Quantum Finite Automata and Quiver Algebras

TL;DR

This paper explores the application of algebraic structures, specifically near-rings derived from quivers, to quantum finite automata, enabling a unified framework for quantum computing and deep learning with optimizable moduli spaces.

Contribution

It introduces a novel algebraic reformulation of quantum finite automata using near-rings from quivers, connecting quantum computing with deep learning optimization techniques.

Findings

Reformulation of quantum finite automata with near-rings

Development of a moduli space of automata with metric

Potential for gradient descent optimization in quantum models

Abstract

We find an application in quantum finite automata for the ideas and results of [JL21] and [JL22]. We reformulate quantum finite automata with multiple-time measurements using the algebraic notion of near-ring. This gives a unified understanding towards quantum computing and deep learning. When the near-ring comes from a quiver, we have a nice moduli space of computing machines with metric that can be optimized by gradient descent.