  In this paper, we first propose two types of concepts of almost periodic
functions on the quantum time scale. Secondly, we study some basic properties
of almost periodic functions on the quantum time scale. Thirdly, based on
these, we study the existence and uniqueness of almost periodic solutions of
dynamic equations on the quantum time scale by Lyapunov method. Then, we give a
equivalent definition of almost periodic functions on the quantum time scale.
Finally, as an application, we propose a class of high-order Hopfield neural
networks on the quantum time scale and establish the existence of almost
periodic solutions of this class of neural networks.
