# -*- coding: utf-8 -*-
# This code is part of Qiskit.
#
# (C) Copyright IBM 2017.
#
# 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.
"""The S and Sdg gate."""
import numpy
from qiskit.qasm import pi
from qiskit.circuit.gate import Gate
from qiskit.circuit.quantumregister import QuantumRegister
[docs]class SGate(Gate):
r"""Single qubit S gate (Z**0.5).
It induces a :math:`\pi/2` phase, and is sometimes called the P gate (phase).
This is a Clifford gate and a square-root of Pauli-Z.
**Matrix Representation:**
.. math::
S = \begin{pmatrix}
1 & 0 \\
0 & i
\end{pmatrix}
**Circuit symbol:**
.. parsed-literal::
┌───┐
q_0: ┤ S ├
└───┘
Equivalent to a :math:`\pi/2` radian rotation about the Z axis.
"""
def __init__(self, label=None):
"""Create new S gate."""
super().__init__('s', 1, [], label=label)
def _define(self):
"""
gate s a { u1(pi/2) a; }
"""
from .u1 import U1Gate
definition = []
q = QuantumRegister(1, 'q')
rule = [
(U1Gate(pi / 2), [q[0]], [])
]
for inst in rule:
definition.append(inst)
self.definition = definition
[docs] def inverse(self):
"""Return inverse of S (SdgGate)."""
return SdgGate()
[docs] def to_matrix(self):
"""Return a numpy.array for the S gate."""
return numpy.array([[1, 0],
[0, 1j]], dtype=complex)
[docs]class SdgGate(Gate):
r"""Single qubit S-adjoint gate (~Z**0.5).
It induces a :math:`-\pi/2` phase.
This is a Clifford gate and a square-root of Pauli-Z.
**Matrix Representation:**
.. math::
Sdg = \begin{pmatrix}
1 & 0 \\
0 & -i
\end{pmatrix}
**Circuit symbol:**
.. parsed-literal::
┌─────┐
q_0: ┤ Sdg ├
└─────┘
Equivalent to a :math:`\pi/2` radian rotation about the Z axis.
"""
def __init__(self, label=None):
"""Create new Sdg gate."""
super().__init__('sdg', 1, [], label=label)
def _define(self):
"""
gate sdg a { u1(-pi/2) a; }
"""
from .u1 import U1Gate
definition = []
q = QuantumRegister(1, 'q')
rule = [
(U1Gate(-pi / 2), [q[0]], [])
]
for inst in rule:
definition.append(inst)
self.definition = definition
[docs] def inverse(self):
"""Return inverse of Sdg (SGate)."""
return SGate()
[docs] def to_matrix(self):
"""Return a numpy.array for the Sdg gate."""
return numpy.array([[1, 0],
[0, -1j]], dtype=complex)