Quantum t-designs: t-wise Independence in the Quantum World
Why this work is in the frame
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Bibliographic record
Abstract
A t-design for quantum states is a finite set of quantum states with the property of simulating the Haar-measure on quantum states w.r.t. any test that uses at most t copies of a state. We give efficient constructions for approximate quantum t-designs for arbitrary t. We then show that an approximate 4-design provides a derandomization of the statedistinction problem considered by Sen (quant-ph/0512085), which is relevant to solving certain instances of the hidden subgroup problem.
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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 | 0.004 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.002 | 0.005 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.005 | 0.001 |
| Research integrity | 0.000 | 0.002 |
| 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