Quantum finite automaton

In quantum computing, quantum finite automata (QFA) or quantum state machines are a quantum analog of probabilistic automata or a Markov decision process. They are related to quantum computers in a similar fashion as finite automata are related to Turing machines. Several types of automata may be defined, including measure-once and measure-many automata. Quantum finite automata can also be understood as the quantization of subshifts of finite type, or as a quantization of Markov chains. QFAs are, in turn, special cases of geometric finite automata or topological finite automata.

The automata work by accepting a finite-length string ${\displaystyle \sigma =(\sigma _{0},\sigma _{1},\cdots ,\sigma _{k})}$ of letters ${\displaystyle \sigma _{i}}$ from a finite alphabet ${\displaystyle \Sigma }$, and assigning to each such string a probability ${\displaystyle \operatorname {Pr} (\sigma )}$ indicating the probability of the automaton being in an accept state; that is, indicating whether the automaton accepted or rejected the string.

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