Before revision:  We also give both  classical and quantum complexity analysis for these circuits and show that the circuits require a few classical computations , and the quantum complexities of them are almost the same  as non-general circuits  .
After revision:  We also give both classical and quantum complexity analysis for these circuits and show that the circuits require a few classical computations , and the quantum complexities of them are almost the same as non-general circuits . Since the presented circuit designs are independent from the matrix decomposition techniques and the global optimization processes used to find quantum circuits for a given operator, high accuracy simulations can be done for the unitary propagators of molecular Hamiltonians on quantum computers. As an example, we show how to build the circuit design for the hydrogen molecule .