Neural Controlled Differential Equations with Quantum Hidden Evolutions

We introduce a class of neural controlled differential equation inspired by quantum mechanics. Neural quantum controlled differential equations (NQDEs) model the dynamics by analogue of the Schr\"{o}dinger equation. Specifically, the hidden state represents the wave function, and its collapse leads to an interpretation of the classification probability. We implement and compare the results of four variants of NQDEs on a toy spiral classification problem.