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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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Efficient geometric integrators for nonadiabatic quantum dynamics. II. The diabatic representation.

Julien Roulet¹, Seonghoon Choi¹, Jiří Vaníček¹

¹Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015, Lausanne, Switzerland.

The Journal of Chemical Physics

|June 3, 2019

Summary

New numerical methods precisely preserve geometric properties in quantum molecular dynamics. Higher-order algorithms offer significant speedups for simulating molecular systems, improving computational efficiency.

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Area of Science:

Quantum Chemistry
Computational Physics
Molecular Dynamics

Background:

Exact nonadiabatic quantum evolution preserves geometric properties of the molecular Hilbert space.
Previous work introduced arbitrary-order accurate integrators for the adiabatic representation.

Purpose of the Study:

Develop and analyze higher-order numerical integrators for the diabatic representation of molecular systems.
Improve computational efficiency and accuracy in quantum molecular simulations.

Main Methods:

Implemented automated recursive symmetric compositions of the split-operator algorithm.
Developed methods for pruning redundant coefficients and identifying unique ones to reduce computational cost.
Analytically justified order of convergence and geometric property preservation.

Main Results:

Achieved arbitrary even-order accurate integrators that exactly preserve geometric properties.
Demonstrated significant speedups (600-fold for NaI, 900-fold for pyrazine) compared to the second-order split-operator algorithm.
Confirmed efficiency gains in higher dimensions using a pyrazine model.

Conclusions:

Higher-order split-operator compositions provide exact geometric property preservation and substantial efficiency improvements.
These advanced numerical methods are crucial for accurate and efficient quantum molecular dynamics simulations.