Add amplitude damping noise model (#497)

[NandanPatel24]

Summary

• Implements amplitude damping noise (issue Implement amplitude damping noise model #497), modeling energy relaxation (T₁ decay) where population flows from the excited state |1⟩ to the ground state |0⟩ with probability γ. Adds the single- and two-qubit channels, the Noise element classes, and an AmplitudeDampingNoiseModel, following DepolarisingNoiseModel as the reference.

Closes #497.

Changes

• graphix/channels.py — adds amplitude_damping_channel(prob) and two_qubit_amplitude_damping_channel(prob), returning KrausChannel objects. Single-qubit operators are K₁ = diag(1, √(1−γ)) and K₂ = [[0, √γ], [0, 0]]; the two-qubit version is the tensor product of two independent single-qubit channels (four operators {Kᵢ⊗Kⱼ}). Unlike the existing Pauli-based channels these operators aren't scalar multiples of Pauli matrices, so they're built explicitly with coef=1.0.

• graphix/noise_models/amplitude_damping.py (new) — defines AmplitudeDampingNoise, TwoQubitAmplitudeDampingNoise (both deriving from Noise), and AmplitudeDampingNoiseModel (deriving from NoiseModel). The model mirrors DepolarisingNoiseModel's command-injection logic. confuse_result returns the result unchanged, since amplitude damping is a purely quantum channel with no classical readout-error component; readout error can be added by composing with another model via ComposeNoiseModel. (This is why the model omits the measure_error_prob parameter that the depolarising model carries.)

• graphix/noise_models/init.py — registers the three new classes for top-level import, alongside the depolarising exports.

A convention note

• The backend (density_matrix.py) applies channels as ρ′ = Σᵢ KᵢρKᵢ† (verified in evolve/evolve_single). The KrausChannel docstring states the daggered-left form Σᵢ Kᵢ†ρKᵢ — for the existing Hermitian Pauli channels this makes no difference, but amplitude damping's K₂ is non-Hermitian, so the operators here are written for the backend's actual KρK† convention (downward |1⟩ → |0⟩ decay). Happy to also fix the docstring in this PR if maintainers prefer.

Tests and soundness

The suite is split between proving the channel matches the Kraus formula (random-state and by-hand-sum tests) and proving it is amplitude damping specifically (deterministic basis-state tests exploiting the channel's asymmetry — these are the soundness argument the issue asks for).

tests/test_kraus.py

• test_amplitude_damping_channel — single-qubit channel builds the correct K₁, K₂ operators.
• test_2_qubit_amplitude_damping_channel — two-qubit channel builds the correct four tensor-product operators.

tests/test_density_matrix.py(https://github.com/TeamGraphix/graphix/blob/master/tests/test_density_matrix.py)

• test_apply_amplitude_damping_channel — channel application matches the by-hand Σ KᵢρKᵢ† sum, on a single qubit and embedded in a larger random register.
• test_amplitude_damping_ground_state_fixed — |0⟩⟨0| is unchanged for any γ (ground state can't decay).
• test_amplitude_damping_excited_state_decays — |1⟩⟨1| → (1−γ)|1⟩⟨1| + γ|0⟩⟨0|, the directional T₁ signature.
• test_amplitude_damping_coherence_decay — off-diagonal coherences scale by √(1−γ), distinguishing amplitude damping from dephasing.
• test_apply_two_qubit_amplitude_damping_channel — the two-qubit channel equals independent damping on each factor.

tests/test_noise_model.py((https://github.com/TeamGraphix/graphix/blob/master/tests/test_noise_model.py)

• test_amplitude_damping_command_injection — noise is injected at the correct positions (after N, after E with two-qubit noise, before M, domain-conditioned on X/Z).
• test_amplitude_damping_confuse_result_is_identity — the model introduces no classical readout error.
• test_compose_amplitude_damping_depolarising_transpile — composing with a depolarising model injects both noises with the correct type and probability at every command position.
• test_compose_amplitude_damping_depolarising_simulation — a composed model with both at default (zero) parameters reproduces the ideal statevector.

All checks pass locally (ruff, ruff-format, mypy, pyright, pytest).

Per unitaryHACK's AI-use guidelines: AI assistance was used while developing this contribution, especially to format this PR content, and for debugging. All ideas remain my own

[NandanPatel24]

Hi, kindly review my PR, I have added a few other tests, testing things that the other PRs didn't seem to address, primarily, evaluating the contribution of each of the noise sources(dephasing and damping) together by running them in the same circuit. I am open to any comments and reviews on this PR

[codecov]

Codecov Report

❌ Patch coverage is 94.02985% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 88.90%. Comparing base (6edaaef) to head (2dc824d).

Files with missing lines	Patch %	Lines
graphix/noise_models/amplitude_damping.py	93.33%	4 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #540      +/-   ##
==========================================
+ Coverage   88.85%   88.90%   +0.04%     
==========================================
  Files          49       50       +1     
  Lines        7135     7202      +67     
==========================================
+ Hits         6340     6403      +63     
- Misses        795      799       +4     

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[pranav97nair]

Hi @NandanPatel24 , thanks for your contribution to Graphix !

Please take a look at the failing ruff and typing checks in CI. Also, Codecov has detected that some lines in your code are not tested. Please include these in your test suite as well.

Your implementation looks correct, and I like the new tests you've added compared to previous PRs. However, something we would really like to do in the test suite is directly comparing the result of a pattern simulation with a random noise probability gamma at a given step against the expected analytical density matrix depending on gamma. This is what we currently do for the depolarizing channel using the Hadamard and RZ patterns in tests/test_noisy_density_matrix.py.

Similarly, we would like to test the resulting density matrix from applying amplitude damping noise at the preparation, entanglement, measurement, and correction steps. This requires computing the state analytically at each step of the pattern. Do you think you could add this to your tests?

[NandanPatel24]

Hi @NandanPatel24 , thanks for your contribution to Graphix !

Please take a look at the failing ruff and typing checks in CI. Also, Codecov has detected that some lines in your code are not tested. Please include these in your test suite as well.

Your implementation looks correct, and I like the new tests you've added compared to previous PRs. However, something we would really like to do in the test suite is directly comparing the result of a pattern simulation with a random noise probability gamma at a given step against the expected analytical density matrix depending on gamma. This is what we currently do for the depolarizing channel using the Hadamard and RZ patterns in tests/test_noisy_density_matrix.py.

Similarly, we would like to test the resulting density matrix from applying amplitude damping noise at the preparation, entanglement, measurement, and correction steps. This requires computing the state analytically at each step of the pattern. Do you think you could add this to your tests?

Hi, I have added the tests that you gave, for both the H and the RZ gates, as well as added the damping at 4 different steps and compared it with the analytical solution

[pranav97nair]

Thanks for the very quick response! Please take a look at the CI as ruff and typecheck are still failing. I will submit a review of your additions as soon as possible.