  We design Latvian quantum finite state automata (LQFAs for short) recognizing
unary regular languages with isolated cut point 1/2. From an architectural
point of view, we combine two LQFAs recognizing with isolated cut point,
respectively, the finite part and the ultimately periodic part of any given
unary regular language L. In both modules, we use a component addressed in the
literature and here suitably adapted to the unary case, to discriminate strings
on the basis of their length. The number of basis states and the isolation
around the cut point of the resulting LQFA for L exponentially depends on the
size of the minimal deterministic finite state automaton for L.
