Add amplitude damping noise model

[automatedsoftwaresystemsllc-eng]

Summary

• Add single- and two-qubit amplitude damping Kraus channels.
• Add AmplitudeDampingNoiseModel matching the existing depolarising model hooks for preparation, entanglement, measurement-channel, conditional X/Z correction noise, and measurement-result flips.
• Export the new model and add focused channel/noise-model/density-matrix tests.

Verification

• python -m py_compile graphix\channels.py graphix\noise_models\amplitude_damping.py graphix\noise_models\init.py graphix\init.py tests\test_kraus.py tests\test_noise_model.py tests\test_noisy_density_matrix.py passed locally.

uff check graphix\channels.py graphix\noise_models\amplitude_damping.py graphix\noise_models\init.py graphix\init.py tests\test_kraus.py tests\test_noise_model.py tests\test_noisy_density_matrix.py passed locally.

uff format --check graphix\channels.py graphix\noise_models\amplitude_damping.py graphix\noise_models\init.py graphix\init.py tests\test_kraus.py tests\test_noise_model.py tests\test_noisy_density_matrix.py passed locally.

• Full focused pytest could not complete in my local Codex runtime because importing quimb hangs before test collection. I aligned quimb to the repo lockfile version (1.13.0 for Python >=3.11), but import quimb still timed out locally. I am leaving this explicit for CI/maintainer visibility rather than claiming a pytest pass I did not get.

Assisted by OpenAI Codex.

[codecov]

Codecov Report

❌ Patch coverage is 89.04110% with 8 lines in your changes missing coverage. Please review.
✅ Project coverage is 88.85%. Comparing base (8bf1ebe) to head (f96d23e).

Files with missing lines	Patch %	Lines
graphix/noise_models/amplitude_damping.py	87.87%	8 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##           master     #529   +/-   ##
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  Coverage   88.85%   88.85%           
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  Files          49       50    +1     
  Lines        7135     7207   +72     
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+ Hits         6340     6404   +64     
- Misses        795      803    +8     

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[pranav97nair]

Thanks for your contribution!

After taking a look through the code, we would like to ask you to please implement the following changes:

• Add tests for verifying the action of amplitude damping noise at the entanglement and measurement steps of the Hadamard pattern . In both cases, we would like to check the simulated output density matrix against the expected analytical one as a function of a randomized error probability.
• For any tests in test_noise_model.py and test_noisy_density_matrix.py that should behave identically regardless of noise model, parametrize them to run for both DepolarisingNoiseModel and AmplitudeDampingNoiseModel. For example, tests that check the action of the confuse_result() method.

Feel free to let us know any comments or questions!