Implement amplitude damping noise model

[pranav97nair]

This issue is part of unitaryHACK 2026. You have to be registered to participate. Please read carefully the unitaryHack rules before submitting a PR for this issue.

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Context

An important aspect of simulating any quantum computation is incorporating potential decoherence of the quantum system due to interaction with the environment. In Graphix, we can do this by specifying a noise model when simulating a pattern with the densitymatrix backend. A noise channel is a completely positive, trace-preserving (CPTP) map. The density matrix backend thus represents noise channels using the Kraus operator formalism:

$$\Phi(\rho)=\sum_i K_i \rho K_i^\dagger$$

where $\rho$ is the density matrix of the quantum state and $\sum_i K_i^\dagger K_i = I$.

Noise models in Graphix, represented by the abstract class graphix.noise_models.noise_model.NoiseModel, essentially transpile patterns into noisy patterns by appending to each command an auxiliary command ApplyNoise. This new command specifies the noise channel to be applied by the backend, the node indices to apply it to, and the domain to be considered. An important feature of NoiseModel is that the noise channel can be tuned individually for each command in a pattern.

Currently, the only built-in noise model in Graphix is the DepolarisingNoiseModel defined in graphix.noise_models.depolarising. The goal of this issue is to define a new noise model, and all required supporting entities, to implement amplitude damping noise in a pattern simulation. The DepolarisingNoiseModel class should be used as a reference for this new model.

Tasks

• Define two new functions called amplitude_damping_channel() and two_qubit_amplitude_damping_channel() that return a KrausChannel representing amplitude damping on a single-qubit and two-qubit state, respectively.
• Define two new classes AmplitudeDampingNoise and TwoQubitAmplitudeDampingNoise that derive from the abstract class Noise.
• Define an AmplitudeDampingNoiseModel class that derives from the abstract class NoiseModel.
• Define a set of tests to verify accurate application of amplitude damping noise to each step of a simple pattern (see tests/test_noisy_density_matrix for reference). The soundness of these tests should be explained in the PR text.

Note

In order for the PR to be accepted:

• Graphix CI should be passing. This includes the test suite, typechecking (mypy and pyright), and linting (ruff).
• New functions and classes should be documented appropiately following numpy style.
• Unitary Hack's AI use guidelines should be respected.
• The contributor must engage in a constructive feedback loop with the maintainers.