A Framework for Quantum Finite-State Languages with Density Mapping

TL;DR

This paper introduces a new framework for constructing quantum finite-state automata (QFAs) that simplifies their design and enhances simulation accuracy, especially on noisy quantum hardware, by providing foundational automata and conversion methods.

Contribution

The framework offers predefined constructions for basic QFAs recognizing MOD and EQU languages and improves their simulation on noisy quantum computers.

Findings

Framework enables easy construction of QFAs from basic automata.

Conversion methods improve simulation accuracy on noisy quantum hardware.

Provides tools for building complex QFAs from foundational automata.

Abstract

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.