  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.
