Deterministic Construction of QFAs based on the Quantum Fingerprinting Technique

TL;DR

This paper presents a deterministic method for constructing quantum finite automata (QFAs) that recognize specific languages more efficiently than classical automata, demonstrated through implementation on IBMQ.

Contribution

It introduces a deterministic construction technique for QFAs recognizing the language MOD_p, improving upon previous probabilistic methods.

Findings

Deterministic QFA construction for MOD_p demonstrated

Implementation on IBMQ simulator validates the approach

QFAs show exponential advantage over classical automata

Abstract

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.