Concept

Quantum finite automaton

Summary
In quantum computing, quantum finite automata (QFA) or quantum state machines are a quantum analog of probabilistic automata or a Markov decision process. They provide a mathematical abstraction of real-world quantum computers. 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 receiving a finite-length string \sigma=(\sigma_0,\sigma_1,\cdots,\sigma_k) of letters \sigma_i from a finite alphabet \Sigma, and assigning to each such string a probability \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. The languages accepted by QF
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