  In this note we explicitly solve the Lindblad equation for a system of three
spins with a three-body interaction, coupled to the environment by bath
operators that inject or absorb spin carriers. We exemplify the properties of
this solution in the context of a simple instance of Feynman's quantum computer
in which a two-qubit program line is executed, applying the $\sqrt{NOT}$
primitive to a one-qubit register.
