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This paper presents a unified accounting framework comparing six distinct quantum algorithmic routes for calculating molecular response functions, correcting previous resource estimates by up to 49x. By establishing rigorous lower bounds and converting between different calibers, the work clarifies the true computational costs and error budgets associated with resolvent and time-domain approaches. These findings are critical for researchers aiming to optimize quantum simulations of complex molecular systems on near-term hardware.
Quantum Algorithms for Molecular Response Functions: Resolvent Kernels, Time-Domain Sampling, Query Lower Bounds with Matched Single-Point Calibers, and a Six-Route Comparison
arXiv:2611.06821v1 Announce Type: new 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.
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.
arXiv:2611.06821 [quant-ph]
(or arXiv:2611.06821v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2611.06821 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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