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aba_decomposer

Module containing classes that inherit from the ABADecomposer class to decompose a circuit into one of the Pauli ABA decompositions.

ABADecomposer

Bases: Decomposer, ABC

Source code in opensquirrel/passes/decomposer/aba_decomposer.py 
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class ABADecomposer(Decomposer, ABC):
    _gate_list: ClassVar[list[Callable[..., SingleQubitGate]]] = [Rx, Ry, Rz]

    def __init__(self, **kwargs: Any) -> None:
        super().__init__(**kwargs)
        self.index_a = self._gate_list.index(self.Ra)
        self.index_b = self._gate_list.index(self.Rb)

    @property
    @abstractmethod
    def Ra(self) -> Callable[..., SingleQubitGate]: ...  # noqa: N802

    @property
    @abstractmethod
    def Rb(self) -> Callable[..., SingleQubitGate]: ...  # noqa: N802

    def decompose(self, gate: Gate) -> list[Gate]:
        """Decomposes a single-qubit gate into (at most) three single-qubit gates following the
        R$a$-R$b$-R$a$ decomposition, where [$ab$] are in $\\{x,y,z\\}$ and $a$ is not equal to $b$.

        For instance, the ZYZ decomposer decomposes a single-qubit gate into Rz-Ry-Rz.

        Args:
            gate (Gate): Single-qubit gate to decompose.

        Returns:
            A sequence of (at most) three gates, following the R$a$-R$b$-R$a$ decomposition.

        """
        if not isinstance(gate, SingleQubitGate):
            return [gate]

        theta_a1, theta_b, theta_a2 = self._determine_rotation_angles(gate.bsr.axis, gate.bsr.angle)
        return filter_out_identities(
            [
                self.Ra(gate.qubit, theta_a1),
                self.Rb(gate.qubit, theta_b),
                self.Ra(gate.qubit, theta_a2),
            ]
        )

    def _b_and_c_components_in_negative_octant(self, b_component: float, c_component: float) -> bool:
        """Checks if the values for
        the B and C axes fall in one of the two negative octants (a positive or negative, and B and
        C negative, or one of them zero).

        Args:
            b_component (float): Value of the B component.
            c_component (float): Value of the C component.

        Returns:
            True if the values for axis B and C are both negative or zero, but not zero at the same time.
            False otherwise.
        """
        return (
            (b_component < 0 or abs(b_component) < ATOL)
            and (c_component < 0 or abs(c_component) < ATOL)
            and not (abs(b_component) < ATOL and abs(c_component) < ATOL)
        )

    def _determine_rotation_angles(self, axis: AxisLike, theta: float) -> tuple[float, float, float]:
        """Determines the rotation angles for the R$a$-R$b$-R$a$ decomposition.

        Args:
            axis (AxisLike): Axis of the Bloch sphere rotation.
            theta (float): Angle $\\theta$ of the Bloch sphere rotation.

        Returns:
            The rotation angles $\\theta_{a_1}$, $\\theta_b$, and $\\theta_{a_2}$ around axes $a$,
            $b$, and $a$, respectively.

        """
        if not (-math.pi + ATOL < theta <= math.pi + ATOL):
            msg = f"angle {theta!r} is not normalized between -pi and pi"
            raise ValueError(msg)

        component_a, component_b, component_c = self._set_components(axis)

        theta_b = 2 * acos(math.cos(theta / 2) * math.sqrt(1 + (component_a * math.tan(theta / 2)) ** 2))
        theta_b = math.copysign(theta_b, theta)

        p = 2 * math.atan2(component_a * math.sin(theta / 2), math.cos(theta / 2))
        if abs(math.sin(theta_b / 2)) < ATOL:
            m = p
        else:
            m = 2 * acos(float(component_b) * math.sin(theta / 2) / math.sin(theta_b / 2))
            if math.pi - abs(m) > ATOL:
                ret_sign = 2 * math.atan2(component_c, component_a)
                m = math.copysign(m, ret_sign)

        if are_axes_consecutive(self.index_a, self.index_b):
            m = -m

        theta_a1 = (p + m) / 2
        theta_a2 = p - theta_a1

        if self._b_and_c_components_in_negative_octant(component_b, component_c):
            theta_a1, theta_a2 = theta_a2, theta_a1

        return theta_a1, theta_b, theta_a2

    def _find_unused_index(self) -> int:
        """Finds the index of the axis component that is not used in the decomposition.
        For example, for the Rz-Ry-Rz decomposition, the index returned is 0 (since it is x).

        Returns:
            Index of the axis component that is not used in the decomposition.

        """
        return ({0, 1, 2} - {self.index_a, self.index_b}).pop()

    def _set_components(self, axis: AxisLike) -> tuple[Any, Any, Any]:
        """Sets a new rotation axis (a, b, c).

        For instance, for an Rz-Ry-Rz decomposition the initial axis (x, y, z) is set to
        (a, b, c) = (z, y, x).

        Parameters:
            axis (AxisLike): Axis of a Bloch sphere rotation

         Returns:
             A triplet (a, b, c) where a, b, and c are the values of x, y, and z reordered.

        """
        axis_ = Axis(axis)
        return axis_[self.index_a], axis_[self.index_b], axis_[self._find_unused_index()]

decompose 

decompose(gate: Gate) -> list[Gate]

Decomposes a single-qubit gate into (at most) three single-qubit gates following the R\(a\)-R\(b\)-R\(a\) decomposition, where [\(ab\)] are in \(\{x,y,z\}\) and \(a\) is not equal to \(b\).

For instance, the ZYZ decomposer decomposes a single-qubit gate into Rz-Ry-Rz.

Parameters:

Name Type Description Default
gate Gate

Single-qubit gate to decompose.

 required

Returns:

Type Description
list[Gate]

A sequence of (at most) three gates, following the R\(a\)-R\(b\)-R\(a\) decomposition.
Source code in opensquirrel/passes/decomposer/aba_decomposer.py 
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def decompose(self, gate: Gate) -> list[Gate]:
    """Decomposes a single-qubit gate into (at most) three single-qubit gates following the
    R$a$-R$b$-R$a$ decomposition, where [$ab$] are in $\\{x,y,z\\}$ and $a$ is not equal to $b$.

    For instance, the ZYZ decomposer decomposes a single-qubit gate into Rz-Ry-Rz.

    Args:
        gate (Gate): Single-qubit gate to decompose.

    Returns:
        A sequence of (at most) three gates, following the R$a$-R$b$-R$a$ decomposition.

    """
    if not isinstance(gate, SingleQubitGate):
        return [gate]

    theta_a1, theta_b, theta_a2 = self._determine_rotation_angles(gate.bsr.axis, gate.bsr.angle)
    return filter_out_identities(
        [
            self.Ra(gate.qubit, theta_a1),
            self.Rb(gate.qubit, theta_b),
            self.Ra(gate.qubit, theta_a2),
        ]
    )

XYXDecomposer

Bases: ABADecomposer

Decomposes single-qubit gates into a Rx-Ry-Rx decomposition.

Source code in opensquirrel/passes/decomposer/aba_decomposer.py 
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class XYXDecomposer(ABADecomposer):
    """Decomposes single-qubit gates into a Rx-Ry-Rx decomposition."""

    @property
    def Ra(self) -> Callable[..., SingleQubitGate]:  # noqa: N802
        return Rx

    @property
    def Rb(self) -> Callable[..., SingleQubitGate]:  # noqa: N802
        return Ry

XZXDecomposer

Bases: ABADecomposer

Decomposes single-qubit gates into a Rx-Rz-Rx decomposition.

Source code in opensquirrel/passes/decomposer/aba_decomposer.py 
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class XZXDecomposer(ABADecomposer):
    """Decomposes single-qubit gates into a Rx-Rz-Rx decomposition."""

    @property
    def Ra(self) -> Callable[..., SingleQubitGate]:  # noqa: N802
        return Rx

    @property
    def Rb(self) -> Callable[..., SingleQubitGate]:  # noqa: N802
        return Rz

YXYDecomposer

Bases: ABADecomposer

Decomposes single-qubit gates into a Ry-Rx-Ry decomposition.

Source code in opensquirrel/passes/decomposer/aba_decomposer.py 
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class YXYDecomposer(ABADecomposer):
    """Decomposes single-qubit gates into a Ry-Rx-Ry decomposition."""

    @property
    def Ra(self) -> Callable[..., SingleQubitGate]:  # noqa: N802
        return Ry

    @property
    def Rb(self) -> Callable[..., SingleQubitGate]:  # noqa: N802
        return Rx

YZYDecomposer

Bases: ABADecomposer

Decomposes single-qubit gates into a Ry-Rz-Ry decomposition.

Source code in opensquirrel/passes/decomposer/aba_decomposer.py 
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class YZYDecomposer(ABADecomposer):
    """Decomposes single-qubit gates into a Ry-Rz-Ry decomposition."""

    @property
    def Ra(self) -> Callable[..., SingleQubitGate]:  # noqa: N802
        return Ry

    @property
    def Rb(self) -> Callable[..., SingleQubitGate]:  # noqa: N802
        return Rz

ZXZDecomposer

Bases: ABADecomposer

Decomposes single-qubit gates into a Rz-Rx-Rz decomposition.

Source code in opensquirrel/passes/decomposer/aba_decomposer.py 
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class ZXZDecomposer(ABADecomposer):
    """Decomposes single-qubit gates into a Rz-Rx-Rz decomposition."""

    @property
    def Ra(self) -> Callable[..., SingleQubitGate]:  # noqa: N802
        return Rz

    @property
    def Rb(self) -> Callable[..., SingleQubitGate]:  # noqa: N802
        return Rx

ZYZDecomposer

Bases: ABADecomposer

Decomposes single-qubit gates into a Rz-Ry-Rz decomposition.

Source code in opensquirrel/passes/decomposer/aba_decomposer.py 
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class ZYZDecomposer(ABADecomposer):
    """Decomposes single-qubit gates into a Rz-Ry-Rz decomposition."""

    @property
    def Ra(self) -> Callable[..., SingleQubitGate]:  # noqa: N802
        return Rz

    @property
    def Rb(self) -> Callable[..., SingleQubitGate]:  # noqa: N802
        return Ry