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

```
# This code is part of Qiskit.
#
# (C) Copyright IBM 2019.
#
# 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 Mølmer–Sørensen gate.
"""
from typing import Union, List
import numpy as np
from qiskit.circuit.quantumcircuit import QuantumCircuit
from qiskit.circuit.quantumregister import QuantumRegister
from qiskit.circuit.library.standard_gates import RXXGate
from qiskit.circuit.gate import Gate
[docs]class GMS(QuantumCircuit):
r"""Global Mølmer–Sørensen gate.
**Circuit symbol:**
.. parsed-literal::
┌───────────┐
q_0: ┤0 ├
│ │
q_1: ┤1 GMS ├
│ │
q_2: ┤2 ├
└───────────┘
**Expanded Circuit:**
.. jupyter-execute::
:hide-code:
from qiskit.circuit.library import GMS
import qiskit.tools.jupyter
import numpy as np
circuit = GMS(num_qubits=3, theta=[[0, np.pi/4, np.pi/8],
[0, 0, np.pi/2],
[0, 0, 0]])
%circuit_library_info circuit.decompose()
The Mølmer–Sørensen gate is native to ion-trap systems. The global MS
can be applied to multiple ions to entangle multiple qubits simultaneously [1].
In the two-qubit case, this is equivalent to an XX(theta) interaction,
and is thus reduced to the RXXGate. The global MS gate is a sum of XX
interactions on all pairs [2].
.. math::
GMS(\chi_{12}, \chi_{13}, ..., \chi_{n-1 n}) =
exp(-i \sum_{i=1}^{n} \sum_{j=i+1}^{n} X{\otimes}X \frac{\chi_{ij}}{2})
**References:**
[1] Sørensen, A. and Mølmer, K., Multi-particle entanglement of hot trapped ions.
Physical Review Letters. 82 (9): 1835–1838.
`arXiv:9810040 <https://arxiv.org/abs/quant-ph/9810040>`_
[2] Maslov, D. and Nam, Y., Use of global interactions in efficient quantum circuit
constructions. New Journal of Physics, 20(3), p.033018.
`arXiv:1707.06356 <https://arxiv.org/abs/1707.06356>`_
"""
[docs] def __init__(self,
num_qubits: int,
theta: Union[List[List[float]], np.ndarray]) -> None:
"""Create a new Global Mølmer–Sørensen (GMS) gate.
Args:
num_qubits: width of gate.
theta: a num_qubits x num_qubits symmetric matrix of
interaction angles for each qubit pair. The upper
triangle is considered.
"""
super().__init__(num_qubits, name="gms")
if not isinstance(theta, list):
theta = [theta] * int((num_qubits**2 - 1) / 2)
gms = QuantumCircuit(num_qubits, name="gms")
for i in range(self.num_qubits):
for j in range(i + 1, self.num_qubits):
gms.append(RXXGate(theta[i][j]), [i, j])
self.append(gms, self.qubits)
class MSGate(Gate):
"""MSGate has been deprecated.
Please use ``GMS`` in ``qiskit.circuit.generalized_gates`` instead.
Global Mølmer–Sørensen gate.
The Mølmer–Sørensen gate is native to ion-trap systems. The global MS can be
applied to multiple ions to entangle multiple qubits simultaneously.
In the two-qubit case, this is equivalent to an XX(theta) interaction,
and is thus reduced to the RXXGate.
"""
def __init__(self, num_qubits, theta, label=None):
"""Create new MS gate."""
super().__init__('ms', num_qubits, [theta], label=label)
def _define(self):
theta = self.params[0]
q = QuantumRegister(self.num_qubits, 'q')
qc = QuantumCircuit(q, name=self.name)
for i in range(self.num_qubits):
for j in range(i + 1, self.num_qubits):
qc._append(RXXGate(theta), [q[i], q[j]], [])
self.definition = qc
```