Unitary Basis Transformations in Mixed Quantum-Classical Dynamics

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.