  Quantum computers are expected to help us to achieve accurate simulation of
the dynamics of many-body quantum systems. However, the limitations of current
NISQ devices prevents us from realising this goal today. Recently an algorithm
for performing quantum simulations called quantum assisted simulator has been
proposed that promises realization on current experimental devices. In this
work, we extend the quantum assisted simulator to simulate the dynamics of a
class of time-dependent Hamiltonians. We show that the quantum assisted
simulator is easier to implement as well as can realize multi-qubit
interactions and challenging driving protocols that are difficult with other
existing methods. We demonstrate this for a time-dependent Hamiltonian on the
IBM Quantum Experience cloud quantum computer by showing superior performance
of the quantum assisted simulator compared to Trotterization and variational
quantum simulation. Further, we demonstrate the capability to simulate the
dynamics of Hamiltonians consisting of 10000 qubits. Our results indicate that
quantum assisted simulator is a promising algorithm for current term quantum
hardware.
