Minimal-memory requirements for pearl-necklace encoders of quantum convolutional codes
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Bibliographic record
Abstract
One of the major goals in quantum information processing is to reduce the overhead associated with the practical implementation of quantum protocols, and often, routines for quantum error correction account for most of this overhead. A particular technique for quantum error correction that may be useful for protecting a stream of quantum information is quantum convolutional coding. The encoder for a quantum convolutional code has a representation as a convolutional encoder or as a "pearl-necklace" encoder. In the pearl-necklace representation, it has not been particularly clear in the research literature how much quantum memory such an encoder would require for implementation. Here, we offer an algorithm that answers this question. The algorithm first constructs a weighted, directed acyclic graph where each vertex of the graph corresponds to a gate string in the pearl-necklace encoder, and each path through the graph represents a path through noncommuting gates in the encoder. We show that the weight of the longest path through the graph is equal to the minimal amount of memory needed to implement the encoder. A dynamic programming search through this graph determines the longest path. The running time for the construction of the graph and search through it is quadratic in the number of gate strings in the pearl-necklace encoder. © 2012 IEEE.
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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 | 0.001 | 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 it