  In this paper we introduce self-dual cyclic and quantum codes over
Z2^{\alpha} x (Z2 + uZ2)^{\beta}. We determine the conditions for any
Z2Z2[u]-cyclic code to be self-dual, that is, C = C^{\perp}. Since the binary
image of a self-orthogonal Z2Z2[u]-linear code is also a self-orthogonal binary
linear code, we introduce quantum codes over Z2^{\alpha} x (Z2 + uZ2)^{\beta}.
Finally, we present some examples of self-dual cyclic and quantum codes that
have good parameters.
