  It is known that for some languages quantum finite automata are more
efficient than classical counterparts. Particularly, a QFA recognizing the
language $MOD_p$ has an exponential advantage over the classical finite
automata. However, the construction of such QFA is probabilistic. In the
current work, we propose a deterministic construction of the QFA for the
language $MOD_p$. We construct a QFA for a promise problem $Palindrome_s$ and
implement this QFA on the IBMQ simulator using qiskit library tools.
