Ranking versus Absolute Accuracy in Matter–Light Simulation Cost Prediction
- 1Department of Physics
- 2Brown University Providence
Abstract
Ordering quantum-dynamical simulations by difficulty is not equivalent to pre-dicting their absolute computational requirements. We examine this distinction using frozen matter–light product-formula benchmarks and descriptors of accessible support, state-space geometry, finite-time Krylov evolution, control-algebra dimension, analytic sufficient steps, and empirical symbolic predictions. Effective Krylov dimension has a median error-stratified Spearman association of 0.8158 with measured steps, but the descriptor comparisons use different eligible populations and cannot establish condi-tional superiority. On its strict dimension holdout, a frozen symbolic predictor retains rank correlation 0.9363 while incurring mean absolute error 626.5785 steps. Analytic sufficient-to-measured step ratios have medians 46.6087 and 7.6583 for the respective formula orders; these measure conservative looseness, not point-prediction error. The benchmark illustrates a domain-limited separation of ranking, absolute accuracy, and conservative error control. Censoring, approximate Krylov bases, and unavailable cir-cuit domains preclude a unified or hardware-level complexity interpretation.
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BibTeX
@misc{kothuri2026ranking,
title = {{Ranking versus Absolute Accuracy in Matter–Light Simulation Cost Prediction}},
author = {Rithvik Kothuri},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15011064/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15011064/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - Ranking versus Absolute Accuracy in Matter–Light Simulation Cost Prediction
AU - Rithvik Kothuri
PY - 2026
DA - 2026/10/26
PB - ChemRxiv
DO - 10.26434/chemrxiv.15011064/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15011064/v1
AB - Ordering quantum-dynamical simulations by difficulty is not equivalent to pre-dicting their absolute computational requirements. We examine this distinction using frozen matter–light product-formula benchmarks and descriptors of accessible support, state-space geometry, finite-time Krylov evolution, control-algebra dimension, analytic sufficient steps, and empirical symbolic predictions. Effective Krylov dimension has a median error-stratified Spearman association of 0.8158 with measured steps, but the descriptor comparisons use different eligible populations and cannot establish condi-tional superiority. On its strict dimension holdout, a frozen symbolic predictor retains rank correlation 0.9363 while incurring mean absolute error 626.5785 steps. Analytic sufficient-to-measured step ratios have medians 46.6087 and 7.6583 for the respective formula orders; these measure conservative looseness, not point-prediction error. The benchmark illustrates a domain-limited separation of ranking, absolute accuracy, and conservative error control. Censoring, approximate Krylov bases, and unavailable cir-cuit domains preclude a unified or hardware-level complexity interpretation.
ER -