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swan m quantum computing brain 2022

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Textbook in PDF format Quantum Computing for the Brain argues that the brain is the killer application for quantum computing. No other system is as complex, as multidimensional in time and space, as dynamic, as less well-understood, as of peak interest, and as in need of three-dimensional modeling as it functions in real-life, as the brain.Quantum computing has emerged as a platform suited to contemporary data processing needs, surpassing classical computing and supercomputing. This book shows how quantum computing's increased capacity to model classical data with quantum states and the ability to run more complex permutations of problems can be employed in neuroscience applications such as neural signaling and synaptic integration. State-of-the-art methods are discussed such as quantum machine learning, tensor networks, Born machines, quantum kernel learning, wavelet transforms, Rydberg atom arrays, ion traps, boson sampling, graph-theoretic models, quantum optical machine learning, neuromorphic architectures, spiking neural networks, quantum teleportation, and quantum walks.Quantum Computing for the Brain is a comprehensive one-stop resource for an improved understanding of the converging research frontiers of foundational physics, information theory, and neuroscience in the context of quantum computing. About the Authors List of Figures List of Tables Introduction to Quantum Neuroscience The Brain Is the “Killer Application” of Quantum Computing The complexity of the brain The Brain and Quantum Computing Status of Neuroscience Whole-brain simulation Status of Quantum Computing n scalability Three-dimensional format Quantum advantage over classical computing Supercomputing versus quantum computing Quantum finance and AdS/Finance Classical-digital-quantum finance progression What This Book Does Not Cover Quantum Neuroscience and AdS/Brain Part Foundations Neural Signaling Basics Scale Levels in the Brain Relative size of neural entities Neural Signaling Overview Electrical-to-chemical interconnects Neural signaling energy budget Sending Neuron (Presynaptic Terminal) Receiving Neuron (Postsynaptic Density) Synaptic (Dendritic) Spike Integration Excitatory and inhibitory postsynaptic potentials Dendritic pathologies Dendritic integration filtering Computational neuroscience and biophysical modeling Neural Signaling and Quantum Computing The AdS/Brain Correspondence The AdS/CFT Correspondence Stating the AdS/CFT correspondence AdS/CFT Correspondence Studies AdS/CFT hybrid approaches Duality lens Applied AdS/CFT AdS/QCD (quantum chromodynamics) AdS/CMT (condensed matter theory) AdS/SYK (SYK model) AdS/Chaos (thermal systems) AdS/QIT (quantum information theory) AdS/TN (tensor networks) AdS/ML (machine learning) AdS/DIY The AdS/CFT equations The AdS/CFT formalism Correspondence formulation example Listing of AdS/CFT correspondence formulations Tabletop Experiments Black Holes and Quantum Gravity in the Lab Particle Accelerator on a Chip Quantum Gravity in the Lab Quantum gravity Justification for quantum gravity in the lab Wormholes and holographic teleportation Operator size and size winding distribution Holographic teleportation protocols Preparing the thermofield double state Obtain wormhole-like physics with size winding Rydberg atoms and trapped ions Rydberg atom arrays Trapped ions Black Hole on a Chip Fast scramblers QSims: The SYK Model and Beyond The SYK model Tabletop platforms for quantum simulation Simulation with ultracold gases Large-scale and small-scale physics Ultracold atoms in optical lattices Black hole in a tabletop gas Simulation with quantum computing SYK simulation with ion traps and circuits Demonstrations with NMR QSims Ryu–Takayanagi entanglement entropy simulation Scrambling Hamiltonian Neuronal Gauge Theory Concept of the Neuronal Gauge Theory Gauge theory The principle of variational free energy Symmetry, gauge invariance, and the Lagrangian Details of the Neuronal Gauge Theory Rebalancing global symmetry Information-theoretic interpretation Implications Diffeomorphism invariance Symmetry and Yang–Mills theory Part Substrate Quantum Information Theory Quantum Information Entropy and quantum information Classical information theory Entropy Superposition, entanglement, and interference Superposition and interference Two-state qubit systems and quantum computing Entanglement and Bell pairs Quantum Toolbox Quantum teleportation Quantum error correction AdS/QECC QECC example: The three-qutrit code Out-of-time-order correlators Quantum walks and Hadamard coins Quantum Computing Quantum Algorithms and Quantum Circuits Qubit Encoding Quantum circuit demonstrations How Does Quantum Computing Work? Input, processing, output, repeat Quantum gate logic Setting up a quantum computation Step : Data encoding (embedding) Classical data Quantum data Step : Data processing Circuit architecture Unitary parametrization Steps and : Results and repetition Results measurement with complexity Advances in Quantum Computing Unitary Transformation Glia Neurotransmitter Synaptome Glial Cells Astrocyte calcium signaling Tripartite synapse Astrocyte tiling: Nonoverlapping territories Astrocyte signaling: Calcium operations Astrocytes and synapse formation Glia and neuropathology Neurotransmitters and Chemical Signaling Glutamate (excitatory) and GABA (inhibitory) Neurotransmitter transport Transport into presynaptic vesicles: Proton gradient Molecular economy Transmitter uptake from cleft: Sodium gradient Synaptome Genome, connectome, and synaptome Quantum computing-level complexity Synapse proteome and neuropathology Mouse synaptome: Aging pathologies Three phases of development, stability, and decline Synapse diversity and plasticity EPSPs and fMRI data Alzheimer’s disease synaptome Synaptic plasticity and long-lived proteins in humans Alzheimer’s disease synaptome and intervention Black Hole Information Theory Black Holes Black holes as a model system Quantum gravity and black hole evaporation Black hole in a box Hologram decoding dictionaries Practical Quantum Communications Protocols UV–IR information compression UV–IR correlations for interrogating bulk structure Part Connectivity Quantum Photonics and High-Dimensional Entanglement Quantum Photonics Technical benefits and qudits Bosons and fermions Boson Sampling Gaussian boson sampling Gaussian boson sampling demonstration Gaussian boson sampling as a NISQ device Gaussian boson sampling/graph theory Application tools for boson sampling/graph theory Space-Division Multiplexing Innovation Information multiplexing Spacetime states Personal brain networks Photonic Qubit Encoding Physics: Angular momentum Polarization: SAM Spatial Modes: OAM Polarization versus OAM encoding Technology: Path and time-frequency bins Propagation path waveguide encoding Time-based encoding: Time, frequency, energy High-dimensional Quantum Entanglement Theoretical development Qudits and optimal information content Greenberger–Horne–Zeilinger (GHZ) state Experimental implementation Polarization: Spin angular momentum Spatial modes: OAM Propagation path waveguide encoding Time-based encoding: Time, frequency, energy Hybrid entanglement: Multiple degrees of freedom Degrees of freedom conversion Planck’s constant Optical Machine Learning and Quantum Networks Quantum Optical Machine Learning Optical quantum computing Optical neural networks All-optical waveguide platforms All-optical reservoir computing Quantum optical machine learning GHZ state preparation and Hamiltonian simulation New protocols Quantum optical autoencoder Quantum reinforcement learning One-way quantum repeaters Global Quantum Networks End-to-end qubits Quantum network stack with entanglement Long-distance entanglement Heralded (confirmed) entanglement Use cases for quantum network entanglement Smart routing and SL A certification Status of long-distance quantum entanglement Global Quantum Clock Network GHZ state and optical oscillators Cooperative quantum clock network Step initialization: Prepare network-wide GHZ states Step : Interrogation of local nodes Step : Feedback and local node clock updating Time trust in the cooperative clock system Paper clocks Connectome and Brain Imaging Connectomics Brain Imaging Connectome parcellation High-Throughput Connectome Imaging Electron microscopy Light sheet microscopy Expansion light sheet microscopy X-ray microtomography High-Throughput Recording Light field microscopy Fruit fly grooming and walking Calcium imaging Brain Networks Brain Networks’ Approach The brain as a communications network Wiring and Circuit Layout The brain is three-dimensional Topographical projection Optimal ratios of axonal to dendritic arbor volumes Connectivity Gray matter and white matter Local gray matter and long-distance white matter Sparse small-world connectivity Energy Consumption Imputing traffic volume from energy consumption Bandwidth Signal Processing Signal conversion Probabilistic signal transmission Signal-to-Noise Ratio Ion channels Molecular channel noise is nonlinear Volumetric connectome data Network Rewiring: Synaptic Plasticity Neural signaling path integral Implications of brain networks’ approach Part System Evolution Quantum Dynamics Dynamics of Quantum Systems Operator Size and Distribution Growth The Holographic SYK Model The Heisenberg uncertainty principle Size-momentum correspondence and holographic SYK Out-of-time-order correlators Quantum dynamics and temperature The Heisenberg equation of motion Thermofield double state Implications for the holographic SYK model Superconductivity and Spacetime Superfluids Time crystals Spacetime superfluids and temperature UV–IR correlations: Order-disorder phase transition Neural Dynamics Multiscale Modeling Centrality of wavefunction modeling Practical perspective: Scale and model integration Nonlinear dynamical systems approach Approaches to Collective Neural Behavior Nonlinear dynamical systems Stochastic calculus and diffusion Neural dynamics in large-scale models Neural Ensemble Models Fokker–Planck dynamics for normal distributions Heavy tail distributions Beyond linear Fokker–Planck equations Recognized nonlinear probability distributions Unknown probability distributions Neural signaling: Orbits and bifurcation Empirical data and oscillatory neural dynamics Neural Mass Models Brain networks approach Technical aspects of neural mass methods Oscillatory dynamics: Jansen–Rit neural mass model Non-smooth dynamics and the Floquet model Neural Field Models Statistical theory of neuron dynamics Oscillatory neural dynamics Neural field theory in practice Multiscale models Synchrony: Simultaneous arrival of signals Neural field theory simulation and filtering Firing synchrony within populations of neurons Statistical neural field theory Quantum neural field theory Part Modeling Toolkit Quantum Machine Learning Machine Learning-Physics Collaboration Quantum machine learning overview Structural similarities Problems in quantum mechanics Variational methods: The method of varying Wavefunction Approximation Quantum state neural networks Traditional approaches to wavefunction modeling Motivation for machine learning Machine learning approach to wavefunction modeling Encoding quantum states Neural network mathematics Demonstration: Quantum spin systems’ ground states Neural network-tensor network comparison Demonstration: Time-dependent quantum dynamics Implications of quantum state neural networks Quantum Transformer Neural Networks Transformer attention mechanism Transformer neural networks and quantum states The attention mechanism Born Machine and Pixel = Qubit The Born Machine Boltzmann machine versus born machine Supervised versus unsupervised learning Unsupervised generative learning Born machine implications for quantum computing Probabilistic Methods: Reduced Density Matrix Modeling classical data with quantum states Quantum entanglement found in classical data Practical implementation Advantages of probabilistic quantum methods Density matrices and density operators Tensor Networks: Pixel = Spin (Qubit) Decomposition of high-dimensional vectors Machine learning algorithm: Weighted data features Step : Encoding input data into tensor networks Step : Selecting network architecture Step : Training the network Step : Testing real-life data Advantages of tensor networks for machine learning Tensor Networks: Wavelet = Spin (Qubit) Wavelet transform Wavelet transform equates to MERA tensor network Step : Data encoding: MERA tensor network Steps and : Network architecture and training Step : Testing real-life datasets Quantum Kernel Learning and Entanglement Design Quantum Kernel Methods Machine learning approaches Kernel methods Kernel methods reduce dimensionality Dimensionality reduction and squeezed light states Quantum algorithm design Quantum kernel methods Quantum kernel methods: Feature map approach Embedded data Hilbert spaces Quantum finance Reproducing kernel Hilbert space formalism Time series analysis and AdS/RKHS Squeezed states of light Squeezed states: Quantum noise reduction technique Global telecommunications networks Continuous basis quantum systems RHKS and machine learning Entanglement as a Design Principle Entanglement and tensor networks Blocks as a renormalization method Density matrix renormalization group Classical data and quantum states Entanglement entropy Brain Modeling and Machine Learning Brain Modeling Compartmental neuroscience models Compartment model classes Synaptic integration The future of compartmental models Theoretical neuroscience Network neuroscience modeling Empirical context: Brain–computer interfaces Classical Machine Learning and Neuroscience Machine learning and biomedicine Machine learning and neuroscience Machine learning and brain tumors Machine learning and neuropathologies of aging Machine learning and connectomics Neuron reconstruction: TeraVR and DeepNeuron Neural connectivity: Synapse detection Brain atlas annotation and deep learning network Generative machine learning for unlabeled data Rapprochement Machine learning applied to neuroscience Machine learning and neuroscience at odds Next-generation machine learning Neuromorphics and Spiking Neural Networks Neuromorphic computing Neuromorphic computing chips and projects Spiking neural networks Spike-based activation Backpropagation and the learning problem Eligibility propagation synaptic plasticity Wider application of spiking neural networks Optical Spiking Neural Networks Conclusion: AdS/Brain Theory and Quantum Neuroscience Quantum Computing for the Brain AdS/Brain Theory Quantum neural signaling AdS/Brain theory of neural signaling Information-theoretic black hole-like physics Implementation of the AdS/Brain theory Risks and limitations Millennium Prize-Type Challenges NISQ device neuroscience applications Physics-based time technologies Standard neuroscience quantum circuits The Future of Quantum Neuroscience

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Swan M. Quantum Computing for the Brain 2022.pdf 24.9 MB

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swan m quantum computing brain 2022

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