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arXiv · 2404.15614

Unitary Basis Transformations in Mixed Quantum-Classical Dynamics

Ken Miyazaki·Alex Krotz·Roel Tempelaar
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Abstract

A common approach to minimizing the cost of quantum computations is by transforming a quantum system into a basis that can be optimally truncated. Here, we derive classical equations of motion subjected to similar unitary transformations, and propose their integration into mixed quantum-classical dynamics, enabling this class of methods to be applied within arbitrary bases for both the quantum and classical coordinates. To this end, canonical positions and momenta are combined into a set of complex-valued classical coordinates amenable to unitary transformations. We demonstrate the potential of the resulting approach by means of surface hopping calculations of an electronic carrier scattering onto a single impurity in the presence of phonons. Appropriate basis transformations, capturing both the localization of the impurity and the delocalization of higher-energy excitations, are shown to faithfully capture the dynamics within a fraction of the classical and quantum basis sets.

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Ken Miyazaki, Alex Krotz, Roel Tempelaar. 2024-04-24. Unitary Basis Transformations in Mixed Quantum-Classical Dynamics. https://arxiv.org/abs/2404.15614

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