Quantum Finite Automata and Quiver Algebras
This work offers a theoretical bridge between quantum computing and deep learning, though it appears incremental as it builds on prior algebraic results.
The authors applied algebraic concepts from near-rings and quivers to reformulate quantum finite automata with multiple-time measurements, providing a unified framework for quantum computing and deep learning, and enabling optimization via gradient descent on a moduli space.
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.