Source code for mimiqcircuits.operations.gates.standard.t

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# Copyright © 2022-2023 University of Strasbourg. All Rights Reserved.
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# Licensed under the Apache License, Version 2.0 (the "License");
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#     http://www.apache.org/licenses/LICENSE-2.0
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from mimiqcircuits.operations.power import Power
from mimiqcircuits.operations.inverse import Inverse
from mimiqcircuits.operations.gates.standard.s import GateS
from mimiqcircuits.operations.gates.standard.u import GateU
from symengine import pi
import mimiqcircuits as mc




class GateT(Power):
    r""" Single qubit T gate.

    **Matrix representation:**

    .. math::
        \operatorname{T} = \begin{pmatrix}
            1 & 0 \\
            0 & \exp\left(\frac{i\pi}{4}\right)
        \end{pmatrix}

    Examples:
        >>> from mimiqcircuits import *
        >>> GateT()
        T
        >>> GateT().matrix()
        [1.0, 0]
        [0, 0.707106781186548 + 0.707106781186548*I]
        <BLANKLINE>
        >>> c = Circuit().push(GateT(), 0)
        >>> c
        1-qubit circuit with 1 instructions:
        └── T @ q[0]
        <BLANKLINE>
        >>> GateT().power(2), GateT().inverse()
        (S, T†)
        >>> GateT().decompose()
        1-qubit circuit with 1 instructions:
        └── U(0, 0, (1/4)*pi, 0.0) @ q[0]
        <BLANKLINE>
    """

    _name = "T"

    def __init__(self):
        super().__init__(GateS(), 1 / 2)



    def isopalias(self):
        return True




    def inverse(self):
        return GateTDG()


    def _power(self, p):
        # T^2 * T^2 * T^2 * T^2 = S^2 * S^2 = Z * Z = ID
        if p % 8 == 0:
            return mc.GateID()

        # T^(8n + 1) = T
        if p % 8 == 1:
            return GateT()

        # T^(8n - 1) = T†
        if p % 8 == 7:
            return GateTDG()

        # T^(4n) = Z^n
        if p % 4 == 0:
            return mc.GateZ().power(p / 4)

        # T^(2n) = S^n
        if p % 2 == 0:
            return mc.GateS().power(p / 2)

        return mc.Power(self, p)

    def __str__(self):
        return f"{self.name}"

    def _decompose(self, circ, qubits, bits):
        q = qubits[0]
        circ.push(GateU(0, 0, pi / 4), q)
        return circ





class GateTDG(Inverse):
    r"""Single qubit T-dagger gate (conjugate transpose of the T gate).

    **Matrix representation:**

    .. math::
        \operatorname{T}^\dagger = \begin{pmatrix}
            1 & 0 \\
            0 & \exp\left(\frac{-i\pi}{4}\right)
        \end{pmatrix}

    Examples:
        >>> from mimiqcircuits import *
        >>> GateTDG()
        T†
        >>> GateTDG().matrix()
        [1.0, 0]
        [0, 0.707106781186547 - 0.707106781186547*I]
        <BLANKLINE>
        >>> c = Circuit().push(GateTDG(), 0)
        >>> c
        1-qubit circuit with 1 instructions:
        └── T† @ q[0]
        <BLANKLINE>
        >>> GateTDG().power(2), GateTDG().inverse()
        (T†**2, T)
        >>> GateTDG().decompose()
        1-qubit circuit with 1 instructions:
        └── U(0, 0, (-1/4)*pi, 0.0) @ q[0]
        <BLANKLINE>
    """

    def __init__(self):
        super().__init__(GateT())



    def isopalias(self):
        return True




    def inverse(self):
        return GateT()


    def _decompose(self, circ, qubits, bits):
        q = qubits[0]
        circ.push(GateU(0, 0, -pi / 4), q)
        return circ