# Quantum Neurobiology

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## Abstract

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## 1. Introduction

^{−9}to 10

^{−15}), namely atoms at the nanometer scale (10

^{−9}), ions and photons at the picometer scale (10

^{−12}), and sub-atomic particles at the femtometer scale (10

^{−15}).

#### 1.1. The Human Brain

#### 1.2. Quantum Neurobiology

## 2. Waves, Protein Folding, and Genomics

#### 2.1. Wavefunctions: EEG, fMRI, CT, PET Integration

#### 2.2. Quantum EEG

#### 2.3. Quantum MRI (Radiology)

#### 2.4. Quantum Protein Folding

#### 2.5. Quantum Genomics

## 3. Neural Dynamics

#### 3.1. Superpositioned Data and Quantum Probability

#### 3.2. Neural Field Theories

#### 3.3. Neurofilamentary Dynamics

^{−6}), which then serves as an input to the ion channel transmission that proceeds on the order of milliseconds (10

^{−3}) [106]. Specifically, four ordered structures in the cytoskeletal filaments were shown to exchange energy approximately 250 microseconds before a neuron fires [107]. The research program integrates multiple time domains into a single temporal architecture, extending the traditional Hodgkin–Huxley model used to study neural signaling, branch selection, spike time-gap regulation, and synaptic plasticity [108]. Understanding filamentary dynamics is important as these proteins are proposed as a blood-based biomarker of neurodegenerative pathology, overcoming some of the challenges of amyloid-beta and tau proteins as the traditional diagnostic markers for Alzheimer’s disease [109]. For example, one study found blood-based neurofilamentary protein fragment levels to be eight times higher in neurological disease patients than controls [110].

#### 3.4. Quantum Nanoscience for Neurobiology

#### 3.4.1. Nanoparticle Neuroscience

#### 3.4.2. Molecular Codes

#### 3.4.3. Autonomous Robotic Nanofabrication

## 4. Neuroscience Physics

#### 4.1. AdS/Brain

^{−2}m), action potentials at the neuron level (10

^{−4}m), dendritic spikes at the synapse level (10

^{−6}m), and ion docking at the molecular level (10

^{−10}m).

#### 4.2. AdS/Memory

#### 4.3. AdS/Superconducting

#### 4.4. AdS/Energy (Brain Hamiltonian)

#### 4.5. Neuronal Gauge Theories

#### 4.6. Network Neuroscience

#### 4.7. Random Tensors

## 5. Discussion

## Author Contributions

## Funding

## Conflicts of Interest

## Glossary

AdS/Brain | Multiscalar neuroscience interpretation of the AdS/CFT correspondence |

AdS/CFT correspondence (anti-de Sitter space/conformal field theory) | Theory positing that a physical system with a bulk volume can be described by a boundary theory in one less dimension |

AlphaFold | Protein folding predictor based on system-level attention to spatial constraints (from DeepMind/Google) |

Biological physics | Study of living processes through the application of physical principles |

Bosonic codes | Self-contained photonic system for quantum error correction (e.g. harmonic oscillator) |

Chaotic dynamics | Dynamical regimes of ballistic spread followed by saturation |

Filamentary dynamics | Role of neurofilaments (neuron-specific proteins) in axonal and synaptic signaling |

GKP bosonic codes (Gottesman, Kitaev, Preskill) | Quantum error correction method by reorienting the position and momentum of a molecule with known symmetric rotations |

Hamiltonian | (Quantum mechanics) operator corresponding to the total energy of a system |

Hamming distance | Sum of positional mismatches of two bit strings |

Hopf bifurcation | System critical point at which a periodic orbit appears or disappears per a local change in stability |

Information biology | Study of information processing activities performed by biosystems |

Information scrambling | Rapid spread of information in a quantum system prohibiting local measurement |

Josephson junction | Device consisting of two or more superconductors coupled by a link that conducts electrons |

Laplacian | (Schrödinger equation) operator representing the flux density of the gradient flow of a function |

Matrix | Array of numbers arranged in rows and columns used to study physical phenomena (probability distribution) |

Melonic diagram | (Melon-shaped) graph expression of a high-dimensional system |

MERA (multiscale entanglement renormalization ansatz) tensor networks | Entangled quantum systems model |

Molecular codes | Quantum error correction by performing rotations on asymmetric rigid bodies in free space |

Nanoparticle neuroscience | Nanoparticles (100 nm objects) that cross the blood-brain barrier to perform an intervention |

Neurobiology | Field investigating the form and function of the nervous system (neurons, glia, axons, and dendrites) |

Neurofilament | Neuron-specific protein implicated in neuronal cytoskeletal structure and signaling |

Neuromorphic computation | Electronic computation inspired by neural systems and spike thresholding |

Neuropeptides | Small chains of amino acids (chemicals) synthesized and released by neurons |

Neuroscience | Study of the structure and function of the nervous system and brain |

Neuroscience physics | Neuroscience interpretation of foundational physics findings |

Path integral | Approach of summing over all possible paths in a system |

Protein folding problem | Predicting a protein’s final 3D structure from the underlying sequence of amino acids |

Quantum biology | Study of how quantum properties may play a governing role in biological functions |

Quantum computing | Use of engineered quantum systems (with atoms, ions, photons) to perform computation |

Quantum information biology | Study of biological systems with quantum information methods |

Quantum internet | Information transmitted with quantum effects (entanglement), using quantum cryptography |

Quantum machine learning | Machine learning applied in a quantum environment |

Quantum memory (QRAM) | Quantum-mechanical computer memory, storing information with greater scalability as quantum states in superposition (vs classical binary states) |

Quantum nanoscience | Study of nanostructured systems that incorporate and exploit quantum effects |

Quantum neurobiology | Discipline within quantum biology and biological physics that studies potential quantum effects in the brain and applies quantum information science methods to neurobiological questions |

Quantum physics | Description of particles making up all matter including living organisms |

Quantum probability | Quantum mechanical rules for assigning probabilities |

Quantum walk | Quantum version of classical random walk based on coin-flip operator and lattice-graph propagation |

Qutrit | Three-level quantum state, simultaneously in 0, 1, 2 until collapsed in a measurement (vs two-state qubit) |

Random tensors | Generalization of random matrices (2 × 2 matrix formulations) to 3+ dimensions |

Renormalization | The ability to view a system at multiple scales by collapsing degrees of freedom (parameters) |

Spike-activated neural networks (SNNs) | Bio-inspired neuromorphic computation based on thresholded activation |

Superdeterminism | Interpretation that quantum effects are the result of hidden variables (vs indeterminism) |

Superpositioned data | Quantum information representation of all possible system states simultaneously |

Tensor field theories | Local field theories whose fields transform as a tensor under a global or local symmetry group |

Tensor networks | Structure for manipulating high-dimensional data (many-body quantum states) as the factorization of high-order tensors (many indices) into low-order tensors whose indices are summed to form a contracted network |

Transcription factors | Proteins regulating gene expression by attaching themselves to DNA |

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No. | Level | Size (Decimal) | Size (m) | Size (m) |
---|---|---|---|---|

1 | Nervous system | 1 | >1 m | 10^{0} |

2 | Subsystem | 0.1 | 10 cm | 10^{−1} |

3 | Neural network | 0.01 | 1 cm | 10^{−2} |

4 | Microcircuit | 0.001 | 1 nm | 10^{−3} |

5 | Neuron | 0.000 1 | 100 μm | 10^{−4} |

6 | Dendritic arbor | 0.000 01 | 10 μm | 10^{−5} |

7 | Synapse | 0.000 001 | 1 μm | 10^{−6} |

8 | Signaling pathway | 0.000 000 001 | 1 nm | 10^{−9} |

9 | Ion channel | 0.000 000 000 001 | 1 pm | 10^{−12} |

1. Waves, Protein Folding, Genomics | 2. Neural Dynamics | 3. Neuroscience Physics |
---|---|---|

Waves | Superpositioned Data | AdS/Neuroscience |

▪Quantum EEG | Quantum Probability | ▪AdS/Brain |

▪Quantum MRI | ▪Updating (QBism) | ▪AdS/Memory |

Quantum Protein Folding | Neural Field Theories | ▪AdS/Superconducting |

Quantum Genomics | ▪Synchrony | ▪AdS/Energy |

▪Sequencing | Filamentary Dynamics | Neuronal Gauge Theories |

▪Gene Expression | Quantum Nanoscience | Network Neuroscience |

▪Secure Transmission | ▪Nanoparticle Fab | Random Tensors |

Quantum SNNs | ▪Molecular Codes | ▪Melonic Diagrams |

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Swan, M.; dos Santos, R.P.; Witte, F.
Quantum Neurobiology. *Quantum Rep.* **2022**, *4*, 107-126.
https://doi.org/10.3390/quantum4010008

**AMA Style**

Swan M, dos Santos RP, Witte F.
Quantum Neurobiology. *Quantum Reports*. 2022; 4(1):107-126.
https://doi.org/10.3390/quantum4010008

**Chicago/Turabian Style**

Swan, Melanie, Renato P. dos Santos, and Franke Witte.
2022. "Quantum Neurobiology" *Quantum Reports* 4, no. 1: 107-126.
https://doi.org/10.3390/quantum4010008