Sufficient condition for the coherent control of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:math>-qubit systems
Bibliographic record
Abstract
We study quantum systems with even numbers $N$ of levels that are completely state controlled by unitary transformations generated by Lie algebras isomorphic to $\mathrm{sp}(N)$ of dimension $N(N+1)∕2$ as discussed by Albertini and D'Allesandro [IEEE Trans. Autom. Control 48, 1399 (2003)]. These Lie algebras are smaller than the corresponding $\mathrm{su}(N)$ with dimension ${N}^{2}\ensuremath{-}1$. We show that this reduction constrains the field-free Hamiltonian to have symmetric energy levels. An example of such a system is an $n$-qubit system with state-independent interaction terms. Using Clifford's geometric algebra to represent the quantum wave function of a finite system, we present an explicit example of a two-qubit system that can be controlled by the elements of the Lie algebra $\mathrm{sp}(4)$ [isomorphic to $\mathrm{spin}(5)$ and $\mathrm{so}(5)$] with dimension 10 rather than $\mathrm{su}(4)$ with dimension 15, but only if its field-free energy levels are symmetrically distributed about an average. These results enable one to envision more efficient algorithms for the design of fields for quantum-state engineering in certain quantum-computing applications, and provide more insight into the fundamental structure of quantum control.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".