We discuss some new approach for derivation of computational algorithms for evolution of quantum systems. The main idea of the algorithm is to make in functional or path representation of quantum observable the transformation of variables, that makes the phase of path integral to be quadric functional. Thus the new representation for observable is reduced to standard multidimensional integral and the solution, for every point in coordinate space of that integral, of the first order partial differential equation system. That problem, although still difficult, can be very effectively parallelyzed. The approach is illustrated with the help of important example - the scattering in molecular system with elementary chemical reactions. The use of proposed approach show substantial speed-up over the standard algorithms and seems to be more effective with the increase of the size of the problem.
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