Characterization of universal two-qubit hamiltonian
Bibliographic record
Abstract
Suppose we can apply a given 2-qubit Hamiltonian H to any (ordered) pair of qubits.We say H is n-universal if it can be used to approximate any unitary operation onn qubits. While it is well known that almost any 2-qubit Hamiltonian is 2-universal(Deutsch, Barenco, Ekert 1995; Lloyd 1995), an explicit characterization of the set ofnon-universal 2-qubit Hamiltonians has been elusive. Our main result is a completecharacterization of 2-non-universal 2-qubit Hamiltonians. In particular, there are threeways that a 2-qubit Hamiltonian H can fail to be universal: (1) H shares an eigenvectorwith the gate that swaps two qubits, (2) H acts on the two qubits independently (inany of a certain family of bases), or (3) H has zero trace (with the third conditionrelevant only when the global phase of the unitary matters). A 2-non-universal 2-qubitHamiltonian can still be n-universal for some n ≥ 3. We give some partial results on3-universality.
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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 | 0.000 | 0.001 |
| Open science | 0.000 | 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".