Summary

Implements amplitude damping noise for the densitymatrix backend, closing #497. The structure follows DepolarisingNoiseModel throughout.

Channels (graphix/channels.py)

• amplitude_damping_channel(gamma) — single-qubit channel with Kraus operators $K_1 = \mathrm{diag}(1, \sqrt{1-\gamma})$ and $K_2 = \begin{psmallmatrix}0 & \sqrt{\gamma}\0 & 0\end{psmallmatrix}$, exactly as specified in the issue.
• two_qubit_amplitude_damping_channel(gamma) — tensor product of two independent single-qubit channels (the four $K_i \otimes K_j$ operators).

Noise elements (graphix/noise_models/amplitude_damping.py)

• AmplitudeDampingNoise and TwoQubitAmplitudeDampingNoise, both deriving from Noise, exposing nqubits and to_kraus_channel(). The gamma parameter is validated to $[0, 1]$ through the existing Probability() descriptor.

Noise model

• AmplitudeDampingNoiseModel(NoiseModel), mirroring DepolarisingNoiseModel: per-command damping for preparation (N), entanglement (E, two-qubit), the pre-measurement channel (M), and X/Z corrections (conditioned on their domains), plus an optional classical readout flip via confuse_result. Parameters carry a _gamma suffix to make clear they are damping parameters rather than probabilities.

Public symbols are exported from graphix/noise_models/__init__.py.

Soundness of the tests

The single-qubit channel has the closed form $\Phi_\gamma(\rho) = K_1 \rho K_1^\dagger + K_2 \rho K_2^\dagger$, which gives $\Phi_\gamma(|0\rangle\langle0|) = |0\rangle\langle0|$ (the ground state is a fixed point) and $\Phi_\gamma(|1\rangle\langle1|) = \gamma|0\rangle\langle0| + (1-\gamma)|1\rangle\langle1|$ (the excited state decays with probability $\gamma$). On $|+\rangle$ the action is $\tfrac{1}{2}\begin{psmallmatrix}1+\gamma & \sqrt{1-\gamma}\\sqrt{1-\gamma} & 1-\gamma\end{psmallmatrix}$. On a product state the two-qubit channel equals the Kronecker product of the single-qubit results. These analytic forms are used directly as references and swept over $\gamma \in {0, 0.2, 0.5, 0.9, 1.0}$; trace preservation (CPTP) is asserted explicitly.

At the model level, test_noise_model_inserts_noise_at_each_step checks that the correct ApplyNoise command (channel type, gamma, target nodes, and domain) is inserted at every command kind — including that the measurement channel is applied before the M. End-to-end tests run a transpiled pattern through the densitymatrix backend and match the resulting density matrix against the analytic prediction, and a zero-damping model is verified to reproduce the noiseless result.

CI

Locally passing on this branch: tests/test_amplitude_damping.py (25 tests), with no regressions in test_kraus/test_noise_model; ruff, mypy, and pyright are all clean on the new files.

Happy to adjust the naming or the per-command $\gamma$ conventions to whatever fits the maintainers' preferences best.