Hybrid Hamiltonian Simulation for Excitation Dynamics

Hamiltonian simulation is one of the most anticipated applications of quantum computing. Quantum circuit depth for implementing Hamiltonian simulation is commonly time dependent using Trotter-Suzuki product formulas so that long time quantum dynamic simulations (QDSs) become impratical for near-term quantum processors. Hamiltonian simulation based on Cartan decomposition (CD) provides an appealing scheme for QDSs with fixed-depth circuits, while it is limited to a time-independent Hamiltonian. In this work, we generalize this CD-based Hamiltonian simulation algorithm for studying time-dependent systems by combining it with variational quantum algorithms. The time-dependent and time-independent parts of the Hamiltonian are treated by using variational and CD-based Hamiltonian simulation algorithms, respectively. As such, this hybrid Hamiltonian simulation requires only fixed-depth quantum circuits to handle time-dependent cases while maintaining a high accuracy. We apply this new algorithm to study the response of spin and molecular systems to δ-kick electric fields and obtain accurate spectra for these excitation processes.