© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

npj Quantum Information

Experimental demonstration of quantum finite automaton

Yuling Tian, Tianfeng Feng, Maolin Luo, Shenggen Zheng, Xiaoqi Zhou

Published Jun 11, 2019• 19 citations

Abstract

Abstract 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.

DOI: 10.1038/s41534-019-0163-x

Related papers

Chapter 8 Quantum computing in automata theory

G. Ignisha Rajathi, R. Vedhapriyavadhana, R. Niranjana +2 more

In the contemporary era we dwell in, every now and then, new technologies are developed by master brains such as researchers and scientists. This also paves the way to discover replacements to classical computers. One such progression among the great inventions is the essence of quantum computing. They are brought to light for the purpose of solving problems and scenarios solved by classical computers but in a more effective way and in the least span of time. The study of quantum computing focuses on finding new ways to compute by using quantum physics phenomena. A qubit, in contrast to a typical computer bit, can be either 0 or 1, or it can be a superposition of both 0 and 1. Quantum theory commemorates with automata theory, thereby formulating quantum finite automata. Quantum finite automaton, or basically a deterministic finite automaton, is one of the simplest models of computation, which is an input-driven model, which takes an input, and according to the input, we just read the machine, and it changes its state. This proves that any quantum finite automata are completely capable of recognizing languages like Tally with given cut point too. Such languages recognized by a cut point, by quantum finite automata, are called stochastic languages. It further collaborates with the chemical industry with its qubit power over molecular collide, interactive models, and collaborative string processing using nonregular languages.

De Gruyter eBooks•Aug 7, 2023•2 citations

Quantum Finite Automaton Using Ternary Rotation Quantum Gates and Chrestenson Family Quantum Gates

Yuchen Huang, Marek A. Perkowski, Xiaoyu Song B +1 more

Abstract Quantum automata can solve certain problems with a smaller state space than classical automata. We developed a quantum finite automaton using ternary rotation quantum gates and the Chrestenson family of ternary quantum gates. The main idea of this paper is to show how to combine rotation ternary quantum circuit-based Quantum Finite Automaton and quantum reversible circuit-based Deterministic Finite Automaton to build a more powerful machine. The combined machine can enable more complex language and pattern recognition. The developed quantum finite automaton and resulting combined machine can be used for robotics applications such as language, gesture, and motion recognition.

Quantum Information and Computation•Feb 20, 2025•1 citation

State-efficient QFA Algorithm for Quantum Computers.

Özlem Salehi, Abuzer Yakaryılmaz

The study of quantum finite automata (QFA's) is one of the possible approaches in exploring quantum computers with finite memory. Despite being one of the most restricted models, Moore-Crutchfield quantum finite automaton (MCQFA) is proven to be exponentially more succinct than classical finite automata models in recognizing certain languages such as $\mathtt{MOD}_{\rm p} = \{a^{j}~ |~ j \equiv 0 \mod p\}$, where $p$ is a prime number. In this paper, we present a modified MCQFA algorithm for the language $\mathtt{MOD}_{\rm p}$, the operators of which are selected based on the basis gates on the available real quantum computers. As a consequence, we obtain shorter quantum programs using less basis gates compared to the implementation of the original algorithm given in the literature.

•Jul 5, 2021•1 citation

A small 1-way quantum finite automaton

Arnolds Ķikusts

We study 1-way quantum finite automata (QFAs) and compare them with their classical counterparts. We show that 1-way QFAs can be very space efficient. We construct a 1-way QFAs that are quadratically smaller than any equivalent deterministic finite automata and give the correct answer with a large probability by recognizing the languages in a two letter alphabet "the number of the letters a and the number of the letters b are divisible by n".

arXiv:quant-ph/9810065•Oct 22, 1998•8 citations

1-way quantum finite automata: strengths, weaknesses and generalizations

Andris Ambainis, Rūsiņš Freivalds

We study 1-way quantum finite automata (QFAs). First, we compare them with their classical counterparts. We show that, if an automaton is required to give the correct answer with a large probability (greater than 7/9), then any 1-way QFAs can be simulated by a 1-way reversible automaton. However, quantum automata giving the correct answer with smaller probabilities are more powerful than reversible automata. Second, we show that 1-way QFAs can be very space-efficient. We construct a 1-way QFA that is exponentially smaller than any equivalent classical (even randomized) finite automaton. We think that this construction may be useful for design of other space-efficient quantum algorithms. Third, we consider several generalizations of 1-way QFAs. Here, our goal is to find a model which is more powerful than 1-way QFAs keeping the quantum part as simple as possible.

arXiv:quant-ph/9802062•Annual Symposium on Foundations of Computer Science•Nov 27, 2002•220 citations

Experimental Demonstration Advantage of Photonic Finite Automata

Yuanyuan Zhao, Keren Li, Chao Li +2 more

Finite automata have abundant applications such as finding reachability and so on. This work presents the first experimental implementation of the two-way quantum finite automaton with the optical platform and demonstrates its potential quantum advantages.

Asia Communications and Photonics Conference•Nov 4, 2023•4 citations

Abstract 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.

In the contemporary era we dwell in, every now and then, new technologies are developed by master brains such as researchers and scientists. This also paves the way to discover replacements to classical computers. One such progression among the great inventions is the essence of quantum computing. They are brought to light for the purpose of solving problems and scenarios solved by classical computers but in a more effective way and in the least span of time. The study of quantum computing focuses on finding new ways to compute by using quantum physics phenomena. A qubit, in contrast to a typical computer bit, can be either 0 or 1, or it can be a superposition of both 0 and 1. Quantum theory commemorates with automata theory, thereby formulating quantum finite automata. Quantum finite automaton, or basically a deterministic finite automaton, is one of the simplest models of computation, which is an input-driven model, which takes an input, and according to the input, we just read the machine, and it changes its state. This proves that any quantum finite automata are completely capable of recognizing languages like Tally with given cut point too. Such languages recognized by a cut point, by quantum finite automata, are called stochastic languages. It further collaborates with the chemical industry with its qubit power over molecular collide, interactive models, and collaborative string processing using nonregular languages.

Abstract Quantum automata can solve certain problems with a smaller state space than classical automata. We developed a quantum finite automaton using ternary rotation quantum gates and the Chrestenson family of ternary quantum gates. The main idea of this paper is to show how to combine rotation ternary quantum circuit-based Quantum Finite Automaton and quantum reversible circuit-based Deterministic Finite Automaton to build a more powerful machine. The combined machine can enable more complex language and pattern recognition. The developed quantum finite automaton and resulting combined machine can be used for robotics applications such as language, gesture, and motion recognition.

The study of quantum finite automata (QFA's) is one of the possible approaches in exploring quantum computers with finite memory. Despite being one of the most restricted models, Moore-Crutchfield quantum finite automaton (MCQFA) is proven to be exponentially more succinct than classical finite automata models in recognizing certain languages such as

\mathtt{MOD}_{\rm p} = \{a^{j}~ |~ j \equiv 0 \mod p\}

, where

p

is a prime number. In this paper, we present a modified MCQFA algorithm for the language

\mathtt{MOD}_{\rm p}

, the operators of which are selected based on the basis gates on the available real quantum computers. As a consequence, we obtain shorter quantum programs using less basis gates compared to the implementation of the original algorithm given in the literature.

We study 1-way quantum finite automata (QFAs). First, we compare them with their classical counterparts. We show that, if an automaton is required to give the correct answer with a large probability (greater than 7/9), then any 1-way QFAs can be simulated by a 1-way reversible automaton. However, quantum automata giving the correct answer with smaller probabilities are more powerful than reversible automata. Second, we show that 1-way QFAs can be very space-efficient. We construct a 1-way QFA that is exponentially smaller than any equivalent classical (even randomized) finite automaton. We think that this construction may be useful for design of other space-efficient quantum algorithms. Third, we consider several generalizations of 1-way QFAs. Here, our goal is to find a model which is more powerful than 1-way QFAs keeping the quantum part as simple as possible.