  To address Quantum Artificial Neural Networks as quantum dynamical computing
systems, a formalization of quantum artificial neural networks as dynamical
systems is developed, expanding the concept of unitary map to the neural
computation setting and introducing a quantum computing field theory on the
network. The formalism is illustrated in a simulation of a quantum recurrent
neural network and the resulting field dynamics is researched upon, showing
emergent neural waves with excitation and relaxation cycles at the level of the
quantum neural activity field, as well as edge of chaos signatures, with the
local neurons operating as far-from-equilibrium open quantum systems,
exhibiting entropy fluctuations with complex dynamics including complex
quasiperiodic patterns and power law signatures. The implications for quantum
computer science, quantum complexity research, quantum technologies and
neuroscience are also addressed.
