Modelling Microtubules in the Brain as n-qudit Quantum Hopfield Network and Beyond

This theoretical paper extends a prior quantum Hopfield neural network model of microtubules to n-dimensional quantum states (n-qudits), arguing that this higher-dimensional mathematical abstraction offers a more powerful framework for modeling consciousness. The authors review neurobiological evidence that the human brain's complexity—approximately 100 billion neurons forming a highly interconnected network—underpins a scientific approach to consciousness. They present Penrose-Hameroff Orch-OR Theory as a promising quantum theory of consciousness and build on Behrman et al.'s simplified model where tubulin dimers are represented as qubits. The proposed n-qudit extension, the authors contend, holds considerable promise for advancing mathematical abstraction in consciousness modeling.

Study at a glance

Abstract

The scientific approach to understand the nature of consciousness revolves around the study of human brain. Neurobiological studies that compare the nervous system of different species have accorded highest place to the humans on account of various factors that include a highly developed cortical area comprising of approximately 100 billion neurons, that are intrinsically connected to form a highly complex network. Quantum theories of consciousness are based on mathematical abstraction and Penrose-Hameroff Orch-OR Theory is one of the most promising ones. Inspired by Penrose-Hameroff Orch-OR Theory, Behrman et. al. (Behrman, 2006) have simulated a quantum Hopfield neural network with the structure of a microtubule. They have used an extremely simplified model of the tubulin dimers with each dimer represented simply as a qubit, a single quantum two-state system. The extension of this model to n-dimensional quantum states, or n-qudits presented in this work holds considerable promise for even higher mathematical abstraction in modelling consciousness systems.