  Motivated by proposals to employ RKKY-coupled spins as building blocks in a
solid-state quantum computer, we analyze how the RKKY interaction in a 2D
electron gas is influenced by spin-orbit interactions. Using a two-impurity
Kondo model with added Dresselhaus and Rashba spin-orbit interactions we find
that spin-rotational invariance of the RKKY interaction - essential for having
a well-controllable two-qubit gate - is restored when tuning the Rashba
coupling to have the same strength as the Dresselhaus coupling. We also discuss
the critical properties of the two-impurity Kondo model in the presence of
spin-orbit interactions, and extract the leading correction to the block
entanglement scaling due to these interactions.
