Add amplitude damping noise model for density-matrix simulation

docs/source/channels.rst

@@ -14,10 +14,14 @@ Kraus channel
 
 .. autofunction:: depolarising_channel
 
+.. autofunction:: amplitude_damping_channel
+
 .. autofunction:: pauli_channel
 
 .. autofunction:: two_qubit_depolarising_channel
 
+.. autofunction:: two_qubit_amplitude_damping_channel
+
 .. autofunction:: two_qubit_depolarising_tensor_channel
 
 
@@ -52,3 +56,14 @@ Noise model classes
 
 .. autoclass:: DepolarisingNoiseModel
     :members:
+
+.. currentmodule:: graphix.noise_models.amplitude_damping
+
+.. autoclass:: AmplitudeDampingNoise
+    :members:
+
+.. autoclass:: TwoQubitAmplitudeDampingNoise
+    :members:
+
+.. autoclass:: AmplitudeDampingNoiseModel
+    :members:

graphix/__init__.py

@@ -13,7 +13,7 @@
 from graphix.graphsim import GraphState
 from graphix.instruction import Instruction
 from graphix.measurements import BlochMeasurement, Measurement, PauliMeasurement
-from graphix.noise_models import DepolarisingNoiseModel, NoiseModel
+from graphix.noise_models import AmplitudeDampingNoiseModel, DepolarisingNoiseModel, NoiseModel
 from graphix.opengraph import OpenGraph
 from graphix.optimization import StandardizedPattern
 from graphix.parameter import Placeholder
@@ -27,6 +27,7 @@
 
 __all__ = [
     "ANGLE_PI",
+    "AmplitudeDampingNoiseModel",
     "Axis",
     "BasicStates",
     "BlochMeasurement",

graphix/channels.py

@@ -258,6 +258,62 @@ def two_qubit_depolarising_channel(prob: float) -> KrausChannel:
     )
 
 
+def amplitude_damping_channel(gamma: float) -> KrausChannel:
+    r"""Single-qubit amplitude damping channel.
+
+    .. math::
+        K_0 = \begin{pmatrix} 1 & 0 \\ 0 & \sqrt{1 - \gamma} \end{pmatrix},
+        \quad
+        K_1 = \begin{pmatrix} 0 & \sqrt{\gamma} \\ 0 & 0 \end{pmatrix}
+
+    Parameters
+    ----------
+    gamma : float
+        Normalized damping parameter, between 0 and 1.
+
+    Returns
+    -------
+    :class:`graphix.channels.KrausChannel`
+        Kraus channel for amplitude damping.
+    """
+    k0 = np.array([[1.0, 0.0], [0.0, np.sqrt(1.0 - gamma)]], dtype=np.complex128)
+    k1 = np.array([[0.0, np.sqrt(gamma)], [0.0, 0.0]], dtype=np.complex128)
+    return KrausChannel(
+        [
+            KrausData(1.0, k0),
+            KrausData(1.0, k1),
+        ]
+    )
+
+
+def two_qubit_amplitude_damping_channel(gamma: float) -> KrausChannel:
+    r"""Two-qubit amplitude damping channel.
+
+    Independent amplitude damping on each qubit, with Kraus operators
+    :math:`K_i \otimes K_j` for :math:`i, j \in \{0, 1\}`.
+
+    Parameters
+    ----------
+    gamma : float
+        Normalized damping parameter, between 0 and 1.
+
+    Returns
+    -------
+    :class:`graphix.channels.KrausChannel`
+        Kraus channel for two-qubit amplitude damping.
+    """
+    k0 = np.array([[1.0, 0.0], [0.0, np.sqrt(1.0 - gamma)]], dtype=np.complex128)
+    k1 = np.array([[0.0, np.sqrt(gamma)], [0.0, 0.0]], dtype=np.complex128)
+    return KrausChannel(
+        [
+            KrausData(1.0, np.kron(k0, k0)),
+            KrausData(1.0, np.kron(k0, k1)),
+            KrausData(1.0, np.kron(k1, k0)),
+            KrausData(1.0, np.kron(k1, k1)),
+        ]
+    )
+
+
 def two_qubit_depolarising_tensor_channel(prob: float) -> KrausChannel:
     r"""Two-qubit tensor channel of single-qubit depolarising channels with same probability.
 

graphix/noise_models/__init__.py

@@ -4,6 +4,11 @@
 
 from typing import TYPE_CHECKING
 
+from graphix.noise_models.amplitude_damping import (
+    AmplitudeDampingNoise,
+    AmplitudeDampingNoiseModel,
+    TwoQubitAmplitudeDampingNoise,
+)
 from graphix.noise_models.depolarising import DepolarisingNoise, DepolarisingNoiseModel, TwoQubitDepolarisingNoise
 from graphix.noise_models.noise_model import (
     ApplyNoise,
@@ -16,11 +21,14 @@
     from graphix.noise_models.noise_model import CommandOrNoise as CommandOrNoise
 
 __all__ = [
+    "AmplitudeDampingNoise",
+    "AmplitudeDampingNoiseModel",
     "ApplyNoise",
     "ComposeNoiseModel",
     "DepolarisingNoise",
     "DepolarisingNoiseModel",
     "Noise",
     "NoiseModel",
+    "TwoQubitAmplitudeDampingNoise",
     "TwoQubitDepolarisingNoise",
 ]

graphix/noise_models/amplitude_damping.py

@@ -0,0 +1,151 @@
+"""Amplitude damping noise model."""
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING
+
+import typing_extensions
+
+from graphix.channels import KrausChannel, amplitude_damping_channel, two_qubit_amplitude_damping_channel
+from graphix.command import BaseM, CommandKind
+from graphix.measurements import toggle_outcome
+from graphix.noise_models.noise_model import ApplyNoise, Noise, NoiseModel
+from graphix.rng import ensure_rng
+from graphix.utils import Probability
+
+if TYPE_CHECKING:
+    from collections.abc import Iterable
+
+    from numpy.random import Generator
+
+    from graphix.measurements import Outcome
+    from graphix.noise_models.noise_model import CommandOrNoise
+
+
+class AmplitudeDampingNoise(Noise):
+    """One-qubit amplitude damping noise with parameter ``gamma``."""
+
+    gamma = Probability()
+
+    def __init__(self, gamma: float) -> None:
+        """Initialize one-qubit amplitude damping noise.
+
+        Parameters
+        ----------
+        gamma : float
+            Normalized damping parameter, between 0 and 1.
+        """
+        self.gamma = gamma
+
+    @property
+    @typing_extensions.override
+    def nqubits(self) -> int:
+        """Return the number of qubits targetted by the noise element."""
+        return 1
+
+    @typing_extensions.override
+    def to_kraus_channel(self) -> KrausChannel:
+        """Return the Kraus channel describing the noise element."""
+        return amplitude_damping_channel(self.gamma)
+
+
+class TwoQubitAmplitudeDampingNoise(Noise):
+    """Two-qubits amplitude damping noise with parameter ``gamma``."""
+
+    gamma = Probability()
+
+    def __init__(self, gamma: float) -> None:
+        """Initialize two-qubit amplitude damping noise.
+
+        Parameters
+        ----------
+        gamma : float
+            Normalized damping parameter, between 0 and 1.
+        """
+        self.gamma = gamma
+
+    @property
+    @typing_extensions.override
+    def nqubits(self) -> int:
+        """Return the number of qubits targetted by the noise element."""
+        return 2
+
+    @typing_extensions.override
+    def to_kraus_channel(self) -> KrausChannel:
+        """Return the Kraus channel describing the noise element."""
+        return two_qubit_amplitude_damping_channel(self.gamma)
+
+
+class AmplitudeDampingNoiseModel(NoiseModel):
+    """Amplitude damping noise model.
+
+    :param NoiseModel: Parent abstract class class:`NoiseModel`
+    :type NoiseModel: class
+    """
+
+    def __init__(
+        self,
+        prepare_error_prob: float = 0.0,
+        x_error_prob: float = 0.0,
+        z_error_prob: float = 0.0,
+        entanglement_error_prob: float = 0.0,
+        measure_channel_prob: float = 0.0,
+        measure_error_prob: float = 0.0,
+    ) -> None:
+        self.prepare_error_prob = prepare_error_prob
+        self.x_error_prob = x_error_prob
+        self.z_error_prob = z_error_prob
+        self.entanglement_error_prob = entanglement_error_prob
+        self.measure_error_prob = measure_error_prob
+        self.measure_channel_prob = measure_channel_prob
+
+    @typing_extensions.override
+    def input_nodes(
+        self, nodes: Iterable[int], rng: Generator | None = None, *, stacklevel: int = 1
+    ) -> list[CommandOrNoise]:
+        """Return the noise to apply to input nodes."""
+        return [ApplyNoise(noise=AmplitudeDampingNoise(self.prepare_error_prob), nodes=[node]) for node in nodes]
+
+    @typing_extensions.override
+    def command(
+        self, cmd: CommandOrNoise, rng: Generator | None = None, *, stacklevel: int = 1
+    ) -> list[CommandOrNoise]:
+        """Return the noise to apply to the command ``cmd``."""
+        match cmd.kind:
+            case CommandKind.N:
+                return [cmd, ApplyNoise(noise=AmplitudeDampingNoise(self.prepare_error_prob), nodes=[cmd.node])]
+            case CommandKind.E:
+                return [
+                    cmd,
+                    ApplyNoise(
+                        noise=TwoQubitAmplitudeDampingNoise(self.entanglement_error_prob), nodes=list(cmd.nodes)
+                    ),
+                ]
+            case CommandKind.M:
+                return [ApplyNoise(noise=AmplitudeDampingNoise(self.measure_channel_prob), nodes=[cmd.node]), cmd]
+            case CommandKind.X:
+                return [
+                    cmd,
+                    ApplyNoise(noise=AmplitudeDampingNoise(self.x_error_prob), nodes=[cmd.node], domain=cmd.domain),
+                ]
+            case CommandKind.Z:
+                return [
+                    cmd,
+                    ApplyNoise(noise=AmplitudeDampingNoise(self.z_error_prob), nodes=[cmd.node], domain=cmd.domain),
+                ]
+            case CommandKind.C | CommandKind.T | CommandKind.ApplyNoise:
+                return [cmd]
+            case CommandKind.S:
+                raise ValueError("Unexpected signal!")
+            case _:
+                typing_extensions.assert_never(cmd.kind)
+
+    @typing_extensions.override
+    def confuse_result(
+        self, cmd: BaseM, result: Outcome, rng: Generator | None = None, *, stacklevel: int = 1
+    ) -> Outcome:
+        """Assign wrong measurement result cmd = "M"."""
+        rng = ensure_rng(rng, stacklevel=stacklevel + 1)
+        if rng.uniform() < self.measure_error_prob:
+            return toggle_outcome(result)
+        return result

tests/test_density_matrix.py

@@ -12,7 +12,7 @@
 import graphix.random_objects as randobj
 from graphix import command
 from graphix.branch_selector import ConstBranchSelector
-from graphix.channels import KrausChannel, dephasing_channel, depolarising_channel
+from graphix.channels import KrausChannel, amplitude_damping_channel, dephasing_channel, depolarising_channel
 from graphix.fundamentals import ANGLE_PI, Plane
 from graphix.ops import Ops
 from graphix.sim.density_matrix import DensityMatrix, DensityMatrixBackend
@@ -736,6 +736,56 @@ def test_apply_depolarising_channel(self, fx_rng: Generator) -> None:
         assert np.allclose(expected_dm.trace(), 1.0)
         assert np.allclose(dm.rho, expected_dm)
 
+    def test_apply_amplitude_damping_channel(self, fx_rng: Generator) -> None:
+        dm = DensityMatrix(randobj.rand_dm(2, fx_rng))
+        rho_test = dm.rho.astype(np.complex128)
+
+        gamma = fx_rng.uniform()
+        ad_channel = amplitude_damping_channel(gamma)
+
+        assert isinstance(ad_channel, KrausChannel)
+
+        dm.apply_channel(ad_channel, [0])
+
+        k0 = np.array([[1.0, 0.0], [0.0, np.sqrt(1.0 - gamma)]], dtype=np.complex128)
+        k1 = np.array([[0.0, np.sqrt(gamma)], [0.0, 0.0]], dtype=np.complex128)
+        expected_dm = k0 @ rho_test @ k0.conj().T + k1 @ rho_test @ k1.conj().T
+
+        assert np.allclose(expected_dm.trace(), 1.0)
+        assert np.allclose(dm.rho, expected_dm)
+
+        nqubits = int(fx_rng.integers(2, 5))
+        i = int(fx_rng.integers(0, nqubits))
+
+        psi = _randstate_raw(nqubits, fx_rng)
+        psi /= np.sqrt(np.sum(np.abs(psi) ** 2))
+
+        dm = DensityMatrix(data=np.outer(psi, psi.conj()))
+
+        gamma = fx_rng.uniform()
+        ad_channel = amplitude_damping_channel(gamma)
+
+        assert isinstance(ad_channel, KrausChannel)
+
+        dm.apply_channel(ad_channel, [i])
+
+        k0 = np.array([[1.0, 0.0], [0.0, np.sqrt(1.0 - gamma)]], dtype=np.complex128)
+        k1 = np.array([[0.0, np.sqrt(gamma)], [0.0, 0.0]], dtype=np.complex128)
+        psi_tensor = psi.reshape((2,) * nqubits)
+
+        psi_k0 = np.tensordot(k0, psi_tensor, (1, i))
+        psi_k0 = np.moveaxis(psi_k0, 0, i)
+
+        psi_k1 = np.tensordot(k1, psi_tensor, (1, i))
+        psi_k1 = np.moveaxis(psi_k1, 0, i)
+
+        psi_k0 = np.reshape(psi_k0, (2**nqubits))
+        psi_k1 = np.reshape(psi_k1, (2**nqubits))
+        expected_dm = np.outer(psi_k0, psi_k0.conj()) + np.outer(psi_k1, psi_k1.conj())
+
+        assert np.allclose(expected_dm.trace(), 1.0)
+        assert np.allclose(dm.rho, expected_dm)
+
     def test_apply_random_channel_one_qubit(self, fx_rng: Generator) -> None:
         """Test using complex parameters."""
         # check against statevector backend by hand for now.