T-count and T-depth of any multi-qubit unitary
Bibliographic record
Abstract
Abstract We design an algorithm to determine the (minimum) T-count of any n -qubit ( n ≥ 1) unitary W of size 2 n × 2 n , over the Clifford+T gate set. The space and time complexity of our algorithm are $$O\left({2}^{2n}\right)$$ O 2 2 n and $$O\left({2}^{2n{{{{\mathcal{T}}}}}_{\epsilon }(W)+4n}\right)$$ O 2 2 n T ϵ ( W ) + 4 n , respectively. $${{{{\mathcal{T}}}}}_{\epsilon }(W)$$ T ϵ ( W ) ( ϵ -T-count) is the (minimum) T-count of an exactly implementable unitary U ( $${{{\mathcal{T}}}}(U)$$ T ( U ) ), such that d ( U , W ) ≤ ϵ and $${{{\mathcal{T}}}}(U)\le {{{\mathcal{T}}}}({U}^{{\prime} })$$ T ( U ) ≤ T ( U ′ ) where $${U}^{{\prime} }$$ U ′ is any exactly implementable unitary with $$d({U}^{{\prime} },W)\le \epsilon$$ d ( U ′ , W ) ≤ ϵ </
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.011 | 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".