A quantum finite-state automaton (QFA) is a theoretical model designed to simulate the evolution of a quantum system with finite memory in response to sequential input strings. We define the language of a QFA as the set of strings that lead the QFA to an accepting state when processed from its initial state. QFAs exemplify how quantum computing can achieve greater efficiency compared to classical computing. While being one of the simplest quantum models, QFAs are still notably challenging to construct from scratch due to the preliminary knowledge of quantum mechanics required for superimposing unitary constraints on the automata. Furthermore, even when QFAs are correctly assembled, the limitations of a current quantum computer may cause fluctuations in the simulation results depending on how an assembled QFA is translated into a quantum circuit. We present a framework that provides a simple and intuitive way to build QFAs and maximize the simulation accuracy. Our framework relies on two methods: First, it offers a predefined construction for foundational types of QFAs that recognize special languages MOD and EQU. They play a role of basic building blocks for more complex QFAs. In other words, one can obtain more complex QFAs from these foundational automata using standard language operations. Second, we improve the simulation accuracy by converting these QFAs into quantum circuits such that the resulting circuits perform well on noisy quantum computers. Our framework is available at https://github.com/sybaik1/qfa-toolkit.

我们提供了一个简单直观的框架，用于构建量子有限状态自动机（QFA）并最大程度地提高模拟准确性。该框架依赖于两种方法：一是为基本类型的QFA提供预定义的构建，可以使用标准语言操作从这些基础自动机获取更复杂的QFA；二是将这些QFA转化为能在嘈杂的量子计算机上表现良好的量子电路，从而提高模拟准确性。

量子有限状态语言的密度映射框架