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**Modelling microtubules in the brain as n-qudit quantum Hopfield network and beyond**

The scientific approach to understand the nature of consciousness revolves around the study of the human brain. Neurobiological studies that compare the nervous system of different species have accorded the highest place to 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.

https://goo.gl/LzmyGB

The scientific approach to understand the nature of consciousness revolves around the study of the human brain. Neurobiological studies that compare the nervous system of different species have accorded the highest place to 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 the Penrose–Hameroff Orch-OR theory is one of the most promising ones.

Inspired by the Penrose–Hameroff Orch-OR theory, Behrman et al. 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.

Thanks for reading Spread the word around and do let me know your thoughts on this

#DEIQntmNanoCntr

#QuantumHopfieldnetwork

#qudits

#contextuality

#powerlaws

#science

#physics

#quantumtheory

#quantumphysics

#quantummechanics

#advancedquantummechanics

#quantumHopfieldnetworks

#graphtheoreticquantumsystemmodelling

#HamiltonianLyapunovenergyfunction

#hierarchicalclustering

#QuantumHopfieldnetwork

#qudits

#contextuality

#powerlaws

http://www.tandfonline.com/doi/full/10.1080/03081079.2015.1076405

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**Graph-theoretic quantum system modelling for neuronal microtubules as hierarchical clustered quantum Hopfield networks**

The paper presents an insight, otherwise difficult to gain, for the complex system of systems represented by clustered quantum Hopfield network, hQHN, through the application of GTQSM construct.

https://goo.gl/cbt7Ke

Graph-theoretic quantum system modelling (GTQSM) is facilitated by considering the fundamental unit of quantum computation and information 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 of information, or computation data, while complementary fundamental quantum through, or flow rate, variables specify probability parameters, or amplitudes, as surrogates for scalar quantum information measure (von Neumann entropy).

This paper applies GTQSM in continuum of protein heterodimer tubulin molecules of self-assembling polymers, viz. microtubules in the brain as a holistic system of interacting components representing hierarchical clustered quantum Hopfield network, hQHN, of networks. The quantum input/output ports of the constituent elemental interaction components, or processes, of tunnelling interactions and Coulombic bidirectional interactions are in cascade and parallel interconnections with each other, while the classical output ports of all elemental components are interconnected in parallel to accumulate micro-energy functions generated in the system as Hamiltonian, or Lyapunov, energy function.

The paper presents an insight, otherwise difficult to gain, for the complex system of systems represented by clustered quantum Hopfield network, hQHN, through the application of GTQSM construct.

Thanks for reading Spread the word around and do let me know your thoughts on this

#DEIQntmNanoCntr

#QuantumHopfieldnetwork

#qudits

#contextuality

#powerlaws

#science

#physics

#quantumtheory

#quantumphysics

#quantummechanics

#advancedquantummechanics

#quantumHopfieldnetworks

#graphtheoreticquantumsystemmodelling

#HamiltonianLyapunovenergyfunction

#hierarchicalclustering

#QuantumHopfieldnetwork

#qudits

#contextuality

#powerlaws

http://www.tandfonline.com/doi/full/10.1080/03081079.2014.893298

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**Graph-theoretic quantum system modelling for information/computation processing circuits**

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.

https://goo.gl/UBbv5z

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.

Thanks for reading Spread the word around and do let me know your thoughts on this

#DEIQntmNanoCntr

#QuantumHopfieldnetwork

#qudits

#contextuality

#powerlaws

#science

#physics

#quantumtheory

#quantumphysics

#quantummechanics

#advancedquantummechanics

#quantumHopfieldnetworks

#graphtheoreticquantumsystemmodelling

#HamiltonianLyapunovenergyfunction

#hierarchicalclustering

#QuantumHopfieldnetwork

#qudits

#contextuality

#powerlaws

http://www.tandfonline.com/doi/abs/10.1080/03081079.2011.602016

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**Modelling microtubules in the brain as n-qudit quantum Hopfield network and beyond**

The scientific approach to understand the nature of consciousness revolves around the study of the human brain. Neurobiological studies that compare the nervous system of different species have accorded the highest place to 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.

https://goo.gl/LzmyGB

The scientific approach to understand the nature of consciousness revolves around the study of the human brain. Neurobiological studies that compare the nervous system of different species have accorded the highest place to 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 the Penrose–Hameroff Orch-OR theory is one of the most promising ones.

Inspired by the Penrose–Hameroff Orch-OR theory, Behrman et al. 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.

Thanks for reading Spread the word around and do let me know your thoughts on this

#DEIQntmNanoCntr

#QuantumHopfieldnetwork

#qudits

#contextuality

#powerlaws

#science

#physics

#quantumtheory

#quantumphysics

#quantummechanics

#advancedquantummechanics

#quantumHopfieldnetworks

#graphtheoreticquantumsystemmodelling

#HamiltonianLyapunovenergyfunction

#hierarchicalclustering

#QuantumHopfieldnetwork

#qudits

#contextuality

#powerlaws

http://www.tandfonline.com/doi/full/10.1080/03081079.2015.1076405

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**Graph-theoretic quantum system modelling for neuronal microtubules as hierarchical clustered quantum Hopfield networks**

The paper presents an insight, otherwise difficult to gain, for the complex system of systems represented by clustered quantum Hopfield network, hQHN, through the application of GTQSM construct.

https://goo.gl/cbt7Ke

Graph-theoretic quantum system modelling (GTQSM) is facilitated by considering the fundamental unit of quantum computation and information 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 of information, or computation data, while complementary fundamental quantum through, or flow rate, variables specify probability parameters, or amplitudes, as surrogates for scalar quantum information measure (von Neumann entropy).

This paper applies GTQSM in continuum of protein heterodimer tubulin molecules of self-assembling polymers, viz. microtubules in the brain as a holistic system of interacting components representing hierarchical clustered quantum Hopfield network, hQHN, of networks. The quantum input/output ports of the constituent elemental interaction components, or processes, of tunnelling interactions and Coulombic bidirectional interactions are in cascade and parallel interconnections with each other, while the classical output ports of all elemental components are interconnected in parallel to accumulate micro-energy functions generated in the system as Hamiltonian, or Lyapunov, energy function.

The paper presents an insight, otherwise difficult to gain, for the complex system of systems represented by clustered quantum Hopfield network, hQHN, through the application of GTQSM construct.

Thanks for reading Spread the word around and do let me know your thoughts on this

#DEIQntmNanoCntr

#QuantumHopfieldnetwork

#qudits

#contextuality

#powerlaws

#science

#physics

#quantumtheory

#quantumphysics

#quantummechanics

#advancedquantummechanics

#quantumHopfieldnetworks

#graphtheoreticquantumsystemmodelling

#HamiltonianLyapunovenergyfunction

#hierarchicalclustering

#QuantumHopfieldnetwork

#qudits

#contextuality

#powerlaws

http://www.tandfonline.com/doi/full/10.1080/03081079.2014.893298

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