  In this research we present a quantum circuit for estimating algorithmic
complexity using the coding theorem method. This accelerates inferring
algorithmic structure in data for discovering causal generative models. The
computation model is restricted in time and space resources to make it
computable in approximating the target metrics. The quantum circuit design
based on our earlier work that allows executing a superposition of automata is
presented. As a use-case, an application framework for protein-protein
interaction ontology based on algorithmic complexity is proposed. Using
small-scale quantum computers, this has the potential to enhance the results of
classical block decomposition method towards bridging the causal gap in entropy
based methods.

Quantum Physics;Computational Complexity;Emerging Technologies;Formal Languages and Automata Theory;Quantitative Methods