NISQ Algorithm for Hamiltonian simulation via truncated Taylor series

Simulating the dynamics of many-body quantum systems is believed to be one first fields that computers can show a advantage over classical computers. Noisy intermediate-scale (NISQ) algorithms aim at effectively using currently available hardware. For simulation, various types NISQ have been proposed with individual advantages as well challenges. In this work, we propose new algorithm, truncated Taylor simulator (TQS), shares existing and alleviates some shortcomings. Our algorithm does not any classical-quantum feedback loop bypasses barren plateau problem by construction. The part in our hybrid quantum-classical corresponds quadratically constrained quadratic program (QCQP) single equality constraint, which admits semidefinite relaxation. QCQP based optimization was recently introduced step assisted eigensolver (QAE), for Hamiltonian ground state problem. Thus, work provides conceptual unification between simulation. We recover differential equation-based simulation such (QAS) variational (VQS) particular cases algorithm. test on toy examples current cloud also provide systematic approach improve accuracy