Experimental demonstration of quantum finite automaton

In quantum information science, a major task is to find the quantum models that can outperform their classical counterparts. Automaton is a fundamental computing model that has wide applications in many fields. It has been shown that the quantum version of automaton can solve certain problem using a much smaller state space compared to the classical automaton. Here we report an experimental demonstration of an optical quantum automaton, which is used to solve the promise problems of determining whether the length of an input string can be divided by a prime number P with no remainder or with a remainder of R. Our quantum automaton can solve such problem using a state space with only three orthonormal states, whereas the classical automaton needs no less than P states. Our results demonstrate the quantum benefits of a quantum automaton over its classical counterpart and paves the way for implementing quantum automaton for more complicated and practical applications.