Almost perfect quantum state transfer on isotropic and anisotropic Heisenberg spin chains with tailored site dependent exchange couplings

Spin chains with site dependent exchange coefficients can achieve near perfect quantum state transfer for Hamiltonians with nearest neighbors XXZ type interactions without external control. The strength of the interactions is obtained using a global optimization method, which can be employed without assuming a particular relationship between the arrival time and the strength of the interactions. This relationship arises naturally when data collapse techniques are used to analyze the results of the optimization method. The arrival times achievable are competitive with respect to those obtained by other methods, for chains of moderate length. The stability of the resulting spin chains against static perturbations is also studied. The differences in the dynamical behavior between the isotropic and anisotropic spin chains are analyzed for some particular cases.