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

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

  • 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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)