Comparison of memory thresholds for planar qudit geometries
Bibliographic record
Abstract
We introduce and analyze a new type of decoding algorithm called general color clustering, based on renormalization group methods, to be used in qudit color codes. The performance of this decoder is analyzed under a generalized bit-flip error model, and is used to obtain the first memory threshold estimates for qudit 6-6-6 color codes. The proposed decoder is compared with similar decoding schemes for qudit surface codes as well as the current leading qubit decoders for both sets of codes. We find that, as with surface codes, clustering performs sub-optimally for qubit color codes, giving a threshold of 5.6% compared to the 8.0% obtained through surface projection decoding methods. However, the threshold rate increases by up to 112% for large qudit dimensions, plateauing around 11.9%. All the analysis is performed using QTop, a new open-source software for simulating and visualizing topological quantum error correcting codes.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".