  We study the spin transport in the quantum Heisenberg spin chain subject to
boundary magnetic fields and driven out of equilibrium by Lindblad dissipators.
An exact solution is given in terms of matrix product states, which allows us
to calculate exactly the spin current for any chain size. It is found that the
system undergoes a discontinuous spin-valve-like quantum phase transition from
ballistic to sub-diffusive spin current, depending on the value of the boundary
fields. Thus, the chain behaves as an extremely sensitive magnonic logic gate
operating with the boundary fields as the base element.
