2011/12/09 by Shenggen Zheng, Zheng, Shenggen, Daowen Qiu +5 · 2 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Machine Learning and Algorithms #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #quant-ph #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1112.2022
Comments are welcome. The paper is for a volume of LNCS Festschifts Series devoted to birthday of Prof. Dr. Juergen Dassov
arxiv created 2011/12/09 · openalex publication_date 2011/12/09 · arxiv updated 2011/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we introduce and explore a new model of \it quantum finite automata (QFA). Namely, \it one-way finite automata with quantum and classical states (1QCFA), a one way version of \it two-way finite automata with quantum and classical states (2QCFA) introduced by Ambainis and Watrous in 2002 \citeAJ. First, we prove that \it one-way probabilistic finite automata (1PFA) \citeAP and \it one-way quantum finite automata with control language (1QFACL) \citeACB as well as several other models of QFA, can be simulated by 1QCFA. Afterwards, we explore several closure properties for the family of languages accepted by 1QCFA. Finally, the state complexity of 1QCFA is explored and the main succinctness result is derived. Namely, for any prime m and any ε1>0, there exists a language Lm that cannot be recognized by any \it measure-many one-way quantum finite automata (MM-1QFA) \citeKon97 with bounded error 7/9+ε1, and any 1PFA recognizing it has at last m states, but Lm can be recognized by a 1QCFA for any error bound ε>0 with \bfO(logm) quantum states and 12 classical states.