Unitary Basis Transformations in Mixed Quantum-Classical Dynamics

TL;DR

This paper introduces a method to incorporate basis transformations into mixed quantum-classical dynamics, allowing for more efficient simulations by optimally truncating quantum systems in arbitrary bases.

Contribution

It derives classical equations of motion for unitary transformations and integrates them into mixed quantum-classical dynamics, enabling basis optimization in both quantum and classical coordinates.

Findings

Efficient basis transformations capture impurity localization and excitation delocalization.

The approach reduces computational basis size while maintaining accuracy.

Demonstrated effectiveness in surface hopping simulations with phonons.

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.