# 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.
"""T and Tdg gate."""
import math
from math import pi
from typing import Optional
import numpy
from qiskit.circuit.gate import Gate
from qiskit.circuit.library.standard_gates.p import PhaseGate
from qiskit.circuit.quantumregister import QuantumRegister
from qiskit.circuit._utils import with_gate_array
[docs]@with_gate_array([[1, 0], [0, (1 + 1j) / math.sqrt(2)]])
class TGate(Gate):
r"""Single qubit T gate (Z**0.25).
It induces a :math:`\pi/4` phase, and is sometimes called the pi/8 gate
(because of how the RZ(\pi/4) matrix looks like).
This is a non-Clifford gate and a fourth-root of Pauli-Z.
Can be applied to a :class:`~qiskit.circuit.QuantumCircuit`
with the :meth:`~qiskit.circuit.QuantumCircuit.t` method.
**Matrix Representation:**
.. math::
T = \begin{pmatrix}
1 & 0 \\
0 & e^{i\pi/4}
\end{pmatrix}
**Circuit symbol:**
.. parsed-literal::
┌───┐
q_0: ┤ T ├
└───┘
Equivalent to a :math:`\pi/4` radian rotation about the Z axis.
"""
def __init__(self, label: Optional[str] = None):
"""Create new T gate."""
super().__init__("t", 1, [], label=label)
def _define(self):
"""
gate t a { u1(pi/4) a; }
"""
# pylint: disable=cyclic-import
from qiskit.circuit.quantumcircuit import QuantumCircuit
from .u1 import U1Gate
q = QuantumRegister(1, "q")
qc = QuantumCircuit(q, name=self.name)
rules = [(U1Gate(pi / 4), [q[0]], [])]
for instr, qargs, cargs in rules:
qc._append(instr, qargs, cargs)
self.definition = qc
[docs] def inverse(self):
"""Return inverse T gate (i.e. Tdg)."""
return TdgGate()
[docs] def power(self, exponent: float):
"""Raise gate to a power."""
return PhaseGate(0.25 * numpy.pi * exponent)
[docs]@with_gate_array([[1, 0], [0, (1 - 1j) / math.sqrt(2)]])
class TdgGate(Gate):
r"""Single qubit T-adjoint gate (~Z**0.25).
It induces a :math:`-\pi/4` phase.
This is a non-Clifford gate and a fourth-root of Pauli-Z.
Can be applied to a :class:`~qiskit.circuit.QuantumCircuit`
with the :meth:`~qiskit.circuit.QuantumCircuit.tdg` method.
**Matrix Representation:**
.. math::
Tdg = \begin{pmatrix}
1 & 0 \\
0 & e^{-i\pi/4}
\end{pmatrix}
**Circuit symbol:**
.. parsed-literal::
┌─────┐
q_0: ┤ Tdg ├
└─────┘
Equivalent to a :math:`-\pi/4` radian rotation about the Z axis.
"""
def __init__(self, label: Optional[str] = None):
"""Create new Tdg gate."""
super().__init__("tdg", 1, [], label=label)
def _define(self):
"""
gate tdg a { u1(pi/4) a; }
"""
# pylint: disable=cyclic-import
from qiskit.circuit.quantumcircuit import QuantumCircuit
from .u1 import U1Gate
q = QuantumRegister(1, "q")
qc = QuantumCircuit(q, name=self.name)
rules = [(U1Gate(-pi / 4), [q[0]], [])]
for instr, qargs, cargs in rules:
qc._append(instr, qargs, cargs)
self.definition = qc
[docs] def inverse(self):
"""Return inverse Tdg gate (i.e. T)."""
return TGate()
[docs] def power(self, exponent: float):
"""Raise gate to a power."""
return PhaseGate(-0.25 * numpy.pi * exponent)