The quantum challenge to structural complexity theory
Bibliographic record
Abstract
A nontechnical survey of recent quantum-mechanical discoveries that challenge generally accepted complexity-theoretic versions of the Church-Turing thesis is presented. In particular, the authors construct an oracle relative to which there exists a set that can be recognized in quantum polynomal time (QP), yet any Turing machine that recognizes it would require exponential time even if allowed to be probabilistic, provided that errors are not tolerated. In particular, QP is not contained in or equal to ZPP relative to this oracle. Furthermore, there are cryptographic tasks that are demonstrably impossible to implement with unlimited computing power probabilistic interactive turning machines, yet they can be implemented even in practice by quantum mechanical apparatus.>
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.008 |
| Scholarly communication | 0.004 | 0.010 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.008 | 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".