![]() ![]() In our experiment, we have proven that a QFA composed with a three-dimensional quantum state suffice to solve a promise problem whereas a classical FA needs much larger state space to solve the same problem. In this letter, we have built a proof-of-principle optical QFA that can solve some certain problems more space-efficiently than a classical FA. ![]() 21, 22 However, to the best of our knowledge, no experiment has been performed to prove the quantum benefits of QFA yet. ![]() 20 It has been theoretically predicted that QFA can solve certain problems more efficiently than its classical counterpart. 17, 18 The concept of quantum finite automaton (QFA) was invented as the quantum version of FA by Kondacs and Watrous 19 and also by Moore and Crutchfield. As one of the most fundamental models in computer science, FA can be used to model problems in many fields, including mathematics, artificial intelligence, games or linguistics. Finite automaton (FA) is another good example. 12, 13, 14, 15, 16Ĭomputer is not the only device whose capability can be boosted by introducing quantum elements. 5, 6, 7, 8, 9, 10, 11 A series of quantum algorithms have been demonstrated on these prototype machines to show the quantum benefits in tackling particular problems. ![]() 2, 3, 4 Extensive efforts have been made to build such computing machine and small-scale quantum computers have already been constructed in different physical systems. The most prominent example is quantum computer-by changing the basic elements of a computer from bits and logic gates to quantum bits and quantum logic gates, quantum computer can achieve an exponential speedup in solving certain problems, including factoring 1 and simulation of complex systems. Transitions − The machine moves from one state to another and is indicated as transition.Quantum information science is a research field focused on enhancing problem-solving efficiency by utilizing quantum effects. Accepting states are usually drawn as a double circle as shown below − Initial states are usually drawn with an arrow pointed to state, as shown below −įinal state − It is a subset of known states that indicates whether the input we processed is valid or not. Initial State − It is the starting point of our system. State − The states are usually drawn with circles and only one state can be active at a time. The components which exists in a finite state machine are explained below − Output Function P(S): This function specifies the output.Next-state function T(S, I): This is used for mapping each current state and input to the next state.These two types are equivalent in capabilities.Ī Finite State Machine consists of the following − Mealy machine − In Mealy machine, the output depends on both the current state and the current input.Moore machine − In Moore machine, the output only depends on the current state.The two types of finite state machines are − The output function generates a set of outputs from the current state and the inputs. The diagram given below explains the functioning of a finite state machine in TOC. The next state function is a combinational logic function that, given the inputs and the current state, determines the next state of the system.If there are n bits of storage, there are 2n possible states. The set of states correspond to all the possible combinations of the internal storage.A finite state machine has a set of states and two functions called the next-state and output function. ![]()
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