Bibliographic record
Abstract
In this paper, we study the optimal simulation of the three-qubit unitary using two-qubit gates. First, we completely characterize the two-qubit gate cost of simulating the Deutsch gate (controlled-controlled gate) by generalizing our result on the two-qubit cost of the Toffoli gate. The function of any Deutsch gate is simply a three-qubit controlled-unitary gate and can be intuitively explained as follows: The gate outputs the states of the two control qubits directly, and applies the given one-qubit unitary $u$ on the target qubit only if both the states of the control qubits are $|1\ensuremath{\rangle}$. Previously, it was only known that five two-qubit gates are sufficient for implementing such a gate [Sleator and Weinfurter, Phys. Rev. Lett. 74, 4087 (1995)]. We show that if the determinant of $u$ is 1, four two-qubit gates are optimal. Otherwise, five two-qubit gates are required. For the Fredkin gate (the controlled-swap gate), we prove that five two-qubit gates are necessary and sufficient, which settles the open problem introduced in Smolin and DiVincenzo [Phys. Rev. A 53, 2855 (1996)].
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".