  In this article we propose a dynamic approach to complex vector
reconstruction in the context of quantum tomography. There are two underlying
assumptions behind our reasoning. The first one claims that the evolution of a
d-level pure quantum system is given by the Schr\"odinger equation with a
time-independent Hamiltonian and the other states that the knowledge about the
quantum state is provided from projective measurements, also called intensity
measurements. The problem of quantum state reconstruction is connected with the
notion known as phase retrieval -- recovering a complex vector from modulus of
inner product with frame vectors. Phase retrieval is widely studied in many
areas of science but still there is a number of problems that remain to be
answered. We believe that the dynamic approach can significantly improve the
effectiveness of the vector reconstruction as it aims to decrease the number of
distinct projectors by taking advantage of the knowledge about the evolution.
General conditions and observations are applied to a specific unitary evolution
model.
