Efficient Construction of Involutory Linear Combinations of Anticommuting Pauli Generators for Large-Scale Iterative Qubit Coupled Cluster Calculations
Bibliographic record
Abstract
We present an efficient method for construction of a fully anticommutative set of Pauli generators (elements of the Pauli group) from a commutative set of operators that are composed exclusively from Pauli x̂ operators (purely X generators) and sorted by an associated numerical measure, such as absolute energy gradients. Our approach uses the Gauss–Jordan elimination applied to a binary matrix that encodes the set of X generators to bring it to the reduced row-echelon form, followed by the construction of an anticommutative system in a standard basis by means of a modified Jordan–Wigner transformation and returning to the original basis. The algorithm complexity is linear in the size of the X set and quadratic in the number of qubits. The resulting anticommutative sets are used to construct the qubit coupled cluster Ansatz with involutory linear combinations of anticommuting Paulis (QCC-ILCAP) proposed in J. Chem. Theory Comput. 2021, 17 (1), 66–78. We applied the iterative qubit coupled cluster method with the QCC-ILCAP Ansatz to calculations of ground-state potential energy curves for symmetric stretching of the water molecule (36 qubits) and dissociation of N 2 (56 qubits).
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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 | 0.001 | 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 | 0.000 |
| 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".