One-way finite automata with quantum and classical states

Abstract

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 \cite{AJ}. First, we prove that {\it one-way probabilistic finite automata} (1PFA) \cite{AP} and {\it one-way quantum finite automata with control language} (1QFACL) \cite{ACB} 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 ${\epsilon }_1>0$, there exists a language $L_m$ that cannot be recognized by any {\it measure-many one-way quantum finite automata} (MM-1QFA) \cite{Kon97} with bounded error $7/9+{\epsilon }_1$, and any 1PFA recognizing it has at last $m$ states, but $L_m$ can be recognized by a 1QCFA for any error bound $\epsilon >0$ with $\mathbf{O}(\log \mathbf{m})$ quantum states and 12 classical states.

Comments are welcome. The paper is for a volume of LNCS Festschifts Series devoted to birthday of Prof. Dr. Juergen Dassov

References in corpus (2)

• Unbounded-error quantum computation with small space bounds
• Exponentially more concise quantum recognition of non-RMM regular languages

Cited by in corpus (3)

• Potential of quantum finite automata with exact acceptance
• State succinctness of two-way finite automata with quantum and classical states
• Time-space tradeoffs for two-way finite automata