![]() We will first introduce some background knowledge about FA and QFA. 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. ![]() Quantum information science is a research field focused on enhancing problem-solving efficiency by utilizing quantum effects.
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