"""This module implements the PauliGate."""
from __future__ import annotations
from typing import Any
import numpy as np
import numpy.typing as npt
import scipy as sp
from bqskit.ir.gates.generalgate import GeneralGate
from bqskit.ir.gates.qubitgate import QubitGate
from bqskit.qis.pauli import PauliMatrices
from bqskit.qis.unitary.differentiable import DifferentiableUnitary
from bqskit.qis.unitary.unitary import RealVector
from bqskit.qis.unitary.unitarymatrix import UnitaryMatrix
from bqskit.utils.docs import building_docs
from bqskit.utils.math import dexpmv
from bqskit.utils.math import dot_product
from bqskit.utils.math import pauli_expansion
from bqskit.utils.math import unitary_log_no_i
[docs]
class PauliGate(QubitGate, DifferentiableUnitary, GeneralGate):
"""
A gate representing an arbitrary rotation.
This gate is given by:
.. math::
\\exp({i(\\vec{\\alpha} \\cdot \\vec{\\sigma^{\\otimes n}})})
Where :math:`\\vec{\\alpha}` are the gate's parameters,
:math:`\\vec{\\sigma}` are the Pauli matrices,
and :math:`n` is the number of qubits this gate acts on.
"""
[docs]
def __init__(self, num_qudits: int) -> None:
"""
Create a PauliGate acting on `num_qudits` qubits.
Args:
num_qudits (int): The number of qudits this gate will act on.
Raises:
ValueError: If `num_qudits` is nonpositive.
"""
if num_qudits <= 0:
raise ValueError('Expected positive integer, got %d' % num_qudits)
self._name = 'PauliGate(%s)' % num_qudits
self._num_qudits = num_qudits
self.paulis = PauliMatrices(self.num_qudits)
self._num_params = len(self.paulis)
if building_docs():
self.sigmav: npt.NDArray[Any] = np.array([])
else:
self.sigmav = (-1j / 2) * self.paulis.numpy
[docs]
def get_unitary(self, params: RealVector = []) -> UnitaryMatrix:
"""Return the unitary for this gate, see :class:`Unitary` for more."""
self.check_parameters(params)
H = dot_product(params, self.sigmav)
eiH = sp.linalg.expm(H)
return UnitaryMatrix(eiH, check_arguments=False)
[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)
H = dot_product(params, self.sigmav)
_, dU = dexpmv(H, self.sigmav)
return dU
[docs]
def get_unitary_and_grad(
self,
params: RealVector = [],
) -> tuple[UnitaryMatrix, npt.NDArray[np.complex128]]:
"""
Return the unitary and gradient for this gate.
See :class:`DifferentiableUnitary` for more info.
"""
self.check_parameters(params)
H = dot_product(params, self.sigmav)
U, dU = dexpmv(H, self.sigmav)
return UnitaryMatrix(U, check_arguments=False), dU
[docs]
def calc_params(self, utry: UnitaryMatrix) -> list[float]:
"""Return the parameters for this gate to implement `utry`"""
return list(-2 * pauli_expansion(unitary_log_no_i(utry.numpy)))
def __eq__(self, o: object) -> bool:
return isinstance(o, PauliGate) and self.num_qudits == o.num_qudits
def __hash__(self) -> int:
return hash((self.__class__.__name__, self.num_qudits))