Unitary Maps and Quantum Artificial Neural Networks

Abstract

Unitary quantum maps provide a bridge between classical and quantum dynamical systems theories, having been applied within the context of quantum chaos research. When applied to quantum artificial neural networks, as models of networked quantum computation, unitary quantum maps allow one to address these networks as quantum networked dynamical systems. In this chapter, we address the application of these maps to quantum artificial neural networks, specifically studying the simulation and implementation of these maps for quantum recurrent neural networks, simulating these networks as dynamical computational systems and researching the topological properties of the series of neural firing operators’ quantum averages for nonstationary network states. We also research the results of a simulation of one of these networks on a quantum computer by cloud-based access to IBM Q Experience resources. The results show the emergence of complex dynamics, fitting into similar classes as those of classical cellular automata and coupled maps, including topological markers of chaos, edge of chaos and fractal attractors in the sequences of quantum averages. The implications for quantum complexity research, quantum chaos theory and quantum computing are addressed.