  Precise knowledge of the Hamiltonian of a system is a key to many of its
applications. Tasks such state transfer or quantum computation have been well
studied with a linear chain, but hardly with systems, which do not possess a
linear structure. While this difference does not disturb the end-to-end
dynamics of a single excitation, the evolution is significantly changed in
other subspaces. Here we quantify the difference between a linear chain and a
pseudo-chain, which have more than one spin at some site (block). We show how
to estimate a number of all spins in the system and the intra-block coupling
constants. We also suggest how it is possible to eliminate excitations trapped
in such blocks, which may disturb the state transfer. Importantly, one uses
only at-ends data and needs to be able to put the system to either the
maximally magnetized or the maximally mixed state. This can obtained by
controlling a global decoherence parameter, such as temperature.
