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This research presents novel correction schemes for simulating Coulombic dynamics on grid-based systems, significantly improving accuracy for hydrogenic models while explicitly addressing compatibility with quantum computing architectures. By encoding corrected operators via Walsh and Fourier series, the study bridges high-precision classical simulations with emerging quantum hardware requirements. The work offers a concrete pathway to reducing circuit depth and managing discretization errors in time-dependent quantum dynamics.
Improved Grid-Based Simulation of Coulombic Dynamics
arXiv:2603.02954v2 Announce Type: replace Abstract: Accurate time-dependent quantum dynamics of Coulombic systems on grid-based representations remains computationally demanding due to the singularity of the Coulomb potential, which necessitates extremely fine spatial grids to mitigate discretisation errors. We propose two complementary correction schemes that, under identical resource budgets, consistently outperform the uncorrected counterparts. The first scheme modifies the potential operator to incorporate grid-basis structure into its representation, while the second introduces a corrected initial wavefunction inspired by analytical solutions of softened Coulomb potentials. Applied to hydrogenic systems, these corrections deliver improved energy accuracy and time fidelity across long evolutions. Beyond classical simulations, the proposed framework aligns naturally with quantum computing architectures, where the corrected operators and states can be encoded through truncated Walsh and Fourier series expansions. A resource analysis for the representative 2D hydrogen system yields a circuit depth of $1.5\times10^{8}$ gates over 6,000 Trotter steps. This study thus establishes practical strategies toward high-accuracy Coulombic dynamics on both classical and emerging quantum platforms.
Abstract:Accurate time-dependent quantum dynamics of Coulombic systems on grid-based representations remains computationally demanding due to the singularity of the Coulomb potential, which necessitates extremely fine spatial grids to mitigate discretisation errors. We propose two complementary correction schemes that, under identical resource budgets, consistently outperform the uncorrected counterparts. The first scheme modifies the potential operator to incorporate grid-basis structure into its representation, while the second introduces a corrected initial wavefunction inspired by analytical solutions of softened Coulomb potentials. Applied to hydrogenic systems, these corrections deliver improved energy accuracy and time fidelity across long evolutions. Beyond classical simulations, the proposed framework aligns naturally with quantum computing architectures, where the corrected operators and states can be encoded through truncated Walsh and Fourier series expansions. A resource analysis for the representative 2D hydrogen system yields a circuit depth of $1.5\times10^{8}$ gates over 6,000 Trotter steps. This study thus establishes practical strategies toward high-accuracy Coulombic dynamics on both classical and emerging quantum platforms.
arXiv:2603.02954 [quant-ph]
(or arXiv:2603.02954v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2603.02954 Focus to learn more arXiv-issued DOI via DataCite
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