Deterministic Construction of QFAs based on the Quantum Fingerprinting Technique

Abstract

It is known that for some languages quantum finite automata are more efficient than classical counterparts. Particularly, a QFA recognizing the language $MO{D}_p$ 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 $MO{D}_p$. We construct a QFA for a promise problem $Palindrom{e}_s$ and implement this QFA on the IBMQ simulator using qiskit library tools.