Two-way finite automata with quantum and classical states

TL;DR

This paper introduces 2-way finite automata with quantum and classical states (2qcfa's), demonstrating their ability to recognize certain languages more efficiently than classical automata, including palindromes and balanced strings.

Contribution

The paper presents a new automaton model combining quantum and classical states, capable of recognizing languages beyond classical automata with improved efficiency.

Findings

2qcfa's can recognize palindromes, which classical 2-way automata cannot.

2qcfa's recognize {a^n b^n} in polynomial time, faster than classical probabilistic automata.

The model is simpler to implement than unrestricted 2qfa's.

Abstract

We introduce 2-way finite automata with quantum and classical states (2qcfa's). This is a variant on the 2-way quantum finite automata (2qfa) model which may be simpler to implement than unrestricted 2qfa's; the internal state of a 2qcfa may include a quantum part that may be in a (mixed) quantum state, but the tape head position is required to be classical. We show two languages for which 2qcfa's are better than classical 2-way automata. First, 2qcfa's can recognize palindromes, a language that cannot be recognized by 2-way deterministic or probabilistic finite automata. Second, in polynomial time 2qcfa's can recognize {a^n b^n | n>=0}, a language that can be recognized classically by a 2-way probabilistic automaton but only in exponential time.