General Bounds for Quantum Biased Oracles
Bibliographic record
Abstract
An oracle with bias ε is an oracle that answers queries correctly with a probability of at least 1/2+ε. In this paper, we study the upper and lower bounds of quantum query complexity of oracles with bias ε. For general upper bounds, we show that for any quantum algorithm solving some problem with high probability using T queries of perfect quantum oracles, i.e., oracles with ε =1/2, there exists a quantum algorithm solving the same problem, also with high probability, using O(T/ε) queries of the corresponding biased quantum oracles. As corollaries we can show robust quantum algorithms and gaps between biased quantum and classical oracles, e.g., by showing a problem where the quantum query complexity is O(N/ε) but the classical query complexity is lower bounded by Ω(N logN/ε2). For general lower bounds, we generalize Ambainis' quantum adversary argument to biased quantum oracles and obtain the first lower bounds with explicit bias factor. As one of its applications we can provide another proof of the optimality of quantum algorithms for the so-called quantum Goldreich-Levin problem which was proved before by Adcock, et al. using different and more complicated methods.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
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 | 0.000 | 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 | 0.001 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".