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Quantum Neuroscience: CRISPR for Alzheimer’s, Connectomes & Quantum BCIs

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This talk provides an introduction to quantum computing and how it may be deployed to study the human brain and its diseases of pathology and aging. Refined to its present state over centuries, the brain is one of the most complex systems known, with 86 billion neurons and 242 trillion synapses connected in intricate patterns and rewired by synaptic plasticity. Research continues to illuminate the mysteries of the brain. Quantum computing provides a more capacious architecture with greater scalability and energy efficiency than current methods of classical computing and supercomputing, and more naturally corresponds to the three-dimensional structure of atomic reality. The vision for quantum neuroscience is to model the nature of the brain exactly as it is, in three-dimensional atomically-accurate representations. Neuroscience (particularly genetic disease modeling, connectomics, and synaptomics) could be the “killer application” of quantum computing. Implementations in other industries are also important, including in quantum finance, quantum cryptography using Shor’s factoring algorithm (“the Y2K of Crypto”), Grover’s search, quantum chemistry, eigensolvers, quantum machine learning, and continuous-time quantum walks. Quantum computing is a high-profile worldwide scientific endeavor with platforms currently available via cloud services (IBM Q 27-qubit, IonQ 32-qubit, Rigetti 19Q Acorn) and is in the process of being applied in various industries including computational neuroscience.

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Quantum Neuroscience: CRISPR for Alzheimer’s, Connectomes & Quantum BCIs

  1. 1. Quantum Neuroscience CRISPR for Alzheimer’s, Connectomes & Quantum BCIs Houston TX, August 24, 2021 Slides: http://slideshare.net/LaBlogga “Biology will be the leading science for the next hundred years” – Physicist Freeman Dyson, 1996 M. Swan, MBA, PhD Quantum Technologies
  2. 2. 24 Aug 2021 Quantum Neuroscience Quantum Neuroscience  Quantum neuroscience: application of quantum information science methods to computational neuroscience problems  EEG wave-based analysis  Quantum biology state modeling  Neuroscience physics 1 Source: Swan, M. dos Santos, R.P., Lebedev, M.A. and Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific. https://www.worldscientific.com/worldscibooks/10.1142/q0313.
  3. 3. 24 Aug 2021 Quantum Neuroscience The brain is the killer app of quantum computing – the outer limits case defining the requirements of the medium No other system is as complex and in need of resolving the pathologies of disease and aging As successive waves of industries become digitized in the information technology revolution (1) news, media, entertainment, stock trading; (2) money, finance, law (blockchains); and (3) now all biotech and matter-based industries; the brain as a frontier comes into view Quantum computing is finally a computational platform adequate to the scale and complexity of modeling the brain Thesis
  4. 4. 24 Aug 2021 Quantum Neuroscience Levels of Organization in the Brain 3  Complex behavior spanning nine orders of magnitude scale tiers Level Size (decimal) Size (m) Size (m) 1 Nervous system 1 > 1 m 100 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 Sources: Sterratt, D., Graham, B., Gillies, A., & Willshaw, D. (2011). Principles of Computational Modelling in Neuroscience. Cambridge: Cambridge University Press. Ch. 9:226-66. Sejnowski, T.J. (2020). The unreasonable effectiveness of deep learning in artificial intelligence. Proc Natl Acad Sci. 117(48):30033-38.
  5. 5. 24 Aug 2021 Quantum Neuroscience Quantum BCI within Reach 4  Advancing quantum computational capacity suggests whole-brain modeling  Quantum BCIs  Personalized connectome, memory chip, genomic errors remediation, enhancement, two-way communication Level Estimated Size 1 Neurons 86 x 109 86,000,000,000 2 Glia 85 x 109 85,000,000,000 3 Synapses 2 x 1014 242,000,000,000,000 4 Avogadro’s number 6 x 1023 602,214,076,000,000,000,000,000 5 19 Qubits (Rigetti-available) 219 524,288 6 27 Qubits (IBM-available) 227 134,217,728 7 53 Qubits (Google-research) 253 9,007,199,254,740,990 8 79 Qubits (needed at CERN LHC) 279 604,462,909,807,315,000,000,000 BCI: brain-computer interface (computer that can speak directly to the brain) Source: Swan, M. dos Santos, R.P., Lebedev, M.A. and Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific. Neural Entities and Quantum Computation Quantum BCI Not “big numbers” in terms of what is available via cloud services quantum computing
  6. 6. 24 Aug 2021 Quantum Neuroscience Neural Signaling Image Credit: Okinawa Institute of Science and Technology NEURON: Standard computational neuroscience modeling software Scale Number Size Size (m) NEURON Microscopy 1 Neuron 86 bn 100 μm 10-4 ODE Electron 2 Synapse 242 tn 1 μm 10-6 ODE Electron/Light field 3 Signaling pathway unknown 1 nm 10-9 PDE Light sheet 4 Ion channel unknown 1 pm 10-12 PDE Light sheet Electrical-Chemical Signaling Math: PDE (Partial Differential Equation: multiple unknowns) Electrical Signaling (Axon) Math: ODE (Ordinary Differential Equation: one unknown) 1. Synaptic Integration: Aggregating thousands of incoming spikes from dendrites and other neurons 2. Electrical-Chemical Signaling: Incorporating neuron- glia interactions at the molecular scale 5 Implicated in neuropathologies of Alzheimer’s, Parkinson’s, stroke, cancer Synaptic Integration Math: PDE (Partial Differential Equation: multiple unknowns)
  7. 7. 24 Aug 2021 Quantum Neuroscience 6 Connectome Fruit fly completed in 2018  Worm to mouse:  10-million-fold increase in brain volume  Brain volume: cubic microns (represented by 1 cm distance)  Quantum computing technology-driven inflection point needed (as with human genome sequencing in 2001)  1 zettabyte storage capacity per human connectome required vs 59 zettabytes of total data generated worldwide in 2020 Sources: Abbott, L.F., Bock, D.D., Callaway, E.M. et al. (2020). The Mind of a Mouse. Cell. 182(6):1372-76. Lichtman, J.W., Pfister, H. & Shavit, N. (2014). The big data challenges of connectomics. Nat Neurosci. 17(11):1448-54. Reinsel, D. (2020). IDC Report: Worldwide Global DataSphere Forecast, 2020-2024: The COVID-19 Data Bump and the Future of Data Growth (Doc US44797920). Neurons Synapses Ratio Volume Complete Worm 302 7,500 25 5 x 104 1992 Fly 100,000 10,000,000 100 5 x 107 2018 Mouse 71,000,000 100,000,000,000 1,408 5 x 1011 NA Human 86,000,000,000 242,000,000,000,000 2,814 5 x 1014 NA Connectome: map of synaptic connections between neurons (wiring diagram), but structure does not equal function
  8. 8. 24 Aug 2021 Quantum Neuroscience Smart Network Thesis Quantum Information Revolution 7 1990-2020 • News, media, entertainment, stock trading, mortgage finance, credit 2010-2050e • Cryptographic assets: blockchain-based cryptocurrencies and smart contracts: digitization of money, economics, finance, legal agreements 2020-2050e • All remaining industries: biology, healthcare, pharmaceuticals, agriculture, building materials, construction, automotive, transportation, energy • The information-based transition of all industries to digital network instantiation • Automation: orders-of-magnitude better-than-human precision (surgery, robotics, driving) • Next phases: solve entirely new problem classes • Aim: Kardashev-plus society marshalling all tangible and intangible resources Digitization (information technologies) Optical Networks 1960-2020 • Fiberoptic wiring of the planet 2020-2050e • Quantum networks, real-time ultra-secure global networks for quantum communication, computation, and sensing Source: Swan, M., dos Santos, R.P. & Witte, F. (2020). Quantum Computing: Physics, Blockchains, and Deep Learning Smart Networks. London: World Scientific.
  9. 9. 24 Aug 2021 Quantum Neuroscience Kardashev Type I Culture 8  Planetary-scale technologies  Coordinating at the level of the planet  ICT technologies (planetary-scale communication)  Telegraph, telephony, internet, SMS (basic connectivity)  Quantum internet (ultra-secure ultra-fast communication)  Economic technologies (blockchains)  Cryptocurrencies (planetary-scale economic system (t=0))  Smart contracts (planetary-scale financial system (t>0))  Cryptographic assets (planetary-scale deployment of value)  NFT genome (Oasis Network), pharma (MediLedger) blockchains  Coin communities (planetary-scale democracy)  Bio-cryptoeconomies (whole-brain smart network quantum BCIs) NFT: non-fungible token (unique digital entity) Sources: Kaku, M. (2018). The Future of Humanity. New York: Doubleday. (p. 250). Swan, M. (2019). Blockchain Economics; (2019). Blockchain Economic Networks; (2020). Black Hole Zero-Knowledge Proofs; (forthcoming) Technophysics, Smart Health Networks, and the Bio-cryptoeconomy. https://hitconsultant.net/2021/05/27/nebula-genomics-launches-worlds-first-genomic-nft-blockchain/ Civilization Energy Marshalling Energy Consumption Type I: Planetary Civilization Use all sunlight energy reaching the planet 1026 W ≈4×1019 erg/sec (4×1012 watts) Type II: Stellar Civilization Use all the energy produced by the sun 1016 W ≈4×1033 erg/sec (4×1026 watts) Luminosity of the Sun Type III: Galactic Civilization Use the energy of the entire galaxy 1036 W ≈4×1044 erg/sec (4×1037 watts) Luminosity of the Milky Way Individuals control and monetize their data with health blockchains
  10. 10. 24 Aug 2021 Quantum Neuroscience Accelerating Change 9  The Law of Accelerating Returns  The rate of change of various systems (technology and otherwise) tends to increase exponentially  (related) The mass use of inventions  Years until an invention is used by a quarter of the population  Smartphones much faster adoption than personal computers  Disruptive technology: a technology that transforms life in an abrupt, step-changing, and overarching way Sources: Kurzweil, R. (1999). The Age of Spiritual Machines. New York: Viking. Kurzweil, R. (2001). The Law of Accelerating Returns. http://www.kurzweilai.net/the-law-of-accelerating-returns. Post-biological intelligence evolutionary journey
  11. 11. 24 Aug 2021 Quantum Neuroscience Recursive Accelerating Change The Law of Accelerating Returns, 1999, 2016  Infotech tools themselves constitute a special class of method that self-improves in recursive acceleration loops  Leads to the creation of core infrastructural technologies  Machine learning (deep generative learning, transformer nets)  AdS/CFT, entanglement entropy, SYK model, OTOCs, scrambling  Quantum error correction, stabilizer codes, non-Clifford gates  Blockchains, smart contracts, zero-knowledge computational proofs 10 Sources: Jurvetson, S. (2016). Moore’s Law update of Kurzweil’s graph. https://www.flickr.com/photos/jurvetson/31409423572/. Swan, M., dos Santos, R.P. & Witte, F. (2020). Quantum Computing: Physics, Blockchains, and Deep Learning Smart Networks. London: World Scientific. https://www.researchgate.net/publication/342184205_Black_Hole_Zero-Knowledge_Proofs Recursive Accelerating Change, 2021
  12. 12. 24 Aug 2021 Quantum Neuroscience 11  Leapfrog mindset: not just new tools, new problems  Tech innovation so rapid that the problem is not the problem  No data? machine learning generates  Unknown distribution? machine learning algorithm finds it  Scale renormalization? tensor networks provide as a feature  Implication: forward-innovation by inventing according to where the technology is going and by seeing how quickly problem definitions are changing Continued application of existing tools and methods Advent of new tools and methods Result: Technology-assisted Innovation Source: Swan, M. dos Santos, R.P., Lebedev, M.A. and Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific. Advance in two dimensions
  13. 13. 24 Aug 2021 Quantum Neuroscience Agenda  Quantum Computing and the Brain  Quantum Information Techniques  Quantum Neuroscience Applications 1. Waves: EEG, fMRI, CT, PET integration 2. Quantum Biology  Superpositioned Data and Operator Technology 3. Neuroscience Physics  AdS/Brain (AdS/CFT Holographic Neuroscience)  Neuronal Gauge Theory  General Relativity of the Brain: Entropy = Energy  Black Hole Superconducting Condensates and Scalar Hair  Random Tensors (High-dimensional Indexing Technology)  Conclusion, Risks, and Future Implications 12
  14. 14. 24 Aug 2021 Quantum Neuroscience Why Quantum?  Quantum computing provides a more capacious architecture with greater scalability and energy efficiency than current methods of classical computing and supercomputing, and more naturally corresponds to the three-dimensional structure of atomic reality Source: Feynman, R.P. (1982) Simulating physics with computers. Int J Theor Phys. 21(6):467-88.  Scalability  Test more permutations (2n) than classically  Find hidden correlations in systems  Entanglement modeling  Model 3D phenomena natively  Feynman: universal quantum simulation  Math: we have more math than we can solve  And need new math for new problem classes 13
  15. 15. 24 Aug 2021 Quantum Neuroscience Quantum Scalability  Quantum computers  Hold all combinations of a problem in superposition simultaneously  10 quantum bits hold 1,024 (210) different numbers simultaneously  Process all possible solutions simultaneously  Classical computers  Hold one data permutation at a time  Process sequentially Source: Hensinger, W.K. (2018). Quantum Computing. In Al-Khalili, J. Ed. What the Future Looks Like. New York: The Experiment. Pp. 133-43. (p 138) 14 Bloch sphere: particle movement in X, Y, Z directions Bloch sphere: the qubit’s Hilbert space Hilbert space: generalization of Euclidean space to infinite-dimensional space (the vector space of all possible wavefunctions)
  16. 16. 24 Aug 2021 Quantum Neuroscience Wavefunction  The wavefunction (Ψ) (psi “sigh”)  The fundamental object in quantum physics  Complex-valued probability amplitude (with real and imaginary wave-shaped components) [intractable]  Contains all the information of a quantum state  For single particle, complex molecule, or many-body system (multiple entities) 15 Source: Carleo, G. & Troyer, M. (2017). Solving the Quantum Many-Body Problem with Artificial Neural Networks. Science. 355(6325):602-26. Ψ = the wavefunction that describes a specific wave EΨ(r) = -ћ2/2m ∇2 Ψ(r) + V(r)Ψ(r) Total Energy = Kinetic Energy + Potential Energy Schrödinger wave equation  Schrödinger equation  Measures positions or speeds (momenta) of complete system configurations Wavefunction: description of the quantum state of a system Wave Packet
  17. 17. 24 Aug 2021 Quantum Neuroscience What is Quantum Computing?  Quantum computing is the use of engineered quantum systems to perform computation: physical systems comprised of quantum objects (atoms, ions, photons) manipulated through configurations of logic gates  Quantum platforms available via cloud services  IBM Q 27-qubit, IonQ 32-qubit, Rigetti 19Q Acorn 16 D-Wave Systems Quantum annealing machine IBM/Rigetti Quantum processor (superconducting circuits) IonQ ion trap Rydberg arrays Cold atom arrays Neutral atoms GBS Optical platforms High-dimensionality (3+) Quantum Computing Platforms GBS: Gaussian Boson Sampling: method for sampling bosons using squeezed light states (classically hard-to-solve) Source: Swan, M. dos Santos, R.P., Lebedev, M.A. and Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific. IBM: systems online https://quantum-computing.ibm.com/services?services=systems
  18. 18. 24 Aug 2021 Quantum Neuroscience Quantum Scale: 10-9 to 10-15 m 17  “Quantum” = anything at the scale of  Atoms (Nano 10-9)  Ions and photons (Pico 10-12)  Subatomic particles (Femto 10-15)  Nanotechnology is already “quantum” Scale Entities Special Properties 1 1 x 101 m Meter Humans 2 1 x 10-9 m Nanometer Atoms Van Der Wals force, surface area tension, melting point, magnetism, fluorescence, conductivity 3 1 x 10-12 m Picometer Ions, photons Superposition, entanglement, interference, entropy (UV-IR correlations), renormalization, thermality, symmetry, scrambling, chaos, quantum probability 4 1 x 10-15 m Femtometer Subatomic particles Strong force (QCD), plasma, gauge theory 5 1 x 10-35 m Planck scale Planck length
  19. 19. 24 Aug 2021 Quantum Neuroscience Primary Quantum Properties  Superposition  An unobserved particle exists in all possible states simultaneously, but collapses to only one state when measured  Entanglement (used in quantum teleportation)  Physical attributes are correlated between a pair or group of particles (position, momentum, polarization, spin), even when separated by large distance  “Heads-tails” relationship: if one particle is in a spin-up state, the other is in a spin-down state  Interference  Wavefunction amplitudes reinforce or cancel each other out (cohering or decohering) 18 Image Credit: Sandia National Laboratories
  20. 20. 24 Aug 2021 Quantum Neuroscience Full Slate of Quantum Properties obtained “for free”  Superposition, Entanglement, and Interference  Wavefunctions computed with density matrices & the Born rule  Quantum probability: find distribution & generate data  Heisenberg uncertainty: position-momentum, energy-time  Entropy (# subsystem microstates & interrelatedness)  UV-IR correlations, topological entanglement entropy  Scale renormalization (renormalization group flow)  Symmetry: gauge-invariant ordering properties  Information scrambling: chaotic vs diffusive spread  Thermality: temperature-based phase transition  Energy levels (ground state, excited state)  Lattices: 3+ dimensional spacetimes 19 Source: Swan, M. dos Santos, R.P., Lebedev, M.A. and Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific.
  21. 21. 24 Aug 2021 Quantum Neuroscience Quantum Uncertainty Relations  Heisenberg uncertainty principle  Trade-off between conjugate variables: the more that is known about position, the less that can be known about momentum  Position-momentum  Energy-time(frequency)  Entropic uncertainty (entropy = measure of uncertainty in a system)  Stronger & easy-to-compute form of Heisenberg uncertainty  Lower bound of Heisenberg uncertainty (Holevo is upper bound)  Min-entropy measures the uniformity in the distribution of a random variable (as a lower bound of the sum of entropies comprised by the temporal and spectral Shannon entropies or (equivalently) as the quantum generalization of conditional Rényi entropies)  The lower the min-entropy, the higher the certainty of the system producing a certain outcome  Apps: unbreakable cryptography, faster search, certified deletion 20 Sources: Halpern, N.Y., Bartolotta, B. & Pollack, J. (2019). Entropic uncertainty relations for quantum information scrambling. Nat Comm Phys. 2(92). Broadbent, A. and Islam, R. (2020). Quantum encryption with certified deletion. arXiv:1910.03551v3. Uncertainty Tech
  22. 22. 24 Aug 2021 Quantum Neuroscience Entropy, Entanglement, UV-IR Correlations  Entropy: # microstates of a system  2nd law of thermodynamics: total entropy of an isolated system cannot decrease over time  # of microscopic arrangements of a system  # air particle configurations all leading to room temperature of 72°F  Minimum # of bits (qubits) to send a message (information-noise)  Entanglement: correlated properties of quantum particles  Entanglement entropy: system interrelatedness  Measure with UV-IR correlations  The degree of interconnectedness of subsystems in a system  Structure emerges from the correlations between quantum subsystems: time, space, gravity 21 UV: ultraviolet, IR: infrared. Source: Horodecki, M., Oppenheim, J. & Winter, A. (2007). Quantum state merging and negative information. Commun Math Phys. 269(1):107-36.
  23. 23. 24 Aug 2021 Quantum Neuroscience UV-IR Correlations and Information  High-energy (UV) and low-energy (IR) phases  Sun: high-energy rays (UV) harmful, low-energy (IR) not  Complex systems have UV-IR correlations  Video: more near-term change (UV) in frame-to-frame action than longer-range change (IR) in characters, overall setting  Implication: streaming protocols use UV-IR correlations in information compression algorithms to send data efficiently  Quantum modeling  Extract UV-IR correlations (even in classical systems)  Measure with sphere-based techniques (geodesics) 22 Geodesic: shortest-length line on a sphere (curve) UV-IR: near and far-range correlations in a system UV: ultraviolet, IR: infrared. Source: Czech, B., Hayden, P., Lashkari, N. & Swingle, B. (2015). The Information Theoretic Interpretation of the Length of a Curve. J High Energ Phys. 06(157). Entanglement Tech
  24. 24. 24 Aug 2021 Quantum Neuroscience Qubit Encoding 23 Sources: Flamini, F., Spagnolo, N. & Sciarrino, F. (2018). Photonic quantum information processing: a review. Rep Prog Phys. 82(016001). Erhard, M., Fickler, R., Krenn, M. & Zeilinger, A. (2018). Twisted photons: new quantum perspectives in high dimensions. Light Sci. Appl. 7(17146). System Quantity Qubit (One-Zero) 1 Electrons Spin Up/Down Charge 0/1 Electrons 2 Josephson junction Charge 0/1 Cooper pair Current Clockwise/Counter-clockwise Energy Ground/Excited state 3 Single photon Spin angular momentum (polarization) H/V, L/R, Diagonals Orbital angular momentum (spatial modes) Left/Right Waveguide propagation path 0/1 Photons Time-bin, Frequency-bin Early/Late arrival bins 4 Optical lattice Spin Up/Down 5 Quantum dot Spin Up/Down 6 Nuclear spin Spin Up/Down 7 Majorana fermions Topology Braiding Photon orbital angular momentum (OAM)  Two-tier physical system
  25. 25. 24 Aug 2021 Quantum Neuroscience Photonics Revolution: SDM 24  Multiplexing: write (modulate) information onto light  Time (TDM)  Wave (WDM) – forward-space  Space (SDM) – transverse-space  Sideways and length-ways transmission over optical fibers (Lynn E. Johnson, AT&T Labs) Source: Richardson, D.J., Fini, J.M. & Nelson, L.E. (2013). Space-division multiplexing in optical fibers. Nat Photon. 7:354-62. Domain Multiplexing Method Modulation Mode Year 1 Time TDM Time-division multiplexing Time synchronization between the sender and the receiver 1880s 2 Wave WDM Wave-division multiplexing Multiplex onto forward direction of wave movement 1990 3 Space SDM Space-division multiplexing Multiplex onto transverse forward direction of wave movement 2013 Moore’s Law for Multiplexing Information
  26. 26. 24 Aug 2021 Quantum Neuroscience Bits vs. Qubits (Qudits)  High-dimensionality needed to solve new problem classes, which suggests photonics and qudits  Qudits: quantum information digits that can exist in more than two states  A qubit exists in a superposition of 0 and 1 before being collapsed to a measurement at the end of the computation  A qutrit exists in the 0, 1, and 2 states until collapsed for measurement (triplet is useful for quantum error correction)  7 and 10 qudit systems tested, 4 optical qudits achieved the processing power of 20 qubits 25 Source: Imany, P., Jaramillo-Villegas, J.A. & Alshaykh, M.S. (2019). High-dimensional optical quantum logic in large operational spaces. npj Quantum Information. 5(59):1-10. Error correction: Qutrit stabilizer code on a torus Quantum System (complex-valued qubits on a Bloch sphere) Classical System (0/1 bits) Wheeler Progression: It from Bit -> It from Qubit -> It from Qudit
  27. 27. 24 Aug 2021 Quantum Neuroscience Quantum Algorithms (quadratic speedup)  Shor’s Algorithm (factoring)  Period-finding function with a quantum Fourier transform  A classical discrete Fourier transform applied to the vector amplitudes of a quantum state (vs general number field sieve)  Grover’s Algorithm (search)  Find a register in an unordered database (only √N queries vs all N entries or at least half classically)  VQE: variational quantum eigensolvers (quantum chemistry)  Finds the eigenvalues of a matrix (Peruzzo, 2014)  QAOA: quantum approximate optimization algorithm  Combinatorial optimization (Farhi, 2014)  QAOA: quantum alternating operator ansatz (guess)  Alternating Hamiltonians (cost-mixing) model (Hadfield, 2021) 26 Quantum Math Tech Status: rewrite computational algorithms to take advantage of known quantum speedups (in processing linear algebra routines, Fourier transforms, and other optimization tasks)
  28. 28. 24 Aug 2021 Quantum Neuroscience Chip Progression: CPU-GPU-TPU-QPU  Graphics processing units (GPUs)  Train machine learning networks 10-20x faster than CPUs  Tensor processing units (TPUs)  Direct flow-through of matrix multiplications without having to store interim values in memory  Quantum processing units (QPUs)  Solve problems quadratically (polynomially) faster than CPUs via quantum properties of superposition and entanglement CPU Sources: Vescovi et al . (2017) Radiography registration for mosaic tomography. J Synchrotron Radiat. 24:686-94. LeCun, Y., Bengio, Y. & Hinton, G. (2015) Deep Learning. Nature. 521(7553):436-44. P. 439. Wang, Y.E., Wei, G.-Y. & Brooks, D. (2019) Benchmarking TPU, GPU, and CPU Platforms for Deep Learning. arXiv:1907.10701. GPU TPU QPU Peak teraFLOPs in 2019 benchmarking analysis 2 125 420 27
  29. 29. 24 Aug 2021 Quantum Neuroscience Computing Architectures  Classical-supercomputer supplanted by quantum and neuromorphic computing (spiking neural network) Source: Neurommorphic SNNs: Boahen, K. (2014). Neurogrid: A Mixed-Analog-Digital Multichip System for Large-Scale Neural Simulations. Proc IEEE. 102(5):699-716. Classical Computing Supercomputing Traditional Von Neumann architectures Beyond Moore‘s Law architectures Neuromorphic Spiking Neural Networks Quantum Computing 28 2500 BC Abacus 20th Century Classical 21st Century Quantum Classical:Quantum as Abacus:Logarithm
  30. 30. 24 Aug 2021 Quantum Neuroscience Interpretations of Quantum Mechanics  Copenhagen interpretation: widely-accepted idea of the probabilistic nature of reality (Bohr-Heisenberg, 1925-27)  Particles exist in a superposition of all possible states, only the probability distribution can be predicted ahead of time, before the particle wavefunction is collapsed in a measurement  Einstein interpretation (EPR) (1935):  (“God does not play dice”) rejects probability in favor of causality  No “spooky action at a distance” since faster-than-light travel is impossible, but entanglement (Bell pairs) now proven as the explanation for how remote particles influence each other  Everett many-worlds interpretation (1956)  All possibilities described by quantum theory occur simultaneously in a multiverse composed of independent parallel universes EPR: Einstein-Podolsky-Rosen paradox 29
  31. 31. 24 Aug 2021 Quantum Neuroscience 30 Source: Alagic et al. (2019). Status Report on the First Round of the NIST Post-Quantum Cryptography Standardization Process. NISTIR 8240.  “Y2K of crypto” problem  Quantum computing threatens existing global cryptographic infrastructure  Online banking, email, blockchains  Solution  Migrate to quantum-secure algorithms  In development to be available as early as 2022 (US NIST)  Mathematical shift  From factoring (number theory)  To methods based on lattices (group theory)  First-line application  Satellite-based quantum key distribution Quantum Computing industries go mainstream Quantum Cryptography Quantum Key Distribution
  32. 32. 24 Aug 2021 Quantum Neuroscience Quantum Computing industries go mainstream Quantum Finance and Econophysics 31 VaR: Value at Risk a quantile of the loss distribution (a widely used risk metric); conditional VaR POVM: positive operator valued measure; RKHS: reproducing kernel Hilbert space € $ ¥ € Ref Application Area Project Quantum Method Classical Method Platform 1 Portfolio optimization S&P 500 subset time- series pricing data Born machine (represent probability distributions using the Born amplitudes of the wavefunction) RBM (shallow two- layer neural networks) Simulation of quantum circuit Born machine (QCBM) on ion-trap 2 Risk analysis Vanilla, multi-asset, barrier options Quantum amplitude estimation Monte Carlo methods IBM Q Tokyo 20- qubit device 3 Risk analysis (VaR and cVaR) T-bill risk per interest rate increase Quantum amplitude estimation Monte Carlo methods IBM Q 5 and IBM Q 20 (5 & 20-qubits) 4 Risk management and derivatives pricing Convex & combinatorial optimization Quantum Monte Carlo methods Monte Carlo methods D-Wave (quantum annealing machine) 5 Asset pricing and market dynamics Price-energy relationship in Schrödinger wavefunctions Anharmonic oscillators Simple harmonic oscillators Simulation, open platform 6 Large dataset classification (trade identification) Non-linear kernels: fast evaluation of radial kernels via POVM Quantum kernel learning (via RKHS property of SVMs arising from coherent states) Classical SVMs (support vector machines) Quantum optical coherent states  Quantum finance: quantum algorithms for portfolio optimization, risk management, option pricing, and trade identification  Model markets with physics: wavefunctions, gas, Brownian motion Chern-Simons topological invariants
  33. 33. 24 Aug 2021 Quantum Neuroscience Quantum Finance (references) 32 1. Alcazar, J., Leyton-Ortega, V. & Perdomo-Ortiz, A. (2020). Classical versus Quantum Models in Machine Learning: Insights from a Finance Application. Mach Learn: Sci Technol. 1(035003). arXiv:1908.10778v2. 2. Stamatopoulos, N., Egger, D.J., Sun, Y. et al. (2020). Option pricing using quantum computers. Quantum. 4(291). arXiv:1905.02666v5. 3. Woerner, S. & Egger, D.J. (2019). Quantum risk analysis. npj Quantum Information. 5(15). arXiv:1806.06893v1. 4. Bouland A., van Dam, W., Joorati, H. et al. (2020). Prospects and challenges of quantum finance. arXiv:2011.06492v1. 5. Lee, R.S.T. (2020). Quantum Finance: Intelligent Forecast and Trading Systems. Singapore: Springer. 6. Chatterjee, R. & Yu, T. (2017). Generalized Coherent States, Reproducing Kernels, and Quantum Support Vector Machines. Quantum Information and Communication. 17(1292). arXiv:1612.03713v2. Evaluating payoff function Quantum amplitude estimation circuit for option pricing Source: Stamatopoulos (2020).
  34. 34. 24 Aug 2021 Quantum Neuroscience Quantum Computing industries go mainstream Quantum Biology  Quantum biology: study of quantum processes used in the natural world (photosynthesis, magnetic navigation, DNA)  Bohr, Light and Life, Copenhagen, 1932  Delbruck, Genetics as an information science, 1937  Schrödinger, What is Life?, 1944  Genes seem to be an aperiodic crystal: an arrangement of atoms that is specific not random, but not regularly repeating as a crystal  Biology occurs at the quantum mechanical scale of molecules and obeys quantum mechanical laws  Special role of quantum effects in biology: debated  Proliferation in fields of Quantum Biology  Quantum Neuroscience, Quantum Pharmacometrics, Quantum Chemistry, Quantum Proteomics 33 Source: Ball, P. (2011). The dawn of quantum biology. Nature. 474:272-74.
  35. 35. 24 Aug 2021 Quantum Neuroscience Higher-order Cognitive Processes: Learning, Attention, Memory Quantum Consciousness Hypothesis  The brain obeys quantum mechanics, but there are no special quantum effects operating in the substrate of the brain to produce consciousness  The brain is too big and too warm (Koch), and has short decoherence timescales (Tegmark)  Quantum neuroscience is inspired by the mathematical structure of quantum mechanics, not that there is something quantum-like taking place in the brain  In any case, the first step is enumerating the underlying physical processes of the brain (neural signaling) as the building blocks of higher-order behavior  Consciousness cannot be explained by classical mechanics and quantum effects such as entanglement and superposition might be involved (Penrose, Hameroff) Argument: Refutation (strongly supported): Sources: Koch, C. & Hepp, K. (2006). Quantum Mechanics in the Brain. Nature. 440(30):611-12. Tegmark, M. (2000). The importance of quantum decoherence in brain processes. Phys Rev E. 61(4):4194. Ball, P. (2011). The dawn of quantum biology. Nature. 474:272-74. 34
  36. 36. 24 Aug 2021 Quantum Neuroscience Agenda  Quantum Computing and the Brain  Quantum Information Techniques  Quantum Neuroscience Applications 1. Waves: EEG, fMRI, CT, PET integration 2. Quantum Biology  Superpositioned Data and Operator Technology 3. Neuroscience Physics  AdS/Brain (AdS/CFT Holographic Neuroscience)  Neuronal Gauge Theory  General Relativity of the Brain: Entropy = Energy  Black Hole Superconducting Condensates and Scalar Hair  Random Tensors (High-dimensional Indexing Technology)  Conclusion, Risks, and Future Implications 35
  37. 37. 24 Aug 2021 Quantum Neuroscience Level 1 Quantum Neuroscience Apps  Waves (quantum mechanics implicated)  Electrical: action potential, dendritic spikes  Calcium: astrocyte signaling, neurotransmitters  EEG, fMRI, CT, PET scan wavefunction data 1. Neural dynamics: integrate EEG-fMRI multiscalar spacetime and dynamics regimes (Breakspear) 2. Signal synchrony (diverse distances) (Nunez) 3. Quantum algorithms for MRI, CT, PET data processing (Lloyd) 4. EEG wavefunction modeling with Quantum Machine Learning  Quantum circuits for EEG machine learning  CNNs (Aishwarya), wavelet RNNs (Taha)  Parkinson’s treatment: 794 features 21 EEG channels (Koch) 36 QML: Quantum Machine Learning CNN: convolutional neural network, RNN: recurrent neural network (sequential data analysis) WAVES
  38. 38. 24 Aug 2021 Quantum Neuroscience EEG and Neural Dynamics Regimes  Integrate EEG and fMRI data at various spatiotemporal scales and dynamics regimes  Epileptic seizure: chaotic dynamics (straightforward)  Resting state: instability-bifurcation dynamics (system organizing parameter interrupted by countersignal)  Neural dynamics regimes vary by scale 37 Scale Dynamics Formulations 1 Single neuron Hodgkin-Huxley, integrate-and-fire, theta neurons 2 Local ensemble FitzHugh-Nagumo, Hindmarsh-Rose, Morris-Lecor 3 Population group (neural mass) Neural mass models (Jansen-Rit), mean-field (Wilson-Cowan), tractography, oscillation, network models 4 Whole brain (neural field theories) Neural field models, Kuramoto oscillators, multistability-bifurcation, directed percolation random graph phase transition, graph-based oscillation, Floquet theory, Hopf bifurcation, beyond-Turing instability Sources: Breakspear (2017). Papadopoulos, L., Lynn, C.W., Battaglia, D. & Bassett, D.S. (2020). Relations between large-scale brain connectivity and effects of regional stimulation depend on collective dynamical state. PLoS Comput Biol. 16(9). Coombes, S. (2005). Waves, bumps, and patterns in neural field theories. Biol Cybern. 93(2):91-108.
  39. 39. 24 Aug 2021 Quantum Neuroscience Neural Dynamics: Complex Statistics 38  Collective behavior of the brain generates unrecognized statistical distributions  Neural ensemble: normal distribution (FPE) and power law distribution (nonlinear FPE, fractional FPE)  Neural mass: Wilson-Cowan, Jansen-Rit, Floquet, ODE  Neural field theory: wavefunction, oscillation, bifurcation, PDE FPE: Fokker-Planck equation: partial differential equation describing the time evolution of the probability density function of particle velocity under the influence of drag forces; equivalent to the convection-diffusion equation in Brownian motion Source: Breakspear, M. (2017). Dynamic models of large-scale brain activity. Nat Neurosci. 20:340-52. Approach Description Statistical Distribution Neural Dynamics 1 Neural ensemble models Small groups of neurons, uncorrelated states Normal (Gaussian) Linear Fokker-Planck equation (FPE) 2 Small groups of neurons, correlated states Non-Gaussian but known (e.g. power law) Nonlinear FPE, Fractional FPE 3 Neural mass models Large-scale populations of interacting neurons Unrecognized Wilson-Cowan, Jansen- Rit, Floquet model, Glass networks, ODE 4 Neural field models (whole brain) Entire cortex as a continuous sheet Unrecognized Wavefunction, PDE, Oscillation analysis
  40. 40. 24 Aug 2021 Quantum Neuroscience Signal Synchrony  Synchrony as a bulk property of the brain  Synaptic signals arrive simultaneously but travel different distances, so speeds must vary  Seamless coordination of diverse signals  Evidence: axon propagation speeds  Electrophysiological data recorded at multiple spatial scales  Microscale current sources (produced by local field potentials at membrane surfaces) modeled in a macro-columnar structure, integrating properties related to  Magnitude, distribution, synchrony 39 Source: Nunez, P.L., Srinivasan, R. & Fields, R.D. (2015). EEG functional connectivity, axon delays and white matter disease. Clin Neurophysiol. 126(1):110-20.
  41. 41. 24 Aug 2021 Quantum Neuroscience Quantum Algorithms for MRI, CT, and PET  Reconstruct medical images captured in MRI, CT, and PET scanners  Quantum algorithms for image reconstruction with exponential speedup compared to classical methods  Input data as quantum states  Image reconstruction algorithms  MRI: inverse Fourier transform (reconstruction from k-space data (Fourier-transformed spatial frequency data from kx, ky space))  CT & PET: inverse Radon transform & Fourier Slice Theorem (reconstruction from a set of projections or line integrals over a function) 40 Source: Kiani, B.T., Villanyi, A. & Lloyd, S. (2020). Quantum Medical Imaging Algorithms. arXiv:2004.02036. Fourier slice theorem: the 1D Fourier transform of a projection at angle theta is equivalent to a slice of the original function’s 2D Fourier transform at angle theta
  42. 42. 24 Aug 2021 Quantum Neuroscience EEG Quantum Machine Learning  Quantum circuits for machine learning EEG data  Variational quantum classifiers (VQE), quantum annealing, hybrid quantum-classical CNNs  Predict macroscale cognitive states in standard decision-making dataset  Quantum wavelet neural networks (RNNs)  Parkinson’s disease practical target  Quantum machine learning classification  EEG data for Parkinson’s disease patients  Evaluate candidates for Deep Brain Stimulation  Extract 794 features from 21 EEG channels 41 Sources: Aishwarya et al. (2020) Quantum Computational Techniques for Prediction of Cognitive State of Human Mind from EEG Signals. J Quantum Comput. 2(4):157-70. Taha et al. (2018) EEG signals classification based on autoregressive and inherently quantum recurrent neural network. Int J Comput Appl Technol. 58(4):340. Koch et al. (2019) Automated machine learning for EEG- based classification of Parkinson’s disease patients. 2019 IEEE Intl Conf on Big Data (Big Data). QML: Quantum Machine Learning CNN: convolutional neural network, RNN: recurrent neural network (sequential data analysis) Quantum circuit for EEG data analysis
  43. 43. 24 Aug 2021 Quantum Neuroscience Level 2 Quantum Neuroscience Apps  Quantum Biology state modeling  Superpositioned data and quantum probability  System evolution with operator technology  Ladder operators and quantum master equations  Biological quantum mathematics  p-adic scaling: more aggressive tumor growth scaling based on p-adic numbers (Fermat’s last theorem proof)  Growth in p-adic number systems (p is prime): compute complex-number differences between prime numbers, to give more of an exponential than unitary scaling model  Environmental feedback loops in biological systems  Quantum version of Helmholtz sensation-perception theory: a unitary operator describes the process of interaction between the sensation and perception states 42 Sources: Dragovich, B., Khrennikov, A.Y., Kozyrev, S.V. & Misic, N.Z. (2021) p-Adic mathematics and theoretical biology. BioSystems. 201(104288). Basieva, I., Khrennikov, A. & Ozawa, M. (2021) Quantum-like modeling in biology with open quantum systems and instruments. BioSystems. 201(104328). DYNAMICS
  44. 44. 24 Aug 2021 Quantum Neuroscience Evolve the Quantum System  Traditional approaches  Schrödinger and Heisenberg dynamics, but limited…  Heisenberg equation of motion: general approximation of movement and does not include temperature  Thermality is an important quantum system attribute (e.g. chaos, superconducting materials, black holes)  Schrödinger wavefunction limited to pure quantum states as opposed to mixed states (combinations of states)  Modern approaches  Ladder operators (straightforward first-line modeling)  Quantum master equations (more nuanced Lindbladian) 43 Sources: Qi, X.-L. & Streicher, A. (2019) Quantum epidemiology: operator growth, thermal effects, and SYK. J High Energ Phys. 08(012). Buice, M.A. & Cowan, J.D. (2009). Statistical Mechanics of the Neocortex. Prog Biophys Mol Biol. 99(2-3):53-86. Schrödinger wave equation Wavefunction (Ψ)
  45. 45. 24 Aug 2021 Quantum Neuroscience Ladder Operators and Master Equations  Ladder operators (creation-annihilation operators)  Standard operator (mathematical function) used to raise and lower quantum system tiers (between eigenvalues)  Use ladder operators to describe the lifecycles of healthy and tumor cells (time evolution given by a non-Hermitian Hamiltonian)  Introduce medical intervention by adding an (energy-based) Hamiltonian term to limit and reverse the growth of the tumor cells  Quantum master equation (Lindbladian)  Quantum version of the classical master equation (system time evolution as a probabilistic combination of states)  Lindbladian (simplest form): quantum Markov model  Stochastic model in which each subsequent event depends only on the previous event, quantum probability replaces classical probability 44 Sources: Bagarello, F. & Gargano, G. (2018) Non-Hermitian operator modelling of basic cancer cell dynamics. Entropy. 20(4):270. Basieva, I., Khrennikov, A. & Ozawa, M. (2021) Quantum-like modeling in biology with open quantum systems and instruments. BioSystems. 201(104328).
  46. 46. 24 Aug 2021 Quantum Neuroscience Superpositioned Data  Superpositioned Data  Data modeled in superposition as the quantum information representation of all possible system states simultaneously  Two-state neural signaling model: Quiescent, Firing  Three-state neural signaling model: Quiescent, Active, Resting 45 Sources: Basieva, I., Khrennikov, A. & Ozawa, M. (2021) Quantum-like modeling in biology with open quantum systems and instruments. BioSystems. 201(104328). Buice, M.A. & Cowan, J.D. (2009). Statistical Mechanics of the Neocortex. Prog Biophys Mol Biol. 99(2-3):53-86. Växjö (Sweden) two-state neural signaling model: Quiescent, Firing Cowan three-state neural signaling model: Quiescent, Active, Resting Ladder operators create and annihilate spikes (instead of neurons) All possible states in superposition
  47. 47. 24 Aug 2021 Quantum Neuroscience Quantum Probability  States evaluated with quantum probability  Quantum probability: quantum mechanical rules for assigning probability  Including due to interference effects that violate the law of total probability and commutativity in conjunction in classical systems  Quantum variant of total probability  POVMs (positive operator valued measures): positive measures on a quantum subsystem of the effect of a measurement performed on the larger system, POVMs give an interference term for incompatible observables  Quantum Bayesianism: QBism (“cubism”)  Incorporates subjective (observer-based) aspects 46 Sources: Fuchs, C.A. & Schack, R. (2011). A quantum-Bayesian route to quantum-state space. Found Phys. 41:345-56. Asano, M., Basieva, I., Khrennikov, A. et al. (2015). Quantum Information Biology. Found Phys. 45(N10):1362-78. Each point in the Bloch sphere is the possible quantum state of a qubit. In QBism, all quantum states are representations of personal probabilities.
  48. 48. 24 Aug 2021 Quantum Neuroscience Operator Technologies  Operator technology: since cannot measure or evolve a quantum system directly, use operators (mathematical functions) as an indirect lever  Scrambling, chaos, OTOCs, uncertainty relation, POVM  SYK Hamiltonian, Scrambling Hamiltonian (streamlined)  Computational complexity  Page-time-based method (black holes are fast-scramblers)  Simple entropy-based method (black holes are not fast-scramblers)  Size-winding: wind-unwind the system  Teleportation-by-operator-size and peaked-size  AdS/ML neural operators: ODE, PDE, RG  POVM: overall system effect on subsystem 47 POVM: positive-operator valued measure (quantum variant of total (classical) probability) Source: Brown, A.R., Gharibyan, H., Leichenauer, S. et al. (2019). Quantum Gravity in the Lab: Teleportation by Size and Traversable Wormholes. aXiv:1911.06314v1. Operator Tech
  49. 49. 24 Aug 2021 Quantum Neuroscience Operator Technologies  Scrambling  How quickly information spreads out in a quantum system so that a local measurement is no longer possible, but recovered later in a different part of the system (quantum memory implication)  Chaos: seemingly random disorder governed by deterministic laws and sensitivity to initial conditions  Lyapunov exponent: ballistic growth followed by saturation  OTOCs (out-of-time-order correlation) functions  Functions (operators) used to evolve a quantum system back or forward in time to measure chaos and scrambling time  Size-winding: wind-unwind the system  Winding-size distributions: coefficients in the size basis acquire an imaginary phase that accelerates the winding and unwinding of operator size distribution  Conventional-size distributions: uniformly summing amplitude coefficients for wavefunction approximation 48 Source: Swingle, B., Bentsen, G., Schleier-Smith, M. & Hayden, P. (2016). Measuring the scrambling of quantum information. Phys Rev A. 94(040302).
  50. 50. 24 Aug 2021 Quantum Neuroscience Operator Tech: Neural Operators  “Neural” = neural network (NN) method (machine learning)  Neural ODE: NN architecture whose weights are smooth functions of continuous depth  Input evolved to output with a trainable differential equation, instead of mapping discrete layers (Chen 2015)  Neural PDE: NN architecture that uses neural operators to map between infinite-dimensional spaces  Fourier neural operator solves all instances of the PDE family in multiple spatial discretizations (by parameterizing the integral kernel directly in Fourier space) (Li 2021)  Neural RG: NN renormalization group  Learns the exact holographic mapping between bulk and boundary partition functions (Hu 2019) 49 Sources: Chen et al. (2018). Neural Ordinary Differential Equations. Adv Neural Info Proc Sys. Red Hook, NY: Curran Associates Inc. Pp. 6571-83. Li et al. (2021). Fourier neural operator for parametric partial differential equations. arXiv:2010.08895v3. Hu et al. (2019). Machine Learning Holographic Mapping by Neural Network Renormalization Group. Phys Rev Res. 2(023369). Neural Operator Tech
  51. 51. 24 Aug 2021 Quantum Neuroscience Agenda  Quantum Computing and the Brain  Quantum Information Techniques  Quantum Neuroscience Applications 1. Waves: EEG, fMRI, CT, PET integration 2. Quantum Biology  Superpositioned Data and Operator Technology 3. Neuroscience Physics  AdS/Brain (AdS/CFT Holographic Neuroscience)  Neuronal Gauge Theory  General Relativity of the Brain: Entropy = Energy  Black Hole Superconducting Condensates and Scalar Hair  Random Tensors (High-dimensional Indexing Technology)  Conclusion, Risks, and Future Implications 50
  52. 52. 24 Aug 2021 Quantum Neuroscience Level 3 Quantum Neuroscience Apps  Neuroscience physics: neuroscience interpretation of foundational physics findings 1. AdS/Brain Theory  Ads/Neural Signaling  AdS/Information Storage (Memory) 2. Neuronal Gauge Theory (Symmetry) 3. GR of the Brain: Entropy = Energy 4. Superconducting Condensates  Putting scalar hair on a black hole 5. Random Tensors (high-dimensionality) 51 Source: Swan, M. dos Santos, R.P., Lebedev, M.A. and Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific. BLACK HOLES
  53. 53. 24 Aug 2021 Quantum Neuroscience Neuroscience Physics 52 Neuroscience Physics Model Quantum Properties 1 AdS/Brain Theory • Ads/Neural Signaling • AdS/Information Storage (Memory) UV-IR correlations, topological entanglement entropy, information scrambling, phase transition [Floquet periodicity dynamics, bMERA TNs] Info scrambling (information storage): highly excited states (energy levels); exploit new matter phases in systems that do not reach thermal equilibrium 2 Neuronal Gauge Theory Symmetry, gauge invariant quantity, gauge field rebalancing, multiscalar environment 3 General Relativity of the Brain: Entropy = Energy Thermality, 3D spacetimes, energy levels, entropy (calculable Hamiltonian entropy=energy) 4 Black Holes and Superconducting Condensates Order-disorder, criticality phase transitions, thermality, apply (EM) fields to induce condensate 5 Random Tensors (High-dimension Indexing Technology) High-d, lattices, color theory, gauge color theory, tree-branching, eigenvalue-based spatiality Source: Swan, M. dos Santos, R.P., Lebedev, M.A. and Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific.  Enabled by quantum properties
  54. 54. 24 Aug 2021 Quantum Neuroscience Neuroscience Physics 1. AdS/Brain Theories  AdS/CFT Correspondence  Mathematics for calculating any physical system with a bulk volume and a boundary surface (planet, brain, this room)  AdS/Neural Signaling (multiscalar phase transitions)  Floquet periodicity-based dynamics, bMERA tensor networks, evolve with continuous-time quantum walks  AdS/Information Storage (memory)  Highly-critical states trigger special functionality in systems (new matter phases, memory storage) Sources: Swan, M. dos Santos, R.P., Lebedev, M.A. and Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific. Dvali, G. (2018). Black Holes as Brains: Neural Networks with Area Law Entropy. arXiv:1801.03918v1. 53
  55. 55. 24 Aug 2021 Quantum Neuroscience  A physical system with a bulk volume can be described by a boundary theory in one less dimension  A gravity theory (bulk volume) is equal to a gauge theory or a quantum field theory (boundary surface) in one less dimension  AdS5/CFT4 (5d bulk gravity)=(4d Yang-Mills supersymmetry QFT)  The AdS/CFT Math: AdS/DIY  Metric (ds=), Operators (O=), Action (S=), Hamiltonian (H=) AdS/CFT Correspondence (Anti-de Sitter Space/Conformal Field Theory) 54 Sources: Maldacena, J. (1998). The large N limit of superconformal field theories and supergravity. Adv Theor Math Phys. 2:231-52. Harlow, D. (2017). TASI Lectures on the Emergence of Bulk Physics in AdS/CFT. Physics at the Fundamental Frontier. arXiv:1802.01040. AdS/CFT Escher Circle Limits Error correction tiling  Implications for  Geometry emerges from entanglement = QECC  Time/space emergence  Black hole information paradox
  56. 56. 24 Aug 2021 Quantum Neuroscience  AdS/SYK (Sachdev-Yi-Kitaev) model  Solvable model of strongly interacting fermions  AdS/SYK: black holes and unconventional materials have similar properties related to mass, temperature, and charge  SYK Hamiltonian (HSYK) finds wavefunctions for 2 or 4 fermions  Or up to 42 in a black-hole-on-a-superconducting-chip formulation AdS/CFT Duality: Solve in either Direction 55 Sources: Sachdev, S. (2010). Strange metals and the AdS/CFT correspondence. J Stat Mech. 1011(P11022).. Pikulin, D.I. & Franz, M. (2017). Black hole on a chip: Proposal for a physical realization of the Sachdev-Ye-Kitaev model in a solid-state system. Physical Review X. 7(031006):1-16. Direction Domain Known Unknown 1 Boundary-to-bulk Theoretical physics Standard quantum field theory (boundary) Quantum gravity (bulk) 2 Bulk-to-boundary (AdS/SYK) Condensed matter, superconducting Classical gravity (bulk) Unconventional materials quantum field theory (boundary) Ψ : Wavefunction HSYK : SYK Hamiltonian (Operator describing evolution and energy of system) Bethe-Salpeter equation
  57. 57. 24 Aug 2021 Quantum Neuroscience  Each level is the boundary for another bulk AdS/Brain: (first) Multi-tier Correspondence 56 Neuron Network AdS/Brain Multi-tier Holographic Correspondence Synapse Molecule Tier Scale Signal AdS/Brain 1 Network 10-2 Local field potential Boundary 2 Neuron 10-4 Action potential Bulk Boundary 3 Synapse 10-6 Dendritic spike Bulk Boundary 4 Molecule 10-10 Ion docking Bulk Bulk regimes all the way down (not turtles) Source: Swan, M. dos Santos, R.P., Lebedev, M.A. and Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific.
  58. 58. 24 Aug 2021 Quantum Neuroscience  Multiscalar renormalization scheme (tensor networks)  Flow from boundary surface (UV) to bulk (IR) and back up to boundary to discover hidden correlations in both AdS/MERA 57 MERA: Multiscale Entanglement Renormalization Ansatz (guess) Source: Vidal, G. (2007). Entanglement renormalization. Phys Rev Lett. 99(220405). Boundary Bulk Boundary Vidal, 2007 Swingle, 2012 McMahon, 2020 Vidal, 2007 Renormalization: physical system viewed at different scales Tensor network: mathematical tool for the efficient representation of quantum states (high-dimensional data in the form of tensors); tensor networks factor a high-order tensor (a tensor with a large number of indices) into a set of low-order tensors whose indices can be summed (contracted) in the form of a network
  59. 59. 24 Aug 2021 Quantum Neuroscience AdS/Brain implementation with bMERA  Different flavors of MERA  All renormalize entanglement (correlation) across system tiers 58 MERA cMERA dMERA bMERA Continuous spacetime MERA Deep MERA tensor network on NISQ devices Multiscalar neural field theory Multiscalar entanglement renormalization network Vidal, 2007 Nozaki et al., 2012 Kim & Swingle, 2017 Swan et al., 2022  bMERA (brainMERA)  Renormalize system entanglement (correlation) to obtain neural signaling action across multiple scale layers Source: Swan, M. dos Santos, R.P., Lebedev, M.A. and Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific.
  60. 60. 24 Aug 2021 Quantum Neuroscience Neuroscience Physics 2. Neuronal Gauge Theory  Model multiscalar neural signaling operation on the basis of gauge invariance and global symmetry  Gauge invariance: overall system ordering property (global symmetry) not changing in the face of small local transformations Sources: Weinberg, S. (1980). Conceptual foundations of the unified theory of weak and electromagnetic interactions. Science. 210(4475):1212-18. (Nobel lecture). Sengupta, B., Tozzi, A., Cooray, G.K. et al. (2016) Towards a Neuronal Gauge Theory. PLoS Biol. 14(3). Symmetry Interpretation Meaning Everyday Balance Looking the same from different points of view Physics Invariance 59 Element Generic Gauge Theory Neuronal Gauge Theory Symmetry Different locations Central nervous system Local transformations Local forces acting on the system Sensory stimuli Gauge field Zone of invariance to local transformations Counter-compensation for local perturbations Lagrangian System dynamics function Free-energy Lagrangian Neuronal Gauge Theory: Four Elements Symmetry: property of physical systems looking the same from different points of view (face, cube, the laws of nature) Symmetry breaking: phase transition Gauge theory: field theory in which the Lagrangian (state of a dynamic system) does not change (is invariant) under local gauge transformations (changes between possible gauges (levels or degrees of freedom) in a system)
  61. 61. 24 Aug 2021 Quantum Neuroscience Neuronal Gauge Theory  Premise: the brain is a multiscalar system with global symmetry; the invariant property (free energy minimization) is broken and rebalanced  Neural signaling breaks the symmetry and gauge fields are applied to rebalance the invariant quantity (free energy)  The gauge fields are part of the brain environment and apply continuous forces to act on the brain elements to produce local perturbations that counteract the effect of the local force stimulus as neural signals are dispatched, in order to bring the system back into a resting state  The gauge field rebalancing mechanism coordinates the multiscalar tiers of the brain on the basis of conserving the gauge-invariant quantity  Here, free energy minimization, but could be otherwise Source: Sengupta, B., Tozzi, A., Cooray, G.K. et al. (2016) Towards a Neuronal Gauge Theory. PLoS Biol. 14(3). Images Source: Serna, M. (2005). Geometry of Gauge Theories. Tiny Physics. 60
  62. 62. 24 Aug 2021 Quantum Neuroscience Symmetry, Order, Matter Phases  Symmetry-facilitated discovery  Ordered-disordered matter phases  Discrete time crystals: novel material phases that do not reach thermal equilibrium (quantum memory implication)  IR physics (low-energy physics) explains the exotic emergent behavior of strange metals (non-Fermi liquids) at low-energy in superconducting systems  Crystals: repeating structure  (Space) crystals: repeating in space  Time crystals: repeating in time  Time translation symmetry: moving the times of events through a common interval Sources: Else, D.V., Thorngren, R. & Senthil, T. (2021). Non-Fermi liquids as ersatz Fermi liquids: general constraints on compressible metals. arXiv:2007.07896v4. Monroe laboratory: Zhang, J., Hess, P.W., Kyprianidis, A. et al. (2016) Observation of a Discrete Time Crystal. Nature. 543:217-20. (many-body localization) Discrete time crystals 61
  63. 63. 24 Aug 2021 Quantum Neuroscience Neuroscience Physics 3. GR of the Brain: Entropy = Energy  Special Relativity (1905)  A theory equating mass and energy (E=mc2), with time dilation effect  Special case of relative motion in which objects are traveling at a constant velocity relative to each other  General relativity (1915)  Theory of gravity based on how mass and energy warp spacetime  A geometry-based theory of gravity (versus Newton’s mass-based theory)  General motion of objects including changes in velocity (acceleration) General Relativity Gμν = Tμν Special Relativity E = mc2 Gravity = Energy Mass has unlocked Energy 62
  64. 64. 24 Aug 2021 Quantum Neuroscience Problem: the Einstein equations for gravity exist, but are intractable General Relativity Source: Tong, D. (2015). What is General Relativity? DAMPT Cambridge. https://plus.maths.org/content/what-general-relativity Gravity = Energy Gμν = Tμν Einstein tensor = Energy-momentum (stress) tensor Spacetime (gravity) = the distribution of energy and momentum in the universe The curvature of spacetime, the warping effect a given amount of mass and energy has on spacetime (reflected as gravity)… …is calculated from the way that energy, momentum (mass), and pressure are distributed throughout the universe Rμν – ½ Rgμν = 8πG/c4 Tμν To find the curvature, the spacetime warping effect (i.e. gravity) of a given amount of mass and energy… …calculate “Einstein’s equations” - the 10 permutations of Tμν implied by the various indices1 for a particular mass and energy (generally an intractable calculation) Rμν : Ricci curvature tensor R : Scalar curvature gμν : Metric tensor 1The energy-momentum tensor Tμν related to energy (T00), momentum (mass) (T01), and pressure (T11) • T00 energy, how causes time to speed or slow (indices: time and time) • T01 momentum (speed and mass) (indices: time and space) • T02 , T03 • T11 pressure, how causes space to stretch (indices: space and space) • T12 , T13 , T22 , T23 , T33 G : Newton’s gravitational constant 63
  65. 65. 24 Aug 2021 Quantum Neuroscience General Relativity workarounds  4d: difficult to calculate due to propagating waves  3d: topological field theory without any local degrees of freedom (easier to calculate)  2d: simplified 2d gravity theories; locally-flat models; solve Einstein gravity in 2d: 1 space dimension, 1 time  CGHS (Callan-Giddings-Harvey-Strominger) (1992)  Jackiw-Teitelboim (2d dilaton coupling theory) (1990)  Liouville gravity (2d conformal field theory) (2003)  Improved method for solving GR  First law of entanglement entropy (2014) 64
  66. 66. 24 Aug 2021 Quantum Neuroscience First Law of Entanglement Entropy (FLEE)  GR: gravity = spacetime curvature (geometry) = energy  Have equations for gravity, but generally intractable  FLEE: entropy = energy  Obtain solvable equations for gravity  First law of entanglement entropy (FLEE)  Provide a first law of thermodynamics (energy conservation) for black hole physics and the AdS/CFT correspondence  Change in boundary CFT entanglement entropy = change in bulk Hamiltonian energy (for a specific ball-shaped spatial region)  Entanglement entropy = energy relation leads to a constraint on bulk spacetimes equivalent to linearized gravitational equations  RESULT: solvable Einstein equations (entropy = energy) Source: Faulkner, T., Guica, M., Hartman, T. et al. (2014). Gravitation from Entanglement in Holographic CFTs. JHEP. 03(2014)051. 65
  67. 67. 24 Aug 2021 Quantum Neuroscience AdS/CFT and General Relativity  AdS/CFT (1998): solvable bulk-boundary model  Bulk structure (spacetime and gravitational physics) emerges from the dynamics of strongly coupled CFT degrees of freedom  Ryu-Takayanagi (2006): entanglement entropy  Use boundary CFT entanglement entropy to calculate bulk spacetime geometry as the area of a bulk extremal surface (geodesics)  First law of entanglement entropy (2014)  Change in boundary entropy = change in bulk energy (Hamiltonian)  Energy = Gravity = Geometry = Entropy Source: Faulkner, T., Guica, M., Hartman, T. et al. (2014). Gravitation from Entanglement in Holographic CFTs. JHEP. 03(2014)051. GR: FLEE: Geometry = Entropy Energy = Entropy Energy = Gravity = Geometry = Entropy Result: FLEE: capstone formulation equating energy and entropy Energy (Hamiltonian) is central to quantum systems but did not have models previously for solving AdS/CFT entropy=energy 66
  68. 68. 24 Aug 2021 Quantum Neuroscience GR of the Brain: Entropy = Energy  How are Einstein’s GR equations relevant to the brain?  Solvable gravity model for problems in this form  Brain (biological systems): energy too is central  AdS/Brain: multiscalar geometric calculation re: entropy  Calculate area of bulk surface using geodesic curves  Model neural signaling as UV-IR correlation-related phase transition  AdS/Brain-FLEE: multiscalar energy calculation  Energy as governing gauge invariant quantity in neuroscience  Model neural signaling as Hamiltonian-based energy transfer  Neuroscience formalism linking entropy and energy  Brain Hamiltonian = brain entanglement entropy (UV-IR)  Energy-based calculation denominated in Hamiltonians Source: Faulkner, T., Guica, M., Hartman, T. et al. (2014). Gravitation from Entanglement in Holographic CFTs. JHEP. 03(2014)051. Benefit of FLEE: solvable Hamiltonian- based energy calculation equated to entropy 67
  69. 69. 24 Aug 2021 Quantum Neuroscience Neuroscience Physics 4. Superconducting Condensates Source: Hartnoll, S.A., Horowitz, G.T., Kruthoff, J. & Santos, J.E. (2021). Diving into a holographic superconductor. SciPost Phys. 10(009). 68  Put scalar hair on a black hole -> phase transition  Black holes = the “model organism” of physics  Properties: entropy, thermality (temperature), mass, UV-IR correlations, information scrambling, chaos  Quantum liquids: systems with order & disorder phases  Black holes, superconducting materials, brains  Solid: organized by order (max particle stability, lattice)  Gas: organized by disorder (max particle interaction, randomness)  AdS/Superconducting: produce superconducting phase transition in quantum liquids  AdS/Brain: brain is a quantum liquid  Neural signaling is a phase transition with both ordered and disordered aspects
  70. 70. 24 Aug 2021 Quantum Neuroscience Black Hole Superconductor Source: Hartnoll, S.A., Horowitz, G.T., Kruthoff, J. & Santos, J.E. (2021). Diving into a holographic superconductor. SciPost Phys. 10(009). 69  Black-hole-in-a-box toy model (gas, particle)  Manipulate to form a condensate halo around the black hole  Apply an external electrical field (battery), condensate becomes superconducting, per the Higgs mechanism  Higgs mechanism “gives particles their mass”  Higgs field is a universal field throughout the universe causing particles to become “heavy” as they pass through a medium, giving them drag, or mass  Black hole model: particles becoming massive are photons  Prevents electric and magnetic fields from getting through the medium, causing the medium to become superconducting (electrons flow freely with infinite conductivity and zero resistance)  Result: Obtain AdS/Superconducting phase transition
  71. 71. 24 Aug 2021 Quantum Neuroscience Neuroscience Physics 5. Random Tensors (High-d Tech)  For strongly interacting quantum many-body systems… 1. SYK model (condensed matter physics)  Limit computational cost with quenched disorder (path integrals and random variable selection from a Gaussian distribution) 2. Random tensors: 3d+ (extend random matrices: 2d)  Limit computational cost with 1/N limit (perturbative expansion), colored-uncolored tensors (index only interacts with its own color), and simplicial (triangle/tetrahedron-based) algebra  Reach melonic limit with tensor indexing mechanism (degree) (vs genus in matrices) and without vector modes in the tensor traces  Tested for 5d systems (tensors of rank-5): using algebras with 5-simplex interaction (stemming from Group Field Theory) 3. Matrix quantum mechanics (more than one matrix) Sources: Carrozza, S. & Harribey, S. (2021). Melonic large N limit of 5-index irreducible random tensors. arXiv:2104.03665v1. Han, X. & Hartnoll, S.A. (2020). Deep Quantum Geometry of Matrices. Phys Rev X. 10(011069). 70
  72. 72. 24 Aug 2021 Quantum Neuroscience Tensors: Naturally High-dimensional  Tackle arbitrarily large dimensions and computational complexity by decomposing into indexed elements  Melonic diagram: (melon-shaped) graph expression of a solvable large N (high-dimensional) model  Graph fermion interactions as system geometry  Fields labeled as (tetrahedral) vertices  Each pair of fields has a pair of indices in common Melonic vacuum diagrams up to order g8 Source: Tarnopolsky, G. (2021). Operator spectrum and spontaneous symmetry breaking in SYK-like models. Strings 2021. ICTP- SAIFR, São Paulo. June 24, 2021. 71
  73. 73. 24 Aug 2021 Quantum Neuroscience Tensor Field Theory of neural signaling  AdS/Brain Tensor Field Theory (enabled by index tech)  Index the four dimensions (network-neuron-synapse-molecule) with rank-4 tensor degree 1/N expansion random tensors  Tensor field theories: local field theories whose fields transform as a tensor under a global or local symmetry group  Neural QCD: Feynman diagram for neural signaling  Feynman weights for neural signaling events (not photon- electron force particles exchange and boson-WZ particles)  Model quiescent-to-firing as the matrix(2d)-to- tensor(3+d) phase transition (planar-to-melonic)  Tune coupling constants to critical values  At the critical point, the model transitions to a continuum theory of random surfaces (random infinitely refined surfaces) Source: Benedetti, D., Gurau, R., Harribey, S. & Suzuki, K. (2020). Long-range multi-scalar models at three loops. arXiv:2007.04603v2. 72 Index Tech
  74. 74. 24 Aug 2021 Quantum Neuroscience Summary Neuroscience Physics Applications  AdS/Brain: multi-tier correspondence  Renormalize dynamics of network-neuron-synapse-molecule  Neuronal gauge theory  Rebalance gauge invariant quantity of global symmetry  GR of the Brain: Gravity = Geometry = Entropy = Energy  Neural signaling as an entropy and energy problem  Superconducting condensate ordered-disordered phases  Produce phase transition (neural signal) by applying field (scalar hair) to trigger superconducting phase  Random tensors (high-dimensionality)  Produce phase transition (neural signal) by tuning 73
  75. 75. 24 Aug 2021 Quantum Neuroscience Agenda  Quantum Computing and the Brain  Quantum Information Techniques  Quantum Neuroscience Applications 1. Waves: EEG, fMRI, CT, PET integration 2. Quantum Biology  Superpositioned Data and Operator Technology 3. Neuroscience Physics  AdS/Brain (AdS/CFT Holographic Neuroscience)  Neuronal Gauge Theory  General Relativity of the Brain: Entropy = Energy  Black Hole Superconducting Condensates and Scalar Hair  Random Tensors (High-dimensional Indexing Technology)  Conclusion, Risks, and Future Implications 74
  76. 76. 24 Aug 2021 Quantum Neuroscience Near-term Neuropathology Interventions  New three-step medical paradigm  DNA technology (genomics-based medicine)  Problem: not producing correct proteins  Sequence: routine genomic sequencing  Edit: CRISPR gene editing (human-approved 2021)  RNA technology (expression, mRNA delivery, RNAi)  Protein technology (proteomics, synaptomics)  Screening + therapeutic intervention  Tackle large-scale biological problem classes  Clear plaques: heart disease, AD, stroke  Atherosclerotic, neurological, arterial  Control mutation damage and unchecked growth  Bioremediation of waste, enhanced immune system 75 Intellia first human-approved CRISPR intervention (amyloidosis Jun 2021). Source: Swan, M. dos Santos, R.P., Lebedev, M.A. and Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific.
  77. 77. 24 Aug 2021 Quantum Neuroscience Consumer-controlled Data  Personalized EHR & genomic sequencing  Whole human genome sequencing (3 bn SNPs)  Nebular Genomics ($299 + monthly subscription)  Dante Labs  Partial human genome sequencing (1.2 mn SNPs)  23andme, 10 mn customers (2019) ($199)  Sequencing.com (DNA App Store)  800 mn – 2 bn personal genome sequences by 2030  Why personal genomic profiles are useful  Ancestry, trait, and health information  Join relevant clinical trials (ClinicalTrails.gov)  Health blockchain data monetization (SOLVE.care)  Immediate status look-up per new research 76 DTC whole genome sequencing $299 Sequencing.com DNA App Store DTC: Direct to Consumer offering (no physician needed)
  78. 78. 24 Aug 2021 Quantum Neuroscience Neurobiological Disease  Degenerative Disease  Alzheimer’s disease, Parkinson’s disease, Huntington’s disease  PTSD, anxiety, autism spectrum  Cancer (Actionable Tumors List)  100+ types of brain cancer: benign neoplasms (pilocytic astrocytoma) to malignant tumors (glioblastoma)  Machine learn methylation profiles  Stroke  Ischemic (blockage) (50%)  Hemorrhagic (leaks) (50%) 77 Blood leak (hemorrhagic) Blood clot (ischemic) Sources: Hanahan, D. & Weinberg, R.A. (2011). Hallmarks of Cancer: The Next Generation. Cell. 144:646-74. Capper, D., Jones, D.T.W., Sill, M. et al. (2018). DNA methylation-based classification of central nervous system tumors. Nature. 555:469-74.
  79. 79. 24 Aug 2021 Quantum Neuroscience Galleri Blood Test Cancer Blood Test for over 50 Cancer Types 78 Source: Galleri multi-cancer early detection. (2021). Types of cancer detected. https://www.healthline.com/health-news/this-new-test-can-detect-50-types-of-cancer-from-a-single-blood-draw Cancer Cancer Cancer 1 Adrenal Cortical Carcinoma 18 Larynx 35 Penis 2 Ampulla of Vater 19 Leukemia 36 Plasma Cell Myeloma and Plasma Cell Disorders 3 Anus 20 Liver 37 Prostate 4 Appendix, Carcinoma 21 Lung 38 Pancreas, exocrine 5 Bile Ducts, Distal 22 Lymphoma (Hodgkin and Non-Hodgkin) 39 Small Intestine 6 Bile Ducts, Intrahepatic 23 Melanoma of the Skin 40 Soft Tissue Sarcoma of the Abdomen and Thoracic Visceral Organs 7 Bile Ducts, Perihilar 24 Mesothelioma, Malignant Pleural 41 Soft Tissue Sarcoma of the Head and Neck 8 Bladder, Urinary 25 Merkel Cell Carcinoma 42 Soft Tissue Sarcoma of the Retroperitoneum 9 Bone 26 Nasal Cavity and Paranasal Sinuses 43 Soft Tissue Sarcoma of the Trunk and Extremities 10 Breast 27 Nasopharynx 44 Soft Tissue Sarcoma Unusual Histologies and Sites 11 Cervix 28 Neuroendocrine Tumors of the Appendix 45 Stomach 12 Colon and Rectum 29 Neuroendocrine Tumors of the Colon and Rectum 46 Testis 13 Esophagus and Esophagogastric Junction 30 Neuroendocrine Tumors of the Pancreas 47 Uterus, Carcinoma and Carcinosarcoma 14 Gallbladder 31 Oral Cavity 48 Uterus, Sarcoma 15 Gastrointestinal Stromal Tumor 32 Oropharynx (HPV-Mediated, p16+) 49 Ureter (and Renal Pelvis) 16 Gestational Trophoblastic Neoplasms 33 Oropharynx (p16-) and Hypopharynx 50 Vagina 17 Kidney 34 Ovary, Fallopian Tube and Primary Peritoneum 51 Vulva  Roll-out 2Q 2021 routine check-up Providence (WA state)
  80. 80. 24 Aug 2021 Quantum Neuroscience Personalized Cancer Immunotherapy  Cancer treatments: surgery, chemotherapy, radiation therapy, immunotherapies  Immunotherapies (stimulate or suppress the immune system to fight cancer)  Personalized vaccines  Neoantigens (individual tumor-specific antigens)  Routine cancer tumor genome sequencing  Checkpoint blockade  Immune-checkpoint inhibitors (PD-L1, PD-L2 ligands)  Adaptive T cell therapy  Antigen receptor T cell therapies (tumor-specific T cells) 79 Source: Blass, E. & Ott, P.A. (2021). Advances in the development of personalized neoantigen-based therapeutic cancer vaccines. Nat Rev Clin Onc. 18:215-29. Personalized Cancer Vaccine Clinical Trials for Melanoma and Glioblastoma
  81. 81. 24 Aug 2021 Quantum Neuroscience Personalized Genomics for Brain Disease  Genome + synaptome (synapse proteome) data analysis  133 brain diseases caused by mutations  Neurological (AD, PD), motor, affective, metabolic disease  Synapse proteins are changed more than 20% in Alzheimer’s disease 80 Sources: Grant, S.G.N. (2019). Synapse diversity and synaptome architecture in human genetic disorders. Hum Mol Gen. 28(R2):R219-25. Hesse, R. Hurtado, M.L., Jackson, R.J. et al. (2019). Comparative profiling of the synaptic proteome from Alzheimer’s disease patients with focus on the APOE genotype. Acta Neuropath. Comm. 7(214). Field Focus Definition Completion 1 Genome Genes All genetic material of an organism Human, 2001 2 Connectome Neurons All neural connections in the brain Fruit fly, 2018 3 Synaptome Synapses All synapses in the brain and their proteins Mouse, 2020  Downregulation of synaptic function  PSD, CaMKIIa, App, Syngap, GluA, Plp1, Vcan, Hapln1, CRMP, Ras, Sh3gl, PKA, Shank3
  82. 82. 24 Aug 2021 Quantum Neuroscience Alzheimer’s Disease Genomics  Alzheimer’s Disease profile  APOE ε2: very low risk (rare)  APOE ε3: neutral risk (predominant genotype)  APOE ε4: higher risk (2-3% population has 2 copies, 25% has one copy)  Non-deterministic  ApoE4 health social network (ApoE4.info) 81 Sources: https://www.nia.nih.gov/health/alzheimers-disease-genetics-fact-sheet , https://www.snpedia.com/index.php/APOE The APOE genomic profile consists of two SNPs: rs429358 and rs7412
  83. 83. 24 Aug 2021 Quantum Neuroscience Alzheimer’s Disease and CRISPR  Therapeutic genome editing strategies  APOe, APP, PSEN1, PSEN2  Alter amyloid-beta Aβ metabolism  Engage protective vs higher risk profile  Parkinson’s disease genomics  LRRK2 (G2019S) rs34637584 rs3761863  GBA (N370S) rs76763715 (23andme: i4000415) 82 Sources: Seto, M., Weiner, R.L., Dumitrescu, L. & Hohman, T.J. (2021). Protective genes and pathways in Alzheimer’s disease: moving towards precision interventions. Molecular Neurodegeneration. 16(29). Hanafy, A.S., Schoch, S. & Lamprecht, A. (2020). CRISPR/Cas9 Delivery Potentials in Alzheimer’s Disease Management: A Mini Review. Pharmaceutics. 12(0801). ~400 SNPs, ~40 higher impact
  84. 84. 24 Aug 2021 Quantum Neuroscience Alzheimer’s Disease Drugs  Alzheimer’s Disease Drugs  Aduhelm (Aducanumab) amyloid-targeting drug  Biogen Cambridge MA; approved (efficacy questioned)  Crenezumab (antibody marking amyloid for destruction by immune cells)  Roche-Genentech, S. San Francisco CA, clinical trials  Flortaucipir (binds to misfolded tau (PET scan))  Rabinovici UCSF Memory and Aging Center  Alzheimer’s Disease Studies  ClinicalTrials.gov  Alzheimer’s studies: 2,633  Recruiting: 506; US: 303  Amyloid: 87; Tau: 57 83 Source: Arboleda-Velasquez J.F., Lopera, F. O’Hare, M. et al. (2019). Resistance to autosomal dominant Alzheimer’s in an APOE3- Christchurch homozygote: a case report. Nat Med. 25(11):1680-83. Drugs targeting the Paisa mutation: Aβ plaque build up and early onset AD
  85. 85. 24 Aug 2021 Quantum Neuroscience Danielle Posthuma laboratory Amsterdam Brain Genomics - Alzheimer’s Disease  Alzheimer’s disease  Most common neurodegenerative disease worldwide  35 million people affected  Highly heritable (2 subgroups)  Familial early-onset cases  Rare variants with strong effect  Late-onset cases  Multiple variants with low effect  Study: 71,880 cases, 383,378 controls  Identification of 29 risk loci, implicating 215 potential causative genes  Extending implicated genes beyond APOE, APP, PSEN 84 Source: Jansen, I.E., Savage, J.E., Watanabe, K. et al. (2019). Genome-wide meta-analysis identifies new loci and functional pathways influencing Alzheimer’s disease risk. Nat Genet. 51(3):404-13. Posthuma Laboratory.
  86. 86. 24 Aug 2021 Quantum Neuroscience Brain Genomics – Cortical Structure  Genome-wide association meta- analysis of brain fMRI (n = 51,665)  Measurement of cortical surface area and thickness from MRI  Identification of genomic locations of genetic variants that influence global and regional cortical structure  Implicated in cognitive function, Parkinson’s disease, insomnia, depression, neuroticism, and attention deficit hyperactivity disorder 85 fMRI: functional magnetic resonance imaging. Source: Grasby, K.L., Jahanshad, N., Painter, J.N. et al. (2020). The genetic architecture of the human cerebral cortex. Science. 367(6484). Posthuma Laboratory.
  87. 87. 24 Aug 2021 Quantum Neuroscience Brain Genomics – Cortical Structure  199 significant loci  Wnt (signaling pathway, progenitor development, areal identity)  The cortex is highly polygenic  Suggesting that distinct genes are involved in the development of specific cortical areas 86 Source: Grasby, K.L., Jahanshad, N., Painter, J.N. et al. (2020). The genetic architecture of the human cerebral cortex. Science. 367(6484). Posthuma Laboratory.
  88. 88. 24 Aug 2021 Quantum Neuroscience Glia and Calcium Signaling 87  Calcium ions diffuse both radially and longitudinally  Non-linear diffusion-reaction system (PDEs required)  Model as wavefunction  Central nervous system glial cells Glial Cells Percentage Function 1 Oligodendrocytes 45-75% Provide myelination to insulate axons 2 Astrocytes 19-40% Calcium signaling, neurotransmitter recycling 3 Microglia 10-20% Destroy pathogens, phagocytose debris 4 Ependymal cells Low Cerebrospinal fluid and the blood-brain barrier 5 Radial glia Low Neuroepithelial development and neurogenesis Source: Allen, N.J. & Eroglu, C. (2017). Cell Biology of Astrocyte-Synapse Interactions. Neuron. 96:697-708.
  89. 89. 24 Aug 2021 Quantum Neuroscience Neuron-Glia Interactions  Glia phagocytosis of dead neurons  Neuron signals apoptosis (Mertk receptor)  Microglia engulf the soma (cell body)  Astrocytes clean up the dendritic arbor  Aging and neurodegenerative disease  Delay in the removal of dying neurons  Glia role in pathogenesis  Oligodendrocytes are active immunomodulators of multiple sclerosis  Oligodendrocyte-microglia crosstalk in neurodegenerative disease  Alzheimer’s disease, spinal cord injury, multiple sclerosis, Parkinson’s disease, amyotrophic lateral sclerosis 88 Division of labor: microglia (green) clean up the soma of a dying neuron (white); astrocytes (red) tidy up distant dendrites; boundary where green meets red Sources: Damisah, E.C., Hill, R.A., Rai, A. et al. (2020). Astrocytes and microglia play orchestrated roles and respect phagocytic territories during neuronal corpse removal in vivo. Science Advances. 6(26):eaba3239. Riddler, C. (2019). Multiple Sclerosis: Oligodendrocytes: active accomplices in MS pathogenesis? Nature Reviews Neurology. 15(3).
  90. 90. 24 Aug 2021 Quantum Neuroscience Stroke: Glial Cell Involvement  Minor stroke  Astrocytes repair damage, provide energy to neurons  Glutamate and potassium uptake, lactate generation  Severe stroke  Chain reaction: astrocytes die, membranes depolarize  Glutamate released, then causing oligodendrocyte death (sensitivity per high metabolic rate)  Stroke recovery  Astrocytes release neuroprotective agents  Erythropoietin and vascular endothelial growth factor (VEGF)  Microglia are activated by damaged neurons  Phagocytose debris and secrete pro-inflammatory cytokines 89 Source: Scimemi, A. (2018). Astrocytes and the Warning Signs of Intracerebral Hemorrhagic Stroke. Neural Plasticity. 2018(7301623).
  91. 91. 24 Aug 2021 Quantum Neuroscience Aging: Causes and Intervention 90 Source: SENS Foundation  Core problem of aging  Build-up of genetic errors  Mitochondria (combustion engine), senescent cells, cancer mutations  Remediate: CRISPR, like therapies  Seven causes of aging 1. Cellular atrophy 2. Cancerous cells 3. Mitochondrial mutations 4. Death-resistant cells 5. Extracellular matrix stiffening 6. Extracellular aggregates 7. Intracellular aggregates SENS Foundation Research Program  Radical life extension  Buy enough time (escape velocity) to await further medical advance
  92. 92. 24 Aug 2021 Quantum Neuroscience Agenda  Quantum Computing and the Brain  Quantum Information Techniques  Quantum Neuroscience Applications 1. Waves: EEG, fMRI, CT, PET integration 2. Quantum Biology  Superpositioned Data and Operator Technology 3. Neuroscience Physics  AdS/Brain (AdS/CFT Holographic Neuroscience)  Neuronal Gauge Theory  General Relativity of the Brain: Entropy = Energy  Black Hole Superconducting Condensates and Scalar Hair  Random Tensors (High-dimensional Indexing Technology)  Conclusion, Risks, and Future Implications 91
  93. 93. 24 Aug 2021 Quantum Neuroscience Future-class Quantum Neuroscience  Applications  Personalized connectomics  Molecular-scale intervention  Local brain area networks  Real-time biological data processing  Neuronanorobot monitoring  Delivery  Quantum BCIs, CRISPR, mRNA, nanoparticles, anti-aging therapies  Goal  Improved quality of life (“healthspan”)  Causal understanding of disease 92 Sources: Swan, M. dos Santos, R.P., Lebedev, M.A. and Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific. Martins, N.R.B., Angelica, A., Chakravarthy, K. et al. (2019). Human Brain/Cloud Interface. Front Neurosci. 13(112):1-23.
  94. 94. 24 Aug 2021 Quantum Neuroscience Smart Network Thesis Information Revolution Progression  Smart network progression to post-biological intelligence  Digital news  Digital money  Digital brains  Gradual adoption of reversible applications  Map: personalized connectomes  Monitor: daily health check, alerts  Cure: plaque removal, stroke & cancer therapies  Enhance: cognition, learning, attention, memory  Phase 1: Brain/computer interfaces: neuroprosthetics  Phase 2: Human brain/cloud interfaces: two-way communication  Cloudmind participation (collaboration, well-being, enjoyment)  Human-artificial intelligence relation  Augmented human brain (cell phone comes on-board via BCI)  Quantum AIs replace machine learning AIs, deepnets, transformers 93 Sources: Swan, M. (forthcoming). B/CI: Quantum Computing, Holographic Control Theory, and Blockchain IPLD for the Brain. In Nanomedical Brain/Cloud Interface: Explorations and Implications. Boca Raton FL: CRC Press. Martins, N.R.B., Angelica, A., Chakravarthy, K. et al. (2019). Human Brain/Cloud Interface. Front Neurosci. 13(112):1-23. No neural dust without neural trust~! zkBCI: crypto-cloudminds using zero knowledge proof computational verification Quantum BCI High Sensitivity Low Sensitivity Medium Sensitivity
  95. 95. 24 Aug 2021 Quantum Neuroscience Summary Quantum Neuroscience 94 PDE: Partial Differential equation (multiple unknowns) Source: Swan, M. dos Santos, R.P., Lebedev, M.A. and Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific.  Substantial ongoing advance in neuroscience and physics  Quantum computing is needed to model the brain  Complexity spanning nine orders-of-magnitude scale tiers  Completing fruit fly connectome (wiring diagram) in 2018, new technology platform needed for human connectome  Neural signaling problems in synaptic integration and electrical-chemical signal transduction require PDE math  Quantum computing status  High-profile worldwide scientific endeavor (security, policy)  Multiple platforms available via cloud services  Core infrastructure development: algorithms, hardware, apps
  96. 96. 24 Aug 2021 Quantum Neuroscience Risks and Limitations  Technology cycle is too early  QPUs do not roll-out through semiconductor supply chains  Error correction stalls  Unable to move from ~100-qubit to million-qubit machines  Materials discovery stalls  Cannot find closer to actual room-temperature superconductors  Limitations of underlying physical theories  Slow pace of quantum algorithm discovery  Lack of QM extensions and beyond-probability theories using spectra, entanglement, entropy (irreversibility), and field flux  Social adoption stalls and alienation  Increasing difficulty adapting to intense presence of technology 95 QPU: Quantum Processing Unit. Source: Swan, M. dos Santos, R.P., Lebedev, M.A. and Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific.
  97. 97. 24 Aug 2021 Quantum Neuroscience The brain is the killer app of quantum computing – the outer limits case defining the requirements of the medium No other system is as complex and in need of resolving the pathologies of disease and aging As successive waves of industries become digitized in the information technology revolution (1) news, media, entertainment, stock trading; (2) money, finance, law (blockchains); and (3) now all biotech and matter-based industries; the brain as a frontier comes into view Quantum computing is finally a computational platform adequate to the scale and complexity of modeling the brain Thesis
  98. 98. 24 Aug 2021 Quantum Neuroscience Standard Quantum Neural Circuits 1. Breakspear-Coombes: multiscalar Floquet periodicity critical dynamics model 2. Amari-Cowan: quantum implementation of classical neural field theories 3. Aishwarya-Taha: test wavefunction circuits on real-life quantum hardware 4. Stoudenmire: computational neuroscience pixel=qubit and wavelet=qubit 5. Martyn-Vidal: entanglement renormalization with block product states 6. Perdomo-Ortiz: quantum circuit Born machine for neural signaling series data 7. Växjö: open superposition-updating quantum information biology circuit 8. Växjö-Cowan: Växjö quantum circuit qutrit implementation of Cowan three-state neural field theory master equation with Doi-Peliti reaction-diffusion dynamics 9. Swan AdS/Brain: renormalized four-tier correspondence matrix quantum mechanics composite neural signaling model of brain network, neuron, synapse, ion channel 10. Dvali AdS/Information Storage: highly-excited state information storage circuit 11. Hartnoll AdS/Superconducting: neural signaling phase transition when ordered- disordered system reaches high-temperature criticality & becomes superconducting 12. Sengupta-Friston: apply force fields to rebalance gauge-theoretic model on the basis of a global symmetry property that remains invariant in a multiscalar system II. BIOL III. ADV I. BASIC 97 Source: Swan, M. dos Santos, R.P., Lebedev, M.A. and Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific.
  99. 99. 24 Aug 2021 Quantum Neuroscience AdS/CFT Correspondence Studies Reference Focus Reference Theoretical Physics 1 AdS/CFT AdS/Conformational Field Theory Maldacena, 1998 2 AdS/QCD AdS/Quantum Chromodynamics Natsuume, 2016 3 AdS/CMT AdS/Condensed Matter Theory Hartnoll et al., 2018 4 AdS/SYK AdS/SYK Model Sachdev, 2010 5 AdS/Chaos AdS/Chaos (Thermal Systems) Shenker & Stanford, 2014 Neuroscience 6 AdS/Brain AdS/Neural Signaling AdS/Information Theory (Memory) Holographic Neuroscience Willshaw et al., 1969 Swan et al., 2022 Dvali, 2018 7 AdS/BCI (Quantum BCI) AdS/Braid/Cloud Interface Swan, forthcoming Information Science 8 AdS/TN AdS/Tensor Networks Swingle, 2012 9 AdS/QIT AdS/Quantum Information Theory Hayden et al., 2016 10 AdS/DLT AdS/Blockchain Technology Kalinin & Berloff, 2018 11 AdS/ML & AdS/QML AdS/(Quantum) Machine Learning Hashimoto et al., 2021; Cottrell et al., 2019 12 AdS/SN & AdS/QSN AdS/(Quantum) Smart Network Swan et al., 2020 98 AdS/QCD: quark-gluon plasma AdS/CFT: Anti-de Sitter Space/Conformal Field Theory: Claim that any physical system with a bulk volume can be described by a boundary theory in one less dimension
  100. 100. 24 Aug 2021 Quantum Neuroscience Resources and Tools  101 Overview of Quantum Computing  Krelina, M. (2021). Quantum Warfare: Definitions, Overview and Challenges. arXiv:2103.12548v1.  Krantz, P. Kjaergaard, M., Yan, F. et al. (2019). A Quantum engineer’s guide to superconducting qubits. arXiv: 1904.06560.  Quantum Computing text books  Nielsen, M.A. & Chuang, I.L. (2010). Quantum computation and quantum information. (10th anniversary Ed.). Cambridge: Cambridge University Press.  Rieffel, E. & Polak, W. (2014). Quantum Computing: A Gentle Introduction. Cambridge: MIT Press.  Roadmaps  Acin, A. Bloch, I., Buhrman, H. et al. (2018). The quantum technologies roadmap: a European community view. New J Phys. 20(8):080201.  Dahlberg, A., Skrzypczyk, M., Coopmans, T. et al. (2019). A Link Layer Protocol for Quantum Networks. In Proceedings of ACM SIGCOMM 2019.  Wehner, S., Elkouss, D. & Hanson, R. (2018). Quantum internet: A vision for the road ahead. Science. 362(6412):eaam9288. 99
  101. 101. 24 Aug 2021 Quantum Neuroscience The Brain in Popular Science A Short History of Humanity, Krause & Trappe, 2021 Archaeogenetics suggests that intelligence is a consequence of walking on two legs, as humans could expound the energy to develop an organ that requires consuming vast amounts of energy (the average human brain is three times heavier than that of the chimpanzee) The Future of the Mind, Kaku, 2014 The Fountain, Monto, 2018 Elastic: Flexible Thinking in a Time of Change, Mlodinow, 2018 Post-biological intelligence: predator-evolved, opposable thumb, langage. Forgetting is an active process, requiring dopamine, which regulates the dCA1 receptor to create new memories, and the DAMB receptor to forget old Fermi paradox: Kaku speculation that given 4000+ known exoplanets, might discover or hear from intelligent life by the end of the century; Filippenko counterargument that intelligence may not be a useful adaptation since there have been billions of forms of life on Earth, but only one as complex, curious, enterprising, and engineering-oriented as humans (also very sensitive to survival conditions) The new skillset: elastic thinking includes neophilia (affinity for novelty), schizotypy (perceiving the unusual), imagination, idea generation, and divergent and integrative thinking Exercise means that 60 really is the new 30, exercise releases anti- inflammatory IL-6 which enhances health and cognitive performance, increases telomere length and mitochondrial genesis 100 Livewired: The Inside Story of the Ever- Changing Brain, David Eagleman, 2020 More than simple neural plasticity, the brain is “livewired” to constantly absorb changes by interacting with its environment, a never- finished project always open for new dreams
  102. 102. Quantum Neuroscience CRISPR for Alzheimer’s, Connectomes & Quantum BCIs Houston TX, August 24, 2021 Slides: http://slideshare.net/LaBlogga “Biology will be the leading science for the next hundred years” – Physicist Freeman Dyson, 1996 M. Swan, MBA, PhD Quantum Technologies Thank you! Questions?
  103. 103. 24 Aug 2021 Quantum Neuroscience Pinky and the Brain  Pinky, are you pondering what I’m pondering?  …how do I collapse my wavefunction?  …with all your thoughts in superposition, how do you remember to tie your shoe?  …if we do a General Relativity of the Brain, putting scalar hair on a black hole, using a superconducting condensate disordered phase transition to produce a neural signal, does it violate the Grandfather Paradox? 102
  104. 104. 24 Aug 2021 Quantum Neuroscience Appendix  Quantum information methods  Quantum machine learning and Born machine  Quantum error correction  Quantum walks  Tensors and tensor networks  Neuroscience methods  Quantum-Classical mathematical problem formulation  Neural signaling basics: glia, parcellation, networks  CRISPR and Alzheimer’s disease, Quantum BCIs 103
  105. 105. 24 Aug 2021 Quantum Neuroscience (Classical) Machine Learning advance  Generative networks (unsupervised learning)  Learn from the distribution of data to create new samples  Discriminative networks (supervised learning)  Learn from data  Adversarial training: game-theoretic method using Nash equilibria  Two networks, a discriminator and a generator  Generator produces new samples, discriminator distinguishes between real and false samples  Transformer neural network (for existing data corpora)  Attention-based mechanism simultaneously evaluates short-range and long-range correlations in input data  Map between a query array, a key array, and a value 104 Sources: Vaswani, A., Shazeer, N., Parmar, N. et al. (2017). Attention is all you need. In Adv Neural Info Proc Sys 30. Eds. Guyon, I., Luxburg, U.V., Bengio, S. et al. (Curran Associates, Inc., 2017). Pp. 5998-6008. Carrasquilla, J., Torlai, G., Melko, R.G. & Aolita, L. (2019). Reconstructing quantum states with generative models. Nat Mach Intel. 1:155-61.
  106. 106. 24 Aug 2021 Quantum Neuroscience Quantum Probabilistic Methods Quantum Machine Learning  Quantum machine learning: application of machine learning techniques in a quantum environment  Simulated quantum circuits or quantum hardware  Early QML demonstrations  Current state-of-the-art  Born Machine (Cheng)  QGANs: quantum Generative Adversarial nets (Dellaire-Demers)  Neural Operators (solve PDEs) (Li) 105 Sources: Dallaire-Demers, P.-L. & Killoran, N. (2018). Quantum generative adversarial networks. Phys Rev A. 98(012324). Li et al. (2021). Fourier neural operator for parametric partial differential equations. arXiv:2010.08895v3. Cong, I., Choi, S. & & Lukin, M.D. (2019). Quantum convolutional neural networks. Nat Phys. 15(12):1273-78. Architecture Data Encoding Data Hardware Reference 1 Quantum neural network Basis embedding (bitstring) MNIST (classical data) Simulation on a classical computer Farhi and Neven, 2018, Classification with Quantum NNs 2 Quantum tensor network Basis embedding (classical data), amplitude embedding (quantum data) IRIS, MNIST (classical data); quantum state data IBM QX4 quantum computer Grant et al., 2018 Hierarchical Quantum Classifiers
  107. 107. 24 Aug 2021 Quantum Neuroscience Born Machine  Machine learning architecture  Automated energy function (“machine”) evaluates output probabilities  Classical machine learning: Boltzmann machine  Interpret results with the Boltzmann distribution  Use an energy-minimizing probability function for sampling based on the Boltzmann distribution in statistical mechanics  Quantum machine learning: Born machine  Interpret results with the Born rule  A computable quantum mechanical formulation that evaluates the probability density of finding a particle at a given point as being proportional to the square of the magnitude of the particle’s wavefunction at that point 106 Sources: Cheng, S., Chen, J. & Wang, L. (2018). Information perspective to probabilistic modeling: Boltzmann machines versus Born machines. Entropy. 20(583). Chen, J., Cheng, S., Xie, H., et al. (2018). Equivalence of restricted Boltzmann machines and tensor network states. Phys. Rev. B. 97(085104). Map RBM to Born machine tensor network
  108. 108. 24 Aug 2021 Quantum Neuroscience Neuroscience example of machine learning Brain Atlas Annotation and Deep Learning  Machine learning smooths individual variation to produce standard reference brain atlas  Multiscalar neuron detection  Deep neural network  Whole-brain image processing  Detect neurons labeled with genetic markers in a range of imaging planes and modalities at cellular scale 107 Source: Iqbal, A., Khan, R. & Karayannis, T. (2019). Developing a brain atlas through deep learning. Nat. Mach. Intell. 1:277-87.
  109. 109. 24 Aug 2021 Quantum Neuroscience Appendix  Quantum information methods  Quantum machine learning and Born machine  Quantum error correction  Quantum walks  Tensors and tensor networks  Neuroscience methods  Quantum-Classical mathematical problem formulation  Neural signaling basics: glia, parcellation, networks  CRISPR and Alzheimer’s disease, Quantum BCIs 108
  110. 110. 24 Aug 2021 Quantum Neuroscience Quantum Error Correction  Fault-tolerant error correction needed for universal quantum computing  Prevent a few errors from escalating to many  Quantum information sensitive to environmental noise  Error correction methods  Classical: redundant copies, check information integrity  Quantum systems: cannot copy or inspect (no-cloning and no-measurement principles of quantum mechanics)  Quantum error correction relies on entanglement instead of redundancy  The quantum state to be protected is entangled with a larger group of states from which it can be corrected indirectly (one qubit might be entangled with a nine-qubit ancilla of extra qubits) 109 Source: Brun, T.A. (2019). Quantum error correction. arXiv: 1910.03672.
  111. 111. 24 Aug 2021 Quantum Neuroscience Quantum Error Correction  Quantum errors  Bit flip, sign flip (the sign of the phase), or both  Quantum error correction process  Diagnose the error with basic codes  Corresponding to Pauli matrices for controlling qubits in the X, Y, and Z dimensions  Express the error as a superposition of basis operations given by the Pauli matrices  Apply the same Pauli operator to act again on the corrupt qubit to reverse the error effect  Result: the unitary correction returns the state to the initial state without measuring the qubit directly 110 Source: Brown, B.J. (2020). A fault-tolerant non-Clifford gate for the surface code in two dimensions. Science Advances. 6(eaay4929):1-13. Pauli Matrices (x, y, z)

This talk provides an introduction to quantum computing and how it may be deployed to study the human brain and its diseases of pathology and aging. Refined to its present state over centuries, the brain is one of the most complex systems known, with 86 billion neurons and 242 trillion synapses connected in intricate patterns and rewired by synaptic plasticity. Research continues to illuminate the mysteries of the brain. Quantum computing provides a more capacious architecture with greater scalability and energy efficiency than current methods of classical computing and supercomputing, and more naturally corresponds to the three-dimensional structure of atomic reality. The vision for quantum neuroscience is to model the nature of the brain exactly as it is, in three-dimensional atomically-accurate representations. Neuroscience (particularly genetic disease modeling, connectomics, and synaptomics) could be the “killer application” of quantum computing. Implementations in other industries are also important, including in quantum finance, quantum cryptography using Shor’s factoring algorithm (“the Y2K of Crypto”), Grover’s search, quantum chemistry, eigensolvers, quantum machine learning, and continuous-time quantum walks. Quantum computing is a high-profile worldwide scientific endeavor with platforms currently available via cloud services (IBM Q 27-qubit, IonQ 32-qubit, Rigetti 19Q Acorn) and is in the process of being applied in various industries including computational neuroscience.

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