Cost-efficient QFA Algorithm for Quantum Computers

• URL: http://arxiv.org/abs/2107.02262v2
• Date: Mon, 12 Dec 2022 13:26:56 GMT
• Title: Cost-efficient QFA Algorithm for Quantum Computers
• Authors: \"Ozlem Salehi, Abuzer Yakary{\i}lmaz
• Abstract summary: We present a modified Moore-Crutchfield quantum finite automaton (MCQFA) algorithm for the language $mathttMOD_p$. We obtain shorter quantum programs using fewer basis gates compared to the implementation of the original algorithm given in the literature.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The study of quantum finite automata (QFAs) is one of the possible approaches in exploring quantum computers with finite memory. Despite being one of the most restricted models, Moore-Crutchfield quantum finite automaton (MCQFA) is proven to be exponentially more succinct than classical finite automata models in recognizing certain languages such as $\mathtt{MOD}_p = \{ a^{j} \mid j \equiv 0 \mod p\}$, where $p$ is a prime number. In this paper, we present a modified MCQFA algorithm for the language $\mathtt{MOD}_p$, the operators of which are selected based on the basis gates on the available real quantum computers. As a consequence, we obtain shorter quantum programs using fewer basis gates compared to the implementation of the original algorithm given in the literature.

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