Recent experiments on quantum hardware are beginning to show advantage, although in very strict cases, over classical computers. While these novel qubits are being developed, it is instructive to study their dynamics on available noisy intermediate-scale quantum (NISQ) hardware. Adiabatic time evolution has emerged in various application sets in quantum simulation. They range from simulating time evolution of Hamiltonians to solving optimization problems where the solution is obtained through simulating a slowly varying Hamiltonian that evolves a known ground state into an unknown desired ground state. We study various strategies for breaking down the time evolution into single-qubit and two-qubit operations with a special emphasis on error analysis of Trotter-Suzuki expansion, adiabatic conditions, and hardware error. We focus on a few sample systems such as the Ising chain as well as the Fermi-Hubbard Hamiltonians.