.circuit.library import GRX
        from qiskit.visualization.library import _generate_circuit_library_visualization
        import numpy as np
        circuit = GRX(num_qubits=3, theta=np.pi/4)
        _generate_circuit_library_visualization(circuit)

    """

    def __init__(self, num_qubits: int, theta: float) -> None:
        """Create a new Global RX (GRX) gate.

        Args:
            num_qubits: number of qubits.
            theta: rotation angle about x-axis
        """
        super().__init__(num_qubits, theta, phi=0)


class GRY(GR):
    r"""Global RY gate.

    **Circuit symbol:**

    .. code-block:: text

             ┌──────────┐
        q_0: ┤0         ├
             │          │
        q_1: ┤1  GRY(ϴ) ├
             │          │
        q_2: ┤2         ├
             └──────────┘

    The global RY gate is native to atomic systems (ion traps, cold neutrals). The global RY
    can be applied to multiple qubits simultaneously.

    In the one-qubit case, this is equivalent to an RY(theta) operation,
    and is thus reduced to the RYGate. The global RY gate is a direct sum of RY
    operations on all individual qubits.

    .. math::

        GRY(\theta) = \exp(-i \sum_{i=1}^{n} Y_i \theta/2)

    **Expanded Circuit:**

    .. plot::
       :alt: Diagram illustrating the previously described circuit.

       from qiskit.circuit.library import GRY
       from qiskit.visualization.library import _generate_circuit_library_visualization
       import numpy as np
       circuit = GRY(num_qubits=3, theta=np.pi/4)
       _generate_circuit_library_visualization(circuit)

    """

    def __init__(self, num_qubits: int, theta: float) -> None:
        """Create a new Global RY (GRY) gate.

        Args:
            num_qubits: number of qubits.
            theta: rotation angle about y-axis
        """
        super().__init__(num_qubits, theta, phi=np.pi / 2)


class GRZ(QuantumCircuit):
    r"""Global RZ gate.

    **Circuit symbol:**

    .. code-block:: text

             ┌──────────┐
        q_0: ┤0         ├
             │          │
        q_1: ┤1  GRZ(φ) ├
             │          │
        q_2: ┤2         ├
             └──────────┘

    The global RZ gate is native to atomic systems (ion traps, cold neutrals). The global RZ
    can be applied to multiple qubits simultaneously.

    In the one-qubit case, this is equivalent to an RZ(phi) operation,
    and is thus reduced to the RZGate. The global RZ gate is a direct sum of RZ
    operations on all individual qubits.

    .. math::

        GRZ(\phi) = \exp(-i \sum_{i=1}^{n} Z_i \phi)

    **Expanded Circuit:**

    .. plot::
       :alt: Diagram illustrating the previously described circuit.

       from qiskit.circuit.library import GRZ
       from qiskit.visualization.library import _generate_circuit_library_visualization
       import numpy as np
       circuit = GRZ(num_qubits=3, phi=np.pi/2)
       _generate_circuit_library_visualization(circuit)

    """

    def __init__(self, num_qubits: int, phi: float) -> None:
        """Create a new Global RZ (GRZ) gate.

        Args:
            num_qubits: number of qubits.
            phi: rotation angle about z-axis
        """
        super().__init__(num_qubits, name="grz")
        self.rz(phi, self.qubits)