"""This module implments the CKMDGate."""
from __future__ import annotations
import numpy as np
import numpy.typing as npt
from bqskit.ir.gates.qutritgate import QutritGate
from bqskit.qis.unitary.differentiable import DifferentiableUnitary
from bqskit.qis.unitary.unitary import RealVector
from bqskit.qis.unitary.unitarymatrix import UnitaryMatrix
from bqskit.utils.cachedclass import CachedClass
[docs]
class CKMdgGate(QutritGate, DifferentiableUnitary, CachedClass):
"""
The Cabibbo-Kobayashi-Maskawa dagger single qutrit gate.
References:
- Particle Data Group review:
https://pdg.lbl.gov/2023/reviews/rpp2022-rev-ckm-matrix.pdf
- https://link.springer.com/article/10.1007/JHEP01(2019)106
Notes:
- Due to the current experimental searches for the exact values
of the mixing parameters, and to allow for beyond standard
model physics, we provide the user with the flexibility of
setting each parameter.
"""
_num_qudits = 1
_num_params = 4
[docs]
def get_unitary(self, params: RealVector = []) -> UnitaryMatrix:
"""Return the unitary for this gate, see :class:`Unitary` for more."""
self.check_parameters(params)
# Parameters are mapped to the reference above as follows:
# - params[0] -> 1-3
# - params[1] -> 1-2
# - params[2] -> 2-3
# - params[3] -> cp
s1 = np.sin(-params[0])
c1 = np.cos(-params[0])
s2 = np.sin(-params[1])
c2 = np.cos(-params[1])
s3 = np.sin(-params[2])
c3 = np.cos(-params[2])
p1 = np.exp(-1j * params[3])
m1 = np.exp(1j * params[3])
u1 = np.array([[1, 0, 0], [0, c3, s3], [0, -s3, c3]])
u2 = np.array([[c1, 0, s1 * m1], [0, 1, 0], [-s1 * p1, 0, c1]])
u3 = np.array([[c2, s2, 0], [-s2, c2, 0], [0, 0, 1]])
return UnitaryMatrix(u1 @ u2 @ u3)
[docs]
def get_grad(self, params: RealVector = []) -> npt.NDArray[np.complex128]:
"""
Return the gradient for this gate.
See :class:`DifferentiableUnitary` for more info.
"""
self.check_parameters(params)
s1 = np.sin(-params[0])
c1 = np.cos(-params[0])
s2 = np.sin(-params[1])
c2 = np.cos(-params[1])
s3 = np.sin(-params[2])
c3 = np.cos(-params[2])
p1 = np.exp(-1j * params[3])
m1 = np.exp(1j * params[3])
u1 = np.array([[1, 0, 0], [0, c3, s3], [0, -s3, c3]])
u2 = np.array([[c1, 0, s1 * m1], [0, 1, 0], [-s1 * p1, 0, c1]])
u3 = np.array([[c2, s2, 0], [-s2, c2, 0], [0, 0, 1]])
u1p = np.array([[0, 0, 0], [0, -s3, c3], [0, -c3, -s3]])
u2p1 = np.array([
[-s1, 0, c1 * m1], [0, 0, 0],
[-c1 * m1, 0, s1],
])
u2p2 = np.array([
[0, 0, -1j * s1 * m1], [0, 0, 0],
[-1j * s1 * p1, 0, 0],
])
u3p = np.array([[s2, c2, 0], [-c2, -s2, 0], [0, 0, 0]])
return np.array(
[
# wrt params[0] -> 1-3
u1 @ u2p1 @ u3,
# wrt params[1] -> 1-2
u1 @ u2 @ u3p,
# wrt params[2] -> 2-3
u1p @ u2 @ u3,
# wrt params[3] -> cp
u1 @ u2p2 @ u3,
], dtype=np.complex128,
)