Most of the numerical simulation in quantum (bilinear) control have used one of the monotonically convergent algorithms of Krotov (introduced by Tannor ) or of Zhu and Rabitz. However, until now no explicit relationship has been revealed between the two algorithms in order to understand their common properties. Within this framework, we propose in this paper a unified formulation that comprises both algorithms and that extends to a new class of monotonically convergent algorithms. Numerical results show that the newly derived algorithms behave as well as (and sometimes better than) the well-known algorithms cited above. (C) 2003 American Institute of Physics.