  Homological mirror symmetry is a conjecture that a category constructed in
the A-model and a category constructed in the B-model are equivalent in some
sense. We construct a cyclic differential graded (DG) category of holomorphic
vector bundles on noncommutative two-tori as a category in the B-model side. We
define the corresponding Fukaya's category in the A-model side, and prove the
equivalence of the two categories at the level of cyclic categories. We further
write down explicitly Feynman rules for higher Massey products derived from the
cyclic DG category. As a background of these arguments, a physical explanation
of the mirror symmetry for noncommutative two-tori is also given.
