diff --git a/pennylane/ops/qutrit/channel.py b/pennylane/ops/qutrit/channel.py index f07811086bc..92643481d51 100644 --- a/pennylane/ops/qutrit/channel.py +++ b/pennylane/ops/qutrit/channel.py @@ -234,39 +234,39 @@ class QutritAmplitudeDamping(Channel): .. math:: K_0 = \begin{bmatrix} 1 & 0 & 0\\ - 0 & \sqrt{1-\gamma_1} & 0 \\ - 0 & 0 & \sqrt{1-(\gamma_2+\gamma_3)} + 0 & \sqrt{1-\gamma_{01}} & 0 \\ + 0 & 0 & \sqrt{1-(\gamma_{02}+\gamma_{12})} \end{bmatrix} .. math:: K_1 = \begin{bmatrix} - 0 & \sqrt{\gamma_1} & 0 \\ + 0 & \sqrt{\gamma_{01}} & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}, \quad K_2 = \begin{bmatrix} - 0 & 0 & \sqrt{\gamma_2} \\ + 0 & 0 & \sqrt{\gamma_{02}} \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}, \quad K_3 = \begin{bmatrix} 0 & 0 & 0 \\ - 0 & 0 & \sqrt{\gamma_3} \\ + 0 & 0 & \sqrt{\gamma_{12}} \\ 0 & 0 & 0 \end{bmatrix} - where :math:`\gamma_1, \gamma_2, \gamma_3 \in [0, 1]` are the amplitude damping + where :math:`\gamma_{01}, \gamma_{02}, \gamma_{12} \in [0, 1]` are the amplitude damping probabilities for subspaces (0,1), (0,2), and (1,2) respectively. .. note:: - When :math:`\gamma_3=0` then Kraus operators :math:`\{K_0, K_1, K_2\}` are adapted from + When :math:`\gamma_{12}=0` then Kraus operators :math:`\{K_0, K_1, K_2\}` are adapted from [`1 `_] (Eq. 8). The Kraus operator :math:`K_3` represents the :math:`|2 \rangle \rightarrow |1 \rangle` transition which is more likely on some devices [`2 `_] (Sec II.A). - To maintain normalization :math:`\gamma_2 + \gamma_3 \leq 1`. + To maintain normalization :math:`\gamma_{02} + \gamma_{12} \leq 1`. **Details:** @@ -275,9 +275,9 @@ class QutritAmplitudeDamping(Channel): * Number of parameters: 3 Args: - gamma_1 (float): :math:`|1 \rangle \rightarrow |0 \rangle` amplitude damping probability. - gamma_2 (float): :math:`|2 \rangle \rightarrow |0 \rangle` amplitude damping probability. - gamma_3 (float): :math:`|2 \rangle \rightarrow |1 \rangle` amplitude damping probability. + gamma_01 (float): :math:`|1 \rangle \rightarrow |0 \rangle` amplitude damping probability. + gamma_02 (float): :math:`|2 \rangle \rightarrow |0 \rangle` amplitude damping probability. + gamma_12 (float): :math:`|2 \rangle \rightarrow |1 \rangle` amplitude damping probability. wires (Sequence[int] or int): the wire the channel acts on id (str or None): String representing the operation (optional) """ @@ -286,25 +286,25 @@ class QutritAmplitudeDamping(Channel): num_wires = 1 grad_method = "F" - def __init__(self, gamma_1, gamma_2, gamma_3, wires, id=None): + def __init__(self, gamma_01, gamma_02, gamma_12, wires, id=None): # Verify input - for gamma in (gamma_1, gamma_2, gamma_3): + for gamma in (gamma_01, gamma_02, gamma_12): if not math.is_abstract(gamma): if not 0.0 <= gamma <= 1.0: raise ValueError("Each probability must be in the interval [0,1]") - if not (math.is_abstract(gamma_2) or math.is_abstract(gamma_3)): - if not 0.0 <= gamma_2 + gamma_3 <= 1.0: - raise ValueError(r"\gamma_2+\gamma_3 must be in the interval [0,1]") - super().__init__(gamma_1, gamma_2, gamma_3, wires=wires, id=id) + if not (math.is_abstract(gamma_02) or math.is_abstract(gamma_12)): + if not 0.0 <= gamma_02 + gamma_12 <= 1.0: + raise ValueError(r"\gamma_{02}+\gamma_{12} must be in the interval [0,1]") + super().__init__(gamma_01, gamma_02, gamma_12, wires=wires, id=id) @staticmethod - def compute_kraus_matrices(gamma_1, gamma_2, gamma_3): # pylint:disable=arguments-differ + def compute_kraus_matrices(gamma_01, gamma_02, gamma_12): # pylint:disable=arguments-differ r"""Kraus matrices representing the ``QutritAmplitudeDamping`` channel. Args: - gamma_1 (float): :math:`|1\rangle \rightarrow |0\rangle` amplitude damping probability. - gamma_2 (float): :math:`|2\rangle \rightarrow |0\rangle` amplitude damping probability. - gamma_3 (float): :math:`|2\rangle \rightarrow |1\rangle` amplitude damping probability. + gamma_01 (float): :math:`|1\rangle \rightarrow |0\rangle` amplitude damping probability. + gamma_02 (float): :math:`|2\rangle \rightarrow |0\rangle` amplitude damping probability. + gamma_12 (float): :math:`|2\rangle \rightarrow |1\rangle` amplitude damping probability. Returns: list(array): list of Kraus matrices @@ -328,21 +328,20 @@ def compute_kraus_matrices(gamma_1, gamma_2, gamma_3): # pylint:disable=argumen ] """ K0 = math.diag( - [1, math.sqrt(1 - gamma_1 + math.eps), math.sqrt(1 - gamma_2 - gamma_3 + math.eps)] + [1, math.sqrt(1 - gamma_01 + math.eps), math.sqrt(1 - gamma_02 - gamma_12 + math.eps)] ) - K1 = math.sqrt(gamma_1 + math.eps) * math.convert_like( - math.cast_like(math.array([[0, 1, 0], [0, 0, 0], [0, 0, 0]]), gamma_1), gamma_1 + K1 = math.sqrt(gamma_01 + math.eps) * math.convert_like( + math.cast_like(math.array([[0, 1, 0], [0, 0, 0], [0, 0, 0]]), gamma_01), gamma_01 ) - K2 = math.sqrt(gamma_2 + math.eps) * math.convert_like( - math.cast_like(math.array([[0, 0, 1], [0, 0, 0], [0, 0, 0]]), gamma_2), gamma_2 + K2 = math.sqrt(gamma_02 + math.eps) * math.convert_like( + math.cast_like(math.array([[0, 0, 1], [0, 0, 0], [0, 0, 0]]), gamma_02), gamma_02 ) - K3 = math.sqrt(gamma_3 + math.eps) * math.convert_like( - math.cast_like(math.array([[0, 0, 0], [0, 0, 1], [0, 0, 0]]), gamma_3), gamma_3 + K3 = math.sqrt(gamma_12 + math.eps) * math.convert_like( + math.cast_like(math.array([[0, 0, 0], [0, 0, 1], [0, 0, 0]]), gamma_12), gamma_12 ) return [K0, K1, K2, K3] - class TritFlip(Channel): r""" Single-qutrit parameter flipping error channel, similar to (GellMann :math:`\{\lambda_1, \lambda_4, \lambda_6\}`). diff --git a/tests/ops/qutrit/test_qutrit_channel_ops.py b/tests/ops/qutrit/test_qutrit_channel_ops.py index 68536a72dc3..fc0c1b2d429 100644 --- a/tests/ops/qutrit/test_qutrit_channel_ops.py +++ b/tests/ops/qutrit/test_qutrit_channel_ops.py @@ -175,7 +175,7 @@ class TestQutritAmplitudeDamping: """Tests for the qutrit quantum channel QutritAmplitudeDamping""" def test_gamma_zero(self, tol): - """Test gamma_1=gamma_2=0 gives correct Kraus matrices""" + """Test gamma_01=gamma_02=0 gives correct Kraus matrices""" kraus_mats = qml.QutritAmplitudeDamping(0, 0, 0, wires=0).kraus_matrices() assert np.allclose(kraus_mats[0], np.eye(3), atol=tol, rtol=0) for kraus_mat in kraus_mats[1:]: @@ -209,55 +209,56 @@ def test_gamma_arbitrary(self, gamma1, gamma2, gamma3, tol): ), ) def test_gamma_invalid_parameter(self, gamma1, gamma2, gamma3): - """Ensures that error is thrown when gamma_1, gamma_2, gamma_3, or (gamma_2 + gamma_3) are outside [0,1]""" + """Ensures that error is thrown when + gamma_01, gamma_02, gamma_12, or (gamma_02 + gamma_12) are outside [0,1]""" with pytest.raises(ValueError, match="must be in the interval"): channel.QutritAmplitudeDamping(gamma1, gamma2, gamma3, wires=0).kraus_matrices() @staticmethod - def expected_jac_fn(gamma_1, gamma_2, gamma_3): + def expected_jac_fn(gamma_01, gamma_02, gamma_12): """Gets the expected Jacobian of Kraus matrices""" partial_1 = [math.zeros((3, 3)) for _ in range(4)] - partial_1[0][1, 1] = -1 / (2 * math.sqrt(1 - gamma_1)) - partial_1[1][0, 1] = 1 / (2 * math.sqrt(gamma_1)) + partial_1[0][1, 1] = -1 / (2 * math.sqrt(1 - gamma_01)) + partial_1[1][0, 1] = 1 / (2 * math.sqrt(gamma_01)) partial_2 = [math.zeros((3, 3)) for _ in range(4)] - partial_2[0][2, 2] = -1 / (2 * math.sqrt(1 - gamma_2 - gamma_3)) - partial_2[2][0, 2] = 1 / (2 * math.sqrt(gamma_2)) + partial_2[0][2, 2] = -1 / (2 * math.sqrt(1 - gamma_02 - gamma_12)) + partial_2[2][0, 2] = 1 / (2 * math.sqrt(gamma_02)) partial_3 = [math.zeros((3, 3)) for _ in range(4)] - partial_3[0][2, 2] = -1 / (2 * math.sqrt(1 - gamma_2 - gamma_3)) - partial_3[3][1, 2] = 1 / (2 * math.sqrt(gamma_3)) + partial_3[0][2, 2] = -1 / (2 * math.sqrt(1 - gamma_02 - gamma_12)) + partial_3[3][1, 2] = 1 / (2 * math.sqrt(gamma_12)) return [partial_1, partial_2, partial_3] @staticmethod - def kraus_fn(gamma_1, gamma_2, gamma_3): + def kraus_fn(gamma_01, gamma_02, gamma_12): """Gets the Kraus matrices of QutritAmplitudeDamping channel, used for differentiation.""" - damping_channel = qml.QutritAmplitudeDamping(gamma_1, gamma_2, gamma_3, wires=0) + damping_channel = qml.QutritAmplitudeDamping(gamma_01, gamma_02, gamma_12, wires=0) return math.stack(damping_channel.kraus_matrices()) @pytest.mark.autograd def test_kraus_jac_autograd(self): """Tests Jacobian of Kraus matrices using autograd.""" - gamma_1 = pnp.array(0.43, requires_grad=True) - gamma_2 = pnp.array(0.12, requires_grad=True) - gamma_3 = pnp.array(0.35, requires_grad=True) + gamma_01 = pnp.array(0.43, requires_grad=True) + gamma_02 = pnp.array(0.12, requires_grad=True) + gamma_12 = pnp.array(0.35, requires_grad=True) - jac = qml.jacobian(self.kraus_fn)(gamma_1, gamma_2, gamma_3) - assert math.allclose(jac, self.expected_jac_fn(gamma_1, gamma_2, gamma_3)) + jac = qml.jacobian(self.kraus_fn)(gamma_01, gamma_02, gamma_12) + assert math.allclose(jac, self.expected_jac_fn(gamma_01, gamma_02, gamma_12)) @pytest.mark.torch def test_kraus_jac_torch(self): """Tests Jacobian of Kraus matrices using PyTorch.""" import torch - gamma_1 = torch.tensor(0.43, requires_grad=True) - gamma_2 = torch.tensor(0.12, requires_grad=True) - gamma_3 = torch.tensor(0.35, requires_grad=True) + gamma_01 = torch.tensor(0.43, requires_grad=True) + gamma_02 = torch.tensor(0.12, requires_grad=True) + gamma_12 = torch.tensor(0.35, requires_grad=True) - jac = torch.autograd.functional.jacobian(self.kraus_fn, (gamma_1, gamma_2, gamma_3)) + jac = torch.autograd.functional.jacobian(self.kraus_fn, (gamma_01, gamma_02, gamma_12)) expected = self.expected_jac_fn( - gamma_1.detach().numpy(), gamma_2.detach().numpy(), gamma_3.detach().numpy() + gamma_01.detach().numpy(), gamma_02.detach().numpy(), gamma_12.detach().numpy() ) for res_partial, exp_partial in zip(jac, expected): @@ -268,26 +269,26 @@ def test_kraus_jac_tf(self): """Tests Jacobian of Kraus matrices using TensorFlow.""" import tensorflow as tf - gamma_1 = tf.Variable(0.43) - gamma_2 = tf.Variable(0.12) - gamma_3 = tf.Variable(0.35) + gamma_01 = tf.Variable(0.43) + gamma_02 = tf.Variable(0.12) + gamma_12 = tf.Variable(0.35) with tf.GradientTape() as tape: - out = self.kraus_fn(gamma_1, gamma_2, gamma_3) - jac = tape.jacobian(out, (gamma_1, gamma_2, gamma_3)) - assert math.allclose(jac, self.expected_jac_fn(gamma_1, gamma_2, gamma_3)) + out = self.kraus_fn(gamma_01, gamma_02, gamma_12) + jac = tape.jacobian(out, (gamma_01, gamma_02, gamma_12)) + assert math.allclose(jac, self.expected_jac_fn(gamma_01, gamma_02, gamma_12)) @pytest.mark.jax def test_kraus_jac_jax(self): """Tests Jacobian of Kraus matrices using JAX.""" import jax - gamma_1 = jax.numpy.array(0.43) - gamma_2 = jax.numpy.array(0.12) - gamma_3 = jax.numpy.array(0.35) + gamma_01 = jax.numpy.array(0.43) + gamma_02 = jax.numpy.array(0.12) + gamma_12 = jax.numpy.array(0.35) - jac = jax.jacobian(self.kraus_fn, argnums=[0, 1, 2])(gamma_1, gamma_2, gamma_3) - assert math.allclose(jac, self.expected_jac_fn(gamma_1, gamma_2, gamma_3)) + jac = jax.jacobian(self.kraus_fn, argnums=[0, 1, 2])(gamma_01, gamma_02, gamma_12) + assert math.allclose(jac, self.expected_jac_fn(gamma_01, gamma_02, gamma_12)) class TestTritFlip: