  Recenty Abrams and Lloyd have proposed a fast algorithm that is based on a
nonlinear evolution of a state of a quantum computer. They have explicitly used
the fact that nonlinear evolutions in Hilbert spaces do not conserve scalar
products of states, and applied a description of separated systems taken from
Weinberg's nonlinear quantum mechanics. On the other hand it is known that
violation of orthogonality combined with the Weinberg-type description
generates unphysical, arbitrarily fast influences between noninteracting
systems. It was not therefore clear whether the algorithm is fast because
arbitrarily fast unphysical effects are involved. In these notes I show that
this is not the case. I analyze both algorithms proposed by Abrams and Lloyd on
concrete, simple models of nonlinear evolution. The description I choose is
known to be free of the unphysical influences (therefore it is not the Weinberg
one). I show, in particular, that the correct local formalism allows even to
simplify the algorithm.
