Added |2> -> |1> amplitude damping to amplitude damping.

doc/releases/changelog-dev.md

@@ -152,6 +152,10 @@
 * ``qml.QutritDepolarizingChannel`` has been added, allowing for depolarizing noise to be simulated on the `default.qutrit.mixed` device.
  [(#5502)](https://github.com/PennyLaneAI/pennylane/pull/5502)
 
+* `qml.QutritAmplitudeDamping` channel has been added, allowing for noise processes modelled by amplitude damping to be simulated on the `default.qutrit.mixed` device.
+ [(#5503)](https://github.com/PennyLaneAI/pennylane/pull/5503)
+ [(#5757)](https://github.com/PennyLaneAI/pennylane/pull/5757)
+
 <h3>Breaking changes 💔</h3>
 
 * A custom decomposition can no longer be provided to `QDrift`. Instead, apply the operations in your custom
@@ -177,9 +181,6 @@
 * `Controlled.wires` does not include `self.work_wires` anymore. That can be accessed separately through `Controlled.work_wires`.
  Consequently, `Controlled.active_wires` has been removed in favour of the more common `Controlled.wires`.
  [(#5728)](https://github.com/PennyLaneAI/pennylane/pull/5728)
-
-* `qml.QutritAmplitudeDamping` channel has been added, allowing for noise processes modelled by amplitude damping to be simulated on the `default.qutrit.mixed` device.
- [(#5503)](https://github.com/PennyLaneAI/pennylane/pull/5503)
 
 <h3>Deprecations 👋</h3>
 

pennylane/__init__.py

@@ -218,6 +218,9 @@ def device(name, *args, **kwargs):
  * :mod:`'default.qutrit' <pennylane.devices.default_qutrit>`: a simple
  state simulator of qutrit-based quantum circuit architectures.
 
+ * :mod:`'default.qutrit.mixed' <pennylane.devices.default_qutrit_mixed>`: a
+ mixed-state simulator of qutrit-based quantum circuit architectures.
+
  * :mod:`'default.gaussian' <pennylane.devices.default_gaussian>`: a simple simulator
  of Gaussian states and operations on continuous-variable circuit architectures.
 

pennylane/ops/qutrit/channel.py

@@ -235,8 +235,10 @@ class QutritAmplitudeDamping(Channel):
  K_0 = \begin{bmatrix}
  1 & 0 & 0\\
  0 & \sqrt{1-\gamma_1} & 0 \\
- 0 & 0 & \sqrt{1-\gamma_2}
- \end{bmatrix}, \quad
+ 0 & 0 & \sqrt{1-(\gamma_2+\gamma_3)}
+ \end{bmatrix}
+
+ .. math::
  K_1 = \begin{bmatrix}
  0 & \sqrt{\gamma_1} & 0 \\
  0 & 0 & 0 \\
@@ -246,70 +248,95 @@ class QutritAmplitudeDamping(Channel):
  0 & 0 & \sqrt{\gamma_2} \\
  0 & 0 & 0 \\
  0 & 0 & 0
+ \end{bmatrix}, \quad
+ K_3 = \begin{bmatrix}
+ 0 & 0 & 0 \\
+ 0 & 0 & \sqrt{\gamma_3} \\
+ 0 & 0 & 0
  \end{bmatrix}
 
- where :math:`\gamma_1 \in [0, 1]` and :math:`\gamma_2 \in [0, 1]` are the amplitude damping
- probabilities for subspaces (0,1) and (0,2) respectively.
+ where :math:`\gamma_1, \gamma_2, \gamma_3 \in [0, 1]` are the amplitude damping
+ probabilities for subspaces (0,1), (0,2), and (1,2) respectively.
 
  .. note::
 
- The Kraus operators :math:`\{K_0, K_1, K_2\}` are adapted from [`1 <https://doi.org/10.48550/arXiv.1905.10481>`_] (Eq. 8).
+ When :math:`\gamma_3=0` then Kraus operators :math:`\{K_0, K_1, K_2\}` are adapted from
+ [`1 <https://doi.org/10.48550/arXiv.1905.10481>`_] (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 <https://arxiv.org/abs/2003.03307>`_] (Sec II.A).
+
+ To maintain normalization :math:`\gamma_2 + \gamma_3 \leq 1`.
+
 
  **Details:**
 
  * Number of wires: 1
- * Number of parameters: 2
+ * 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.
  wires (Sequence[int] or int): the wire the channel acts on
  id (str or None): String representing the operation (optional)
  """
 
- num_params = 2
+ num_params = 3
  num_wires = 1
  grad_method = "F"
 
- def __init__(self, gamma_1, gamma_2, wires, id=None):
- # Verify gamma_1 and gamma_2
- for gamma in (gamma_1, gamma_2):
- if not (math.is_abstract(gamma_1) or math.is_abstract(gamma_2)):
+ def __init__(self, gamma_1, gamma_2, gamma_3, wires, id=None):
+ # Verify input
+ for gamma in (gamma_1, gamma_2, gamma_3):
+ if not math.is_abstract(gamma):
  if not 0.0 <= gamma <= 1.0:
  raise ValueError("Each probability must be in the interval [0,1]")
- super().__init__(gamma_1, gamma_2, wires=wires, id=id)
+ 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)
 
  @staticmethod
- def compute_kraus_matrices(gamma_1, gamma_2): # pylint:disable=arguments-differ
+ def compute_kraus_matrices(gamma_1, gamma_2, gamma_3): # 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.
 
  Returns:
  list(array): list of Kraus matrices
 
  **Example**
 
- >>> qml.QutritAmplitudeDamping.compute_kraus_matrices(0.5, 0.25)
+ >>> qml.QutritAmplitudeDamping.compute_kraus_matrices(0.5, 0.25, 0.36)
  [
  array([ [1. , 0. , 0. ],
  [0. , 0.70710678, 0. ],
- [0. , 0. , 0.8660254 ]]),
+ [0. , 0. , 0.6244998 ]]),
  array([ [0. , 0.70710678, 0. ],
  [0. , 0. , 0. ],
  [0. , 0. , 0. ]]),
  array([ [0. , 0. , 0.5 ],
  [0. , 0. , 0. ],
  [0. , 0. , 0. ]])
+ array([ [0. , 0. , 0. ],
+ [0. , 0. , 0.6 ],
+ [0. , 0. , 0. ]])
  ]
  """
- K0 = math.diag([1, math.sqrt(1 - gamma_1 + math.eps), math.sqrt(1 - gamma_2 + math.eps)])
+ K0 = math.diag(
+ [1, math.sqrt(1 - gamma_1 + math.eps), math.sqrt(1 - gamma_2 - gamma_3 + 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
  )
  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
  )
- return [K0, K1, K2]
+ 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
+ )
+ return [K0, K1, K2, K3]

tests/devices/qutrit_mixed/test_qutrit_mixed_preprocessing.py

@@ -126,6 +126,7 @@ def test_measurement_is_swapped_out(self, mp_fn, mp_cls, shots):
  (qml.Snapshot(), True),
  (qml.TRX(1.1, 0), True),
  (qml.QutritDepolarizingChannel(0.4, 0), True),
+ (qml.QutritAmplitudeDamping(0.1, 0.2, 0.12, 0), True),
  ],
  )
  def test_accepted_operator(self, op, expected):

tests/ops/qutrit/test_qutrit_channel_ops.py

@@ -176,58 +176,75 @@ class TestQutritAmplitudeDamping:
 
  def test_gamma_zero(self, tol):
  """Test gamma_1=gamma_2=0 gives correct Kraus matrices"""
- kraus_mats = qml.QutritAmplitudeDamping(0, 0, wires=0).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)
- assert np.allclose(kraus_mats[1], np.zeros((3, 3)), atol=tol, rtol=0)
- assert np.allclose(kraus_mats[2], np.zeros((3, 3)), atol=tol, rtol=0)
+ for kraus_mat in kraus_mats[1:]:
+  assert np.allclose(kraus_mat, np.zeros((3, 3)), atol=tol, rtol=0)
 
- @pytest.mark.parametrize("gamma1,gamma2", ((0.1, 0.2), (0.75, 0.75)))
- def test_gamma_arbitrary(self, gamma1, gamma2, tol):
- """Test the correct Kraus matrices are returned, also ensures that the sum of gammas can be over 1."""
- K_0 = np.diag((1, np.sqrt(1 - gamma1), np.sqrt(1 - gamma2)))
+ @pytest.mark.parametrize("gamma1,gamma2,gamma3", ((0.1, 0.2, 0.3), (0.75, 0.75, 0.25)))
+ def test_gamma_arbitrary(self, gamma1, gamma2, gamma3, tol):
+ """Test the correct Kraus matrices are returned."""
+ K_0 = np.diag((1, np.sqrt(1 - gamma1), np.sqrt(1 - gamma2 - gamma3)))
 
  K_1 = np.zeros((3, 3))
  K_1[0, 1] = np.sqrt(gamma1)
 
  K_2 = np.zeros((3, 3))
  K_2[0, 2] = np.sqrt(gamma2)
 
- expected = [K_0, K_1, K_2]
- damping_channel = qml.QutritAmplitudeDamping(gamma1, gamma2, wires=0)
+ K_3 = np.zeros((3, 3))
+ K_3[1, 2] = np.sqrt(gamma3)
+
+ expected = [K_0, K_1, K_2, K_3]
+ damping_channel = qml.QutritAmplitudeDamping(gamma1, gamma2, gamma3, wires=0)
  assert np.allclose(damping_channel.kraus_matrices(), expected, atol=tol, rtol=0)
 
- @pytest.mark.parametrize("gamma1,gamma2", ((1.5, 0.0), (0.0, 1.0 + math.eps)))
- def test_gamma_invalid_parameter(self, gamma1, gamma2):
- """Ensures that error is thrown when gamma_1 or gamma_2 are outside [0,1]"""
- with pytest.raises(ValueError, match="Each probability must be in the interval"):
- channel.QutritAmplitudeDamping(gamma1, gamma2, wires=0).kraus_matrices()
+ @pytest.mark.parametrize(
+ "gamma1,gamma2,gamma3",
+ (
+ (1.5, 0.0, 0.0),
+ (0.0, 1.0 + math.eps, 0.0),
+ (0.0, 0.0, 1.1),
+ (0.0, 0.33, 0.67 + math.eps),
+ ),
+ )
+ 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]"""
+ 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):
+ def expected_jac_fn(gamma_1, gamma_2, gamma_3):
  """Gets the expected Jacobian of Kraus matrices"""
- partial_1 = [math.zeros((3, 3)) for _ in range(3)]
+ 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_2 = [math.zeros((3, 3)) for _ in range(3)]
- partial_2[0][2, 2] = -1 / (2 * math.sqrt(1 - gamma_2))
+ 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))
 
- return [partial_1, partial_2]
+ 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))
+
+ return [partial_1, partial_2, partial_3]
 
  @staticmethod
- def kraus_fn(gamma_1, gamma_2):
+ def kraus_fn(gamma_1, gamma_2, gamma_3):
  """Gets the Kraus matrices of QutritAmplitudeDamping channel, used for differentiation."""
- damping_channel = qml.QutritAmplitudeDamping(gamma_1, gamma_2, wires=0)
+ damping_channel = qml.QutritAmplitudeDamping(gamma_1, gamma_2, gamma_3, 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)
- jac = qml.jacobian(self.kraus_fn)(gamma_1, gamma_2)
- assert math.allclose(jac, self.expected_jac_fn(gamma_1, gamma_2))
+ gamma_3 = 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))
 
  @pytest.mark.torch
  def test_kraus_jac_torch(self):
@@ -236,11 +253,15 @@ def test_kraus_jac_torch(self):
 
  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)
 
- jac = torch.autograd.functional.jacobian(self.kraus_fn, (gamma_1, gamma_2))
- expected = self.expected_jac_fn(gamma_1.detach().numpy(), gamma_2.detach().numpy())
- assert math.allclose(jac[0].detach().numpy(), expected[0])
- assert math.allclose(jac[1].detach().numpy(), expected[1])
+ jac = torch.autograd.functional.jacobian(self.kraus_fn, (gamma_1, gamma_2, gamma_3))
+ expected = self.expected_jac_fn(
+ gamma_1.detach().numpy(), gamma_2.detach().numpy(), gamma_3.detach().numpy()
+ )
+
+ for res_partial, exp_partial in zip(jac, expected):
+ assert math.allclose(res_partial.detach().numpy(), exp_partial)
 
  @pytest.mark.tf
  def test_kraus_jac_tf(self):
@@ -249,10 +270,12 @@ def test_kraus_jac_tf(self):
 
  gamma_1 = tf.Variable(0.43)
  gamma_2 = tf.Variable(0.12)
+ gamma_3 = tf.Variable(0.35)
+
  with tf.GradientTape() as tape:
- out = self.kraus_fn(gamma_1, gamma_2)
- jac = tape.jacobian(out, (gamma_1, gamma_2))
- assert math.allclose(jac, self.expected_jac_fn(gamma_1, gamma_2))
+ 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))
 
  @pytest.mark.jax
  def test_kraus_jac_jax(self):
@@ -261,5 +284,7 @@ def test_kraus_jac_jax(self):
 
  gamma_1 = jax.numpy.array(0.43)
  gamma_2 = jax.numpy.array(0.12)
- jac = jax.jacobian(self.kraus_fn, argnums=[0, 1])(gamma_1, gamma_2)
- assert math.allclose(jac, self.expected_jac_fn(gamma_1, gamma_2))
+ gamma_3 = 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))