Source code for qiskit.circuit.library.standard_gates.t

# 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 numpy
from qiskit.qasm import pi
from qiskit.circuit.gate import Gate
from qiskit.circuit.quantumregister import QuantumRegister


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.

    **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=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

    def inverse(self):
        """Return inverse T gate (i.e. Tdg)."""
        return TdgGate()

    def __array__(self, dtype=None):
        """Return a numpy.array for the T gate."""
        return numpy.array([[1, 0], [0, (1 + 1j) / numpy.sqrt(2)]], dtype=dtype)


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.

    **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/2` radian rotation about the Z axis.
    """

    def __init__(self, label=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

    def inverse(self):
        """Return inverse Tdg gate (i.e. T)."""
        return TGate()

    def __array__(self, dtype=None):
        """Return a numpy.array for the inverse T gate."""
        return numpy.array([[1, 0], [0, (1 - 1j) / numpy.sqrt(2)]], dtype=dtype)