Today I read a paper titled “1-way quantum finite automata: strengths, weaknesses and generalizations”

The abstract is:

*We study 1-way quantum finite automata (QFAs).*

*First, we compare them with their classical counterparts.*

*We show that, if an automaton is required to give the correct answer with a large probability (over 0.98), then the power of 1-way QFAs is equal to the power of 1-way reversible automata.*

*However, quantum automata giving the correct answer with smaller probabilities are more powerful than reversible automata.*

*Second, we show that 1-way QFAs can be very space-efficient.*

*Namely, we construct a 1-way QFA which is exponentially smaller than any equivalent classical (even randomized) finite automaton.*

*This construction may be useful for design of other space-efficient quantum algorithms.*

*Third, we consider several generalizations of 1-way QFAs.*

*Here, our goal is to find a model which is more powerful than 1-way QFAs keeping the quantum part as simple as possible..*