# -*- coding: utf-8 -*-
# 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.
"""iSWAP gate."""
import numpy as np
from qiskit.circuit.gate import Gate
from qiskit.circuit.quantumregister import QuantumRegister
[docs]class iSwapGate(Gate):
r"""iSWAP gate.
A 2-qubit XX+YY interaction.
This is a Clifford and symmetric gate. Its action is to swap two qubit
states and phase the :math:`|01\rangle` and :math:`|10\rangle`
amplitudes by i.
**Circuit Symbol:**
.. parsed-literal::
q_0: ─⨂─
│
q_1: ─⨂─
**Reference Implementation:**
.. parsed-literal::
┌───┐┌───┐ ┌───┐
q_0: ┤ S ├┤ H ├──■──┤ X ├─────
├───┤└───┘┌─┴─┐└─┬─┘┌───┐
q_1: ┤ S ├─────┤ X ├──■──┤ H ├
└───┘ └───┘ └───┘
**Matrix Representation:**
.. math::
iSWAP = R_{XX+YY}(-\frac{\pi}{2})
= exp(i \frac{\pi}{4} (X{\otimes}X+Y{\otimes}Y)) =
\begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & 0 & i & 0 \\
0 & i & 0 & 0 \\
0 & 0 & 0 & 1
\end{pmatrix}
This gate is equivalent to a SWAP up to a diagonal.
.. math::
iSWAP =
\begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 0 & 1
\end{pmatrix}
. \begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & i & 0 & 0 \\
0 & 0 & i & 0 \\
0 & 0 & 0 & 1
\end{pmatrix}
"""
def __init__(self):
"""Create new iSwap gate."""
super().__init__('iswap', 2, [])
def _define(self):
"""
gate iswap a,b {
s q[0];
s q[1];
h q[0];
cx q[0],q[1];
cx q[1],q[0];
h q[1];
}
"""
from .h import HGate
from .s import SGate
from .x import CXGate
q = QuantumRegister(2, 'q')
self.definition = [
(SGate(), [q[0]], []),
(SGate(), [q[1]], []),
(HGate(), [q[0]], []),
(CXGate(), [q[0], q[1]], []),
(CXGate(), [q[1], q[0]], []),
(HGate(), [q[1]], [])
]
[docs] def to_matrix(self):
"""Return a numpy.array for the iSWAP gate."""
return np.array([[1, 0, 0, 0],
[0, 0, 1j, 0],
[0, 1j, 0, 0],
[0, 0, 0, 1]], dtype=complex)