  This article is devoted to the development of analytical and numerical
approaches to the problem of the end-to-end quantum state transfer along the
spin-1/2 chain using two methods: (a) a homogeneous spin chain with week end
bonds and equal Larmor frequencies and (b) a homogeneous spin chain with end
Larmor frequencies different from inner ones. A tridiagonal matrix
representation of the XY Hamiltonian with nearest neighbor interactions
relevant to the quantum state transfer is exactly diagonalized for a
combination of the above two methods. In order to take into account
interactions of the remote spins we used numerical simulations of the quantum
state transfer in ten-node chains. We compare the state transfer times obtained
using the two above methods for chains governed by the both XY and XXZ
Hamiltonians and using both nearest neighbor and all node interactions.
