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This paper introduces graph-theoretic quantum system modelling (GTQSM), which is facilitated by considering the fundamental unit of quantum computation and information, viz. a quantum bit or qubit as a basic building block. Unit directional vectors 'ket 0' and 'ket 1' constitute two distinct fundamental quantum across variable orthonormal basis vectors (for the Hilbert space) specifying the direction of propagation, as it were, of information (or computation data) while complementary fundamental quantum through (flow rate) variables specify probability parameters (or amplitudes) as surrogates for scalar quantum information measure (von Neumann entropy). Applications of GTQSM are presented for quantum information/computation processing circuits ranging from a simple qubit and superposition or product of two qubits through controlled NOT and Hadamard gate operations to a substantive case of 3-port, 5-stage circuit for quantum teleportation. An illustrative circuit for teleporting a qubit is modelled as a complex 'system of systems' resulting in four probable transfer function models. It has the potential of extending the applications of GTQSM further to systems at the higher end of complexity scale too. The key contribution of this paper lies in generalization or extension of the graph-theoretic system modelling framework, hitherto used for classical (mostly deterministic) systems, to quantum random systems. Further extension of the graph-theoretic system modelling framework to quantum field modelling is the subject of future work.

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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.