Quantum Query Complexity of Hypergraph Search Problems
Bibliographic record
Abstract
In the study of quantum query complexity, it is natural to study the problems of \nfinding triangles and spanning trees in a simple graph. Over the past decades, many \ntechniques are developed for finding the upper and lower quantum query bounds of these \ngraph problems. We can generalize these problems to detecting certain properties of higher \nrank hypergraphs and ask whether these techniques are still available. In this thesis, we \nwill see that when the rank increase, complexity bounds still holds for some problems, \nalthough less effectively. For some other problems, their nontrivial complexity bounds \nvanish. Moreover, we will focused on using the generalized adversary and learning graph \ntechniques for finding nontrivial quantum query bounds for different hypergraph search \nproblems. The following results are presented. \n \n• Discover a general quantum query lower bound for subhypergraph-closed properties \nand monotone properties over r-partite r-uniform hypergraphs. \n• Provide tight quantum query bounds for the connectivity and acyclicity problems \nover r-uniform hypergraphs. \n• Present a nontrivial learning graph algorithm for the 3-simplex finding problem. \n• Formulate nested quantum walk in the adaptive learning context and use it to present \na nontrivial quantum query algorithm for the 4-simplex finding problem. \n• Present a natural relationship of lower bounds for simplex finding of different ranks. \n• Use the learning graph formalization of tetrahedron certificate structure to find a \nnontrivial quantum query lower bound of the 3-simplex sum problem.
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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 | 0.004 | 0.026 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.005 | 0.013 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.013 | 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".