Unitary Basis Transformations in Mixed Quantum-Classical Dynamics

• URL: http://arxiv.org/abs/2404.15614v1
• Date: Wed, 24 Apr 2024 03:08:05 GMT
• Title: Unitary Basis Transformations in Mixed Quantum-Classical Dynamics
• Authors: Ken Miyazaki, Alex Krotz, Roel Tempelaar,
• Abstract summary: 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. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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