Growth Reduction of Similarity-Transformed Electronic Hamiltonians in Qubit Space
Bibliographic record
Abstract
Accurately solving the electronic structure problem through the variational quantum eigensolver (VQE) is hindered by the available quantum resources of current and near-term devices. One approach to relieving the circuit depth requirements for VQE is to “pre-process” the electronic Hamiltonian by a similarity transformation incorporating some degree of electronic correlation, with the remaining correlation left to be addressed by the circuit ansatz. This often comes at the price of a substantial increase in the number of terms to measure in the similarity-transformed Hamiltonian. In this work, we propose an efficient approach to sampling elements from the complete Pauli group for N qubits which minimizes the onset of new terms in the transformed Hamiltonian while facilitating substantial energy lowering. We benchmark the growth-mitigating generator selection technique for ground state energy estimations applied to models of the H 4, N 2, and H 2 O molecular systems. It is found that utilizing a selection procedure which obtains the growth-minimizing generator from the set of operators with the maximal energy gradient is the most competitive approach to reducing the onset of Hamiltonian terms while achieving systematic energy lowering of the reference state.
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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 | 0.001 |
| 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".