# Source code for qiskit.circuit.library.generalized_gates.gr

```
# 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
[docs]class GR(QuantumCircuit):
r"""Global R gate.
**Circuit symbol:**
.. parsed-literal::
┌──────────┐
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:**
.. jupyter-execute::
:hide-code:
from qiskit.circuit.library import GR
import qiskit.tools.jupyter
import numpy as np
circuit = GR(num_qubits=3, theta=np.pi/4, phi=np.pi/2)
%circuit_library_info circuit
"""
[docs] def __init__(self,
num_qubits: int,
theta: float,
phi: float) -> None:
"""Create a new Global R (GR) gate.
Args:
num_qubits: number of qubits.
theta: rotation angle about axis determined by phi
phi: angle of rotation axis in xy-plane
"""
super().__init__(num_qubits, name="gr")
self.r(theta, phi, self.qubits)
[docs]class GRX(GR):
r"""Global RX gate.
**Circuit symbol:**
.. parsed-literal::
┌──────────┐
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:**
.. jupyter-execute::
:hide-code:
from qiskit.circuit.library import GRX
import qiskit.tools.jupyter
import numpy as np
circuit = GRX(num_qubits=3, theta=np.pi/4)
%circuit_library_info circuit
"""
[docs] 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)
[docs]class GRY(GR):
r"""Global RY gate.
**Circuit symbol:**
.. parsed-literal::
┌──────────┐
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:**
.. jupyter-execute::
:hide-code:
from qiskit.circuit.library import GRY
import qiskit.tools.jupyter
import numpy as np
circuit = GRY(num_qubits=3, theta=np.pi/4)
%circuit_library_info circuit
"""
[docs] 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)
[docs]class GRZ(QuantumCircuit):
r"""Global RZ gate.
**Circuit symbol:**
.. parsed-literal::
┌──────────┐
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:**
.. jupyter-execute::
:hide-code:
from qiskit.circuit.library import GRZ
import qiskit.tools.jupyter
import numpy as np
circuit = GRZ(num_qubits=3, phi=np.pi/2)
%circuit_library_info circuit
"""
[docs] 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)
```