Surface code model for Fibonacci helical pathways of the Orch OR microtubule

The Objective Reduction (OR) theory suggested by Sir Roger Penrose presented a novel perspective on the measurement problem of quantum mechanics and consciousness. Subsequently, based on the assertion of anesthesiologist Dr. Hameroff, the theory proposed that the phenomenon of OR could also manifest in microtubules within neurons. This would, serve as the trigger for consciousness, thereby forming the basis of Orchestrated OR (Orch OR). The peculiarity of this theory lies in the claim that tubulin and its higher neuronal information structures are not simply additive, rather, they are formed in a topological manner. Specifically, higher information structure of tubulin, helical pathways are presumed to form an intersecting pattern in both left-handed and right-handed directions, following a repeating Fibonacci series (3, 5, 8, 13, …), and are interconnected with each other. There have been attempts to examine these unique characteristics. However, experimenting upon these quantum characteristics in the microtubule appears to be plagued by certain limitations. Therefore, this study proposed a surface code model to implement this biological model on a quantum computer, focusing on its quantum properties. To the best of our knowledge, this is the first study to attempt this. The study emphasizes that interpreting asymmetric Fibonacci helical pathways as logical qubits can stabilize surface code. In addition, we analyzed the conditions required for experimenting with this model based on the development of current quantum computer. Although the experimental feasibility of this study is dependents on future quantum computer development, it provides significant insights into Orch OR research by offering a novel perspective.