Spectrally extremal vertices, strong cospectrality, and state transfer
Bibliographic record
Abstract
A fim de obter transferência de estado perfeita entre dois sites em uma rede de qubits interagindo, seus vértices correspondentes no grafo subjacente devem satisfazer uma propriedade chamada cospectralidade forte. Aqui nós determinamos a estrutura dos grafos contendo pares de vértices que são fortemente cospectrais e satisfazem um certo extremo propriedade relacionada ao espectro do grafo. Se o grafo satisfaz essa propriedade globalmente e é regular, também mostramos que a existência de uma partição do conjunto de vértices em pares de vértices na distância máxima admitindo transferência de estado perfeita força o grafo a ser regular em distância. Finalmente, apresentamos alguns novos exemplos de transferência de estado perfeita em grafos simples construídos com nossa tecnologia. Em particular, para distâncias ímpares, melhoramos o trade-off conhecido entre a distância que a transferência de estado perfeita ocorre em grafos simples e o tamanho do grafo.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".