The time complexity for an adiabatic algorithm is the time taken to complete the adiabatic evolution which is dependent on the gap in the energy eigenvalues (spectral gap) of the Hamiltonian. Specifically, if the system is to be kept in the ground state, the energy gap between the ground state and the first excited state of H ( t ) provides an upper bound on the rate at which the Hamiltonian can be evolved at time t . When the spectral gap is small, the Hamiltonian has to be evolved slowly. The runtime for the entire algorithm can be bounded by: