Quantum Algorithms for Molecular Response Functions: Resolvent Kernels, Time-Domain Sampling, Query Lower Bounds with Matched Single-Point Calibers, and a Six-Route Comparison
Abstract
Quantum algorithms for molecular response functions have mostly been studied one route at a time, most prominently the indicator-binning algorithm of Kharazi et al. We compare six routes within one accounting framework and state the conversions between their resource calibers. On the resolvent route the Lorentz-broadened spectrum is exactly a resolvent expectation; at finite gamma two boundary terms, a reversal term and a permanent-dipole pseudo-line, enter a disjoint error budget. Because the kernel subnormalization is exactly 1, the published binning accounting carries a removable Theta(alpha+1+omega) factor (49.69x and 7.75x at the definitional caliber), a correction that applies to both routes. Estimating the square root of the kernel amplitude lowers the readout cost from beta^2/mu_tilde_2 to beta/sqrt(mu_tilde_2). On the time-domain route we prove a single-point amplitude-estimation theorem and convert the generalized QPE of Loaiza et al. to the same accounting. The lower bounds are Theta_tilde(1/gamma) for parameter location, Theta(1/(gamma epsilon)) for windowed values, Omega(n/gamma) inside a restricted correlation-sampling class, and Omega(1/(epsilon gamma^2)) on the Lorentzian object; in the single-circuit-resolution caliber, gamma^(-n) is a grid-coverage artifact. Six routes, their calibers, an n=2 assembly with a component-grade coherence, and a phase diagram over the tested ensembles form one accounting map.
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BibTeX
@misc{liu2026quantum,
title = {{Quantum Algorithms for Molecular Response Functions: Resolvent Kernels, Time-Domain Sampling, Query Lower Bounds with Matched Single-Point Calibers, and a Six-Route Comparison}},
author = {Yunlong Liu and Yujin Tang and Miao Xu and Qing-Xing Xie},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06821},
eprint = {2611.06821},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06821},
}
RIS
TY - UNPB
TI - Quantum Algorithms for Molecular Response Functions: Resolvent Kernels, Time-Domain Sampling, Query Lower Bounds with Matched Single-Point Calibers, and a Six-Route Comparison
AU - Yunlong Liu
AU - Yujin Tang
AU - Miao Xu
AU - Qing-Xing Xie
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.06821
UR - https://arxiv.org/abs/2611.06821
AB - Quantum algorithms for molecular response functions have mostly been studied one route at a time, most prominently the indicator-binning algorithm of Kharazi et al. We compare six routes within one accounting framework and state the conversions between their resource calibers. On the resolvent route the Lorentz-broadened spectrum is exactly a resolvent expectation; at finite gamma two boundary terms, a reversal term and a permanent-dipole pseudo-line, enter a disjoint error budget. Because the kernel subnormalization is exactly 1, the published binning accounting carries a removable Theta(alpha+1+omega) factor (49.69x and 7.75x at the definitional caliber), a correction that applies to both routes. Estimating the square root of the kernel amplitude lowers the readout cost from beta^2/mu_tilde_2 to beta/sqrt(mu_tilde_2). On the time-domain route we prove a single-point amplitude-estimation theorem and convert the generalized QPE of Loaiza et al. to the same accounting. The lower bounds are Theta_tilde(1/gamma) for parameter location, Theta(1/(gamma epsilon)) for windowed values, Omega(n/gamma) inside a restricted correlation-sampling class, and Omega(1/(epsilon gamma^2)) on the Lorentzian object; in the single-circuit-resolution caliber, gamma^(-n) is a grid-coverage artifact. Six routes, their calibers, an n=2 assembly with a component-grade coherence, and a phase diagram over the tested ensembles form one accounting map.
ER -