def decompose_ua(phi, wires=None):
r"""Implements the circuit decomposing the controlled application of the unitary
:math:`U_A(\phi)`
.. math::
U_A(\phi) = \left(\begin{array}{cc} 0 & e^{-i\phi} \\ e^{-i\phi} & 0 \\ \end{array}\right)
in terms of the quantum operations supported by PennyLane.
:math:`U_A(\phi)` is used in `arXiv:1805.04340 <https://arxiv.org/abs/1805.04340>`_,
to define two-qubit exchange gates required to build particle-conserving
VQE ansatze for quantum chemistry simulations. See :func:`~.ParticleConservingU1`.
:math:`U_A(\phi)` is expressed in terms of ``PhaseShift``, ``Rot`` and ``PauliZ`` operations
:math:`U_A(\phi) = R_\phi(-2\phi) R(-\phi, \pi, \phi) \sigma_z`.
Args:
phi (float): angle :math:`\phi` defining the unitary :math:`U_A(\phi)`
wires (list[Wires]): the wires ``n`` and ``m`` the circuit acts on
"""
n, m = wires
CZ(wires=wires)
CRot(-phi, np.pi, phi, wires=wires)
# decomposition of C-PhaseShift(2*phi) gate
PhaseShift(-phi, wires=m)
CNOT(wires=wires)
PhaseShift(phi, wires=m)
CNOT(wires=wires)
PhaseShift(-phi, wires=n)
def entangler(par1, par2, wires):
"""Implements a two qubit unitary consisting of a controlled-Z entangler and Pauli-Y rotations.
Args:
par1 (float or qml.Variable): parameter of first Pauli-Y rotation
par2 (float or qml.Variable): parameter of second Pauli-Y rotation
wires (Wires): two wire indices that unitary acts on
"""
CZ(wires=wires)
RY(par1, wires=wires[0])
RY(par2, wires=wires[1])
class TestKrausOps:
"""Unit tests for the method `_get_kraus_ops()`"""
unitary_ops = [
(PauliX, np.array([[0, 1], [1, 0]])),
(Hadamard, np.array([[INV_SQRT2, INV_SQRT2], [INV_SQRT2,
-INV_SQRT2]])),
(CNOT,
np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]])),
]
@pytest.mark.parametrize("ops", unitary_ops)
def test_unitary_kraus(self, ops, tol):
"""Tests that matrices of non-diagonal unitary operations are retrieved correctly"""
dev = qml.device("default.mixed", wires=2)
assert np.allclose(dev._get_kraus(ops[0]), [ops[1]], atol=tol, rtol=0)
diagonal_ops = [
(PauliZ(wires=0), np.array([1, -1])),
(CZ(wires=[0, 1]), np.array([1, 1, 1, -1])),
]
@pytest.mark.parametrize("ops", diagonal_ops)
def test_diagonal_kraus(self, ops, tol):
"""Tests that matrices of non-diagonal unitary operations are retrieved correctly"""
dev = qml.device("default.mixed", wires=2)
assert np.allclose(dev._get_kraus(ops[0]), ops[1], atol=tol, rtol=0)
p = 0.5
K0 = np.sqrt(1 - p) * np.eye(2)
K1 = np.sqrt(p / 3) * np.array([[0, 1], [1, 0]])
K2 = np.sqrt(p / 3) * np.array([[0, -1j], [1j, 0]])
K3 = np.sqrt(p / 3) * np.array([[1, 0], [0, -1]])
channel_ops = [
(
AmplitudeDamping(p, wires=0),
[
np.diag([1, np.sqrt(1 - p)]),
np.sqrt(p) * np.array([[0, 1], [0, 0]])
],
),
(DepolarizingChannel(p, wires=0), [K0, K1, K2, K3]),
]
@pytest.mark.parametrize("ops", channel_ops)
def test_channel_kraus(self, ops, tol):
"""Tests that kraus matrices of non-unitary channels are retrieved correctly"""
dev = qml.device("default.mixed", wires=1)
assert np.allclose(dev._get_kraus(ops[0]), ops[1], atol=tol, rtol=0)