  In this letter we propose a superadiabatic protocol where quantum state
transfer can be achieved with arbitrarily high accuracy and minimal control
across long spin chains with an odd number of spins. The quantum state transfer
protocol only requires the control of the couplings between the qubits on the
edge and the spin chain. We predict fidelities above 0.99 for an evolution of
nanoseconds using typical spin exchange coupling values of {\mu}eV.
Furthermore, by building a superadiabatic formalism on top of this protocol, we
propose a effective superadiabatic protocol that retains the minimal control
over the spin chain and improves the fidelity by up to 20%.
