Open-system QRC via QuTiP + Notebook 06 (Gilbert damping)

[rosspeili]

Context

Workstream B3 in OVERVIEW.md lists an open-system extension: Gilbert damping as a Lindblad operator. pyproject.toml already declares the [open] extra with qutip>=5.0. gates.py Issue #11 ships a damping_channel_spec() stub; this issue implements the actual dissipative reservoir dynamics.

Notebook 06 is planned in docs/notebooks.md:

• File: notebooks/06_open_system_qrc.ipynb
• Output: figures/open_system_qrc.png
• Install: pip install -e "./spintronic-qrc[open]" or [all]

PennyLane can represent some channels, but the canonical approach for Lindblad master-equation validation is QuTiP. Compare open-system features against the closed-system pipeline from Issue #1 on a short NARMA-10 or impulse run.

Goal

1. Add src/spintronic_qrc/open_system.py — QuTiP Lindblad evolution for the XXZ chain + damping
2. Bridge open-system states to Pauli expectation readout features compatible with trainer.py
3. Create notebooks/06_open_system_qrc.ipynb with committed figure
4. Optional: benchmarks/run_open_system.py for reproducibility

Requirements

1. Lindblad model

Open XXZ chain with Gilbert-type amplitude/phase damping on each site (document chosen model):

d rho / dt = -i [H, rho] + sum_i D_i[rho]

Start with independent amplitude damping per site (one Lindblad operator per site) or collective dephasing — pick one, cite Breuer & Petruccione (REFERENCES.md O1) and Manzano (O2) in docstring.

Build H as QuTiP operator from the same parameters as xxz_chain_hamiltonian (J_xy, J_z, disorder field).

@dataclass
class OpenSystemConfig:
    n_sites: int
    J_xy: float = 1.0
    J_z: float = 1.0
    disorder: float = 0.5
    gamma: float = 0.01          # damping rate
    evolution_time: float = 0.8
    seed: int | None = 42

2. Evolution API

def evolve_density_matrix(
    rho0,
    config: OpenSystemConfig,
) -> object:  # qutip.Qobj
    """Mesolve one step or full interval; document time grid."""

def collect_open_features(
    inputs: np.ndarray,
    config: OpenSystemConfig,
    *,
    washout: int = 100,
) -> np.ndarray:
    """
    Open-system analogue of pipeline.collect_features:
    encode input -> Lindblad step -> Pauli expectations from rho.
    """

Encoding: map scalar u(t) to local field Hamiltonian perturbation for that timestep (consistent with encoder.py local-field picture).

Readout: Tr(rho sigma_i^alpha) for configured Pauli set.

3. Comparison helper

def compare_closed_vs_open_narma10(
    qrc_config,
    open_config: OpenSystemConfig,
    length: int = 500,
    seed: int = 42,
) -> dict[str, float]:
    """Return test_rmse closed vs open on short NARMA-10."""

Expect open error >= closed at moderate gamma — validates damping hurts performance (or document noise-assisted regime if not).

4. Tests — tests/test_open_system.py

Mark tests requiring QuTiP:

pytest.importorskip("qutip")

Test	Verifies
test_density_matrix_trace_one	Tr(rho) = 1 after evolution
test_collect_open_features_shape	Correct feature matrix shape
test_zero_gamma_matches_closed_limit	gamma=0 close to closed features (tolerance)
test_open_features_no_nan	Finite features

Skip entire module if qutip not installed (default dev install may not include [open]).

5. Notebook 06 structure

• Title: Open-system QRC with Gilbert damping
• Setup with [open] install note
• Plot: closed vs open NARMA-10 test_rmse vs gamma sweep (e.g. gamma in [0, 0.001, 0.01, 0.05])
• Panel: example rho dynamics (one-site expectation vs time)
• Save figures/open_system_qrc.png
• Optional CSV: data/open_system_results.csv

6. Documentation

• docs/api.md — open_system section
• README.md — note Notebook 06 requires [open]
• REFERENCES.md O1–O4 already present

Scope limits

• No full pipeline.py rewrite — open path is parallel module
• No mtj-quantum-noise integration (future repo)
• gamma sweep in notebook only; Optuna not required

Acceptance criteria

• open_system.py with Lindblad evolution and collect_open_features()
• tests/test_open_system.py passes with pip install -e "./spintronic-qrc[open,dev]"
• notebooks/06_open_system_qrc.ipynb runs top-to-bottom
• figures/open_system_qrc.png committed
• OVERVIEW.md deliverables: check off notebook 06; check open-system design question
• QuTiP not added to core dependencies (stays in [open])

Files likely touched

• src/spintronic_qrc/open_system.py (new)
• tests/test_open_system.py (new)
• notebooks/06_open_system_qrc.ipynb (new)
• figures/open_system_qrc.png (new)
• docs/api.md
• README.md (minor)

Depends on

• Issue Implement end-to-end QRC pipeline (ApproxTimeEvolution + feature matrix builder) #1 (closed pipeline conventions) — required
• Issue Notebook 02 — NARMA-10 end-to-end QRC + committed results #4 (NARMA evaluation pattern) — recommended
• Issue Spintronic gate library — custom PennyLane operations (Workstream C1) #11 (damping metadata) — recommended

Blocks

• Full [all] extra validation
• Paper discussion section on dissipation