RZ gate

[jessding]

No description provided.

[Hanrui-Wang]

I think in pennylane and qiskit they use this implementation: https://www.quantum-inspire.com/kbase/rz-gate/
https://qiskit.org/documentation/stubs/qiskit.circuit.library.RZGate.html

They differ in a global phase. We'd better implement the one as them.

Below is the code from pennylane for your reference

class RZ(DiagonalOperation):
    r"""RZ(phi, wires)
    The single qubit Z rotation

    .. math:: R_z(\phi) = e^{-i\phi\sigma_z/2} = \begin{bmatrix}
                e^{-i\phi/2} & 0 \\
                0 & e^{i\phi/2}
            \end{bmatrix}.

    **Details:**

    * Number of wires: 1
    * Number of parameters: 1
    * Gradient recipe: :math:`\frac{d}{d\phi}f(R_z(\phi)) = \frac{1}{2}\left[f(R_z(\phi+\pi/2)) - f(R_z(\phi-\pi/2))\right]`
      where :math:`f` is an expectation value depending on :math:`R_z(\phi)`.

    Args:
        phi (float): rotation angle :math:`\phi`
        wires (Sequence[int] or int): the wire the operation acts on
    """
    num_params = 1
    num_wires = 1
    par_domain = "R"
    grad_method = "A"
    generator = [PauliZ, -1 / 2]

    @classmethod
    def _matrix(cls, *params):
        theta = params[0]
        p = cmath.exp(-0.5j * theta)

        return np.array([[p, 0], [0, p.conjugate()]])

    @classmethod
    def _eigvals(cls, *params):
        theta = params[0]
        p = cmath.exp(-0.5j * theta)

        return np.array([p, p.conjugate()])

[jessding]

updated