Mixed Quantum-Classical Dynamics under Arbitrary Unitary Basis Transformations

A common approach to minimizing the cost of quantum computations is by unitarily 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, allowing this class of methods to be applied within arbitrary bases for both the quantum and classical coordinates. To this end, canonical positions and momenta of the classical degrees of freedom are combined into a set of complex-valued 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.