Beat MWPM: decode quantum error-correction color codes

You inherit a plain PyMatching (minimum-weight perfect matching) decoder and a labeled development pack for four superdense color-code memory experiments. Your decoder is then re-run by a sealed grader on four HELD-OUT color settings (same code family, calibrated to the same anchors) that you never see. MWPM is the field standard for surface codes but is structurally wrong for color codes. Each setting is scored on a relative scale whose 1.0 is a reference level recorded in its meta.json; the top of the range is for beating it. You submit a decoder, not answers.

Hard Constraints

• Edit /app/methods/main/solver.py. Expose decode(setting, dets) -> predictions, a boolean array of shape [n_shots, n_observables] — per shot, the predicted logical-observable flips.
• stim + pymatching + numpy + scipy + standard library ONLY. No other decoding package is installed, and none can be added — whatever decoder you submit has to be built from these.
• Predictions are compared bit-for-bit against hidden ground-truth flips: LER = fraction of shots with ANY observable mispredicted. The shape must match the truth exactly or the setting scores 0.
• Per-setting decode wall-clock budget = setting["meta"]["decode_budget_sec"] (600 s for d5, 900 s for d7/d9). Over budget = 0 for that setting.

What You Have

• /app/methods/main/solver.py: the inherited weak decoder — plain PyMatching on the published DEM (force-decomposed hyperedges on color codes). This file is graded — improve it in place.
• /app/arena_harness.py: the verifier's exact scoring code (load_setting, ler_of, setting_score, SCORE_CAP).
• /app/settings_visible/{color_d5,color_d5_Z,color_d7,color_d9}/: four VISIBLE color-code settings. Each carries meta.json (with the calibrated ler_base / ler_sota anchors), model.dem and model.stim (the published, deliberately miscalibrated noise model), dev.npz (a LABELED dev pack: dets + true obs), and eval.npz (here dets + obs, so you can score locally). The sealed graded settings are siblings of these four.
• /app/selfcheck.py: free local dry-run using the grader's exact scoring.

What You Submit

Edit /app/methods/main/solver.py, keeping the contract:

def decode(setting, dets):
    # setting: dict from arena_harness.load_setting, keys:
    #   meta       (name, family, style, distance, rounds, n_dev, n_eval,
    #               decode_budget_sec, n_detectors, n_observables, ...)
    #   name, dem (published DEM text), model_stim (published circuit text),
    #   dev_dets [n_dev, n_detectors] bool, dev_obs [n_dev, n_observables] bool,
    #   eval_dets [n_eval, n_detectors] bool  (eval_obs is withheld when graded)
    # dets: the syndromes to decode (== setting["eval_dets"]).
    # Return predictions [n_shots, n_observables] bool.
    ...

Iterate against selfcheck.py, then leave your best solver.py in place.

How It Is Judged

For each sealed color-code setting the grader runs your decode() in an isolated subprocess (never seeing the ground truth), computes ler_agent, and scores

score = clip( (ln ler_base - ln ler_agent) / (ln ler_base - ln ler_sota), 0, CAP )

with LERs floored at 1/(2*shots). ler_base is plain MWPM on the published DEM; ler_sota is the reference level recorded with each setting. metric = mean over the four sealed color settings of that per-setting score. Higher is better; the inherited baseline sits at 0 and the reference level at 1.0. Each per-setting score is capped at 2.5.

Two facts about the setup, stated without a recommended approach: MWPM is the inherited decoder and it is structurally wrong for color codes, and the published DEM is deliberately miscalibrated versus the noise the eval shots were drawn from. The labeled dev pack (dev_dets / dev_obs) is yours to use however you see fit. Only stim, pymatching, numpy and scipy are available.