Efficient quantum computation of molecular forces and other energy gradients
Why this work is in the frame
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Bibliographic record
Abstract
While most work on the quantum simulation of chemistry has focused on computing energy surfaces, a similarly important application requiring subtly different algorithms is the computation of energy derivatives. Almost all molecular properties can be expressed an energy derivative, including molecular forces, which are essential for applications such as molecular dynamics simulations. Here, we introduce new quantum algorithms for computing molecular energy derivatives with significantly lower complexity than prior methods. Under cost models appropriate for noisy-intermediate scale quantum devices, we demonstrate how low-rank factorization and other tomography schemes can be optimized for energy derivative calculations. We numerically demonstrate that our techniques reduce the number of circuit repetitions required by many orders of magnitude for even modest systems, and that the cost of estimating an entire force vector may in some systems be lower than the cost of estimating the energy. In the context of fault-tolerant algorithms, we develop new methods of estimating energy derivatives with Heisenberg limited scaling, incorporating state-of-the-art techniques for block encoding fermionic operators. In contrast to our near-term results, we find that the cost of estimating forces with any of our Heisenberg-limited methods is bounded by the cost of estimating energies, due to inner loops requiring either energy estimation or reflections around the ground state. This implies that applications such as geometry optimization, coupling parameter estimation, and spectral prediction may be practical on fault-tolerant quantum devices, but tractable molecular dynamics simulations of large-scale systems requires further algorithmic advances.
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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 | 0.001 | 0.001 |
| 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 it