Gradient-based reconstruction of molecular Hamiltonians and density matrices from time-dependent quantum observables
Bibliographic record
Abstract
We consider a quantum system with a time-independent Hamiltonian parametrized by a set of unknown parameters $\ensuremath{\alpha}$. The system is prepared in a general quantum state by an evolution operator that depends on a set of unknown parameters $P$. After the preparation, the system evolves in time, and it is characterized by a time-dependent observable $\mathcal{O}(t)$. We show that it is possible to obtain closed-form expressions for the gradients of the distance between $\mathcal{O}(t)$ and a calculated observable with respect to $\ensuremath{\alpha}, P$, and all elements of the system density matrix, whether for pure or mixed states. These gradients can be used in projected gradient descent to infer $\ensuremath{\alpha}, P$, and the relevant density matrix from dynamical observables. We combine this approach with random phase wave function approximation to obtain closed-form expressions for gradients that can be used to infer population distributions from averaged time-dependent observables in problems with a large number of quantum states participating in dynamics. The approach is illustrated by determining the temperature of molecular gas (initially, in thermal equilibrium at room temperature) from laser-induced time-dependent molecular alignment.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".