Leveraging Quantum Superposition to Infer the Dynamic Behavior of a Spatial-Temporal Neural Network Signaling Model

The exploration of new problem classes for quantum computation is an active area of research. In this paper, we introduce and solve a novel problem class related to dynamics on large-scale networks relevant to neurobiology and machine learning. Specifically, we ask if a network can sustain inherent dynamic activity beyond some arbitrary observation time or if the activity ceases through quiescence or saturation via an epileptic-like state. We show that this class of problems can be formulated and structured to take advantage of quantum superposition and solved efficiently using a coupled workflow between the Grover and Deutsch-Jozsa quantum algorithms. To do so, we extend their functionality to address the unique requirements of how input (sub)sets into the algorithms must be mathematically structured while simultaneously constructing the inputs so that measurement outputs can be interpreted as meaningful properties of the network dynamics. This, in turn, allows us to answer the question we pose.