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Cost-efficient QFA Algorithm for Quantum Computers
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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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Cited by 1 Pith paper
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Shallow Implementation of Quantum Fingerprinting with Application to Quantum Finite Automata
A proposed shallow quantum-fingerprinting circuit based on generalized arithmetic progressions has a core theorem that is vacuous in the bounded-error regime, leaving only heuristic numerical support.
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