Hierarchical quantum circuit model of microtubule for the Orch-OR theory

The Orch-OR theory has been proposed as a framework for explaining consciousness based on quantum-gravitational effects in microtubules. To further support and examine this theory, a more concrete quantum circuit model is required, one that can be theoretically analyzed and experimentally tested in comparison with biological observations. In this work, we propose a hierarchical quantum circuit model that incorporates an orchestration mechanism across three structural levels: the tubulin dimer, the helical pathway, and the microtubule as a whole. The proposed model describes how a higher-level OR unit may emerge through the orchestration of lower-level OR units. We analyze the ratio of OR oscillation frequencies between the tubulin dimer and the entire microtubule and show that the predicted ratio is in close agreement with reported biological experimental data. These results suggest that microtubules may be described by a hierarchical quantum circuit model within the framework of the Orch-OR theory.