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Melanie Swan, PhD
Quantum Technologies
University College London
Quantum Information
Space, Biology, and Computation
“Outside there was silence, as there is and has been and
always should be. The perfect silence of the spheres.”
- Elizabeth Bear, Ancestral Night, 2019, p. 384
4 Sep 2022
Quantum Information 1
The fast pace of quantum information study is
enabling a new tier of scientific problem-solving
Early-adopter fields: space science, biology, chemistry,
finance, cryptography, physics
Thesis
4 Sep 2022
Quantum Information 2
Quantum Technologies Research Program
2015 2019 2020
Blockchain Blockchain
Economics
Quantum
Computing
Quantum
Computing
for the Brain
2022
4 Sep 2022
Quantum Information 3
 What are Quantum Technologies?
 Foundational Tools
 Quantum Cryptography
 Quantum Machine Learning
 Quantum Chemistry
 Advanced Applications
 Quantum Space Science
 Quantum Finance
 Quantum Biology
Agenda
4 Sep 2022
Quantum Information
Space: We are Here~!
4
Source: Tully, R.B., Courtois, H., Hoffman, Y. & Pomarede, D. (2014). The Laniakea supercluster of galaxies. Nature. 513(7516):71.
Distribution of Galaxies
Location of the Milky Way Galaxy (Virgo
Supercluster) within the Laniakea Supercluster
 Decentered in the supercluster, the local
group, the galaxy, and the solar system
Laniakea
Supercluster
Milky Way
Galaxy
Novel method: analyze relative velocities of
galaxies as watershed divides (turbulence)
4 Sep 2022
Quantum Information
Time: Seeing farther back into the Big Bang
5
Source: https://www.jwst.nasa.gov/content/about/comparisonWebbVsHubble.html
Hubble (HST) can see “toddler galaxies”
Webb (JWST) can see “baby galaxies”
6.25x larger collecting area than Hubble
 James Webb Space Telescope (launched Dec 2021)
 “See” farther back
in time with
infrared spectrum
4 Sep 2022
Quantum Information
Other Potential Life
5,125+ Exoplanets Discovered (Aug 2022)
 1/3 each super-earths, neptunes, jupiters
 Over 800 with more than one planet
 Atmosphere, volcanism, sun-planet relation
 Habitable zone (CHON carbon-hydrogen-oxygen-nitrogen)
6
Source: https://www.jwst.nasa.gov/content/about/comparisonWebbVsHubble.html
Radial Velocity
(Yellow: Kepler, Pink: Terrestrial)
Transit
(Blue: space-based telescopes)
Detection
Method:
4 Sep 2022
Quantum Information
The Large and Small Scale Universe
7
Scale Measure Comment
1 5.1 x 1096 Planck density Kg/Meter3 Density of the universe immediately after the Big Bang
2 1 x 1080 Particles Total particles in the observable universe (est.)
3 1 x 1014 Cells Cells in the human body (9 out of 10 are bacteria)
4 8 x 1010 Stars Number of stars in the Milky Way galaxy (est.)
5 1 x 102 Meter Earth Earth’s atmosphere: 10,000 ft life support, 62 mi to space
6 1 x 101 Meter Human Human-scale: Classical Mechanics
7 1 x 10-9 Nanometer Atoms Quantum mechanics (nanotechnology)
8 1 x 10-12 Picometer Ions, photons Optics, photonics
9 1 x 10-15 Femtometer Subatomic Gauge theories
10 1 x 10-35 Planck scale Meters Smallest known length scale
11 5.4 x 10-44 Planck time Seconds Shortest meaningful interval of time
Source: The Universe by Numbers. https://www.physicsoftheuniverse.com/numbers.html
Large-scale:
General
Relativity
(GR)
Small-scale:
Quantum
Mechanics
(QM)
Human-scale:
Classical
Mechanics
 Quantum mechanics, classical mechanics, general relativity
 Quantum effects visible at 10-9 m
 Relativistic effects present at any speed (matter of precision)
4 Sep 2022
Quantum Information
Quantum Scale
8
QCD: Quantum Chromodynamics
Subatomic particles
Matter particles: fermions (quarks)
Force particles: bosons (gluons)
Scale Entities Physical Theory
1 1 x101 m Meter Humans Newtonian mechanics
2 1 x10-9 m Nanometer Atoms Quantum mechanics
(nanotechnology)
3 1 x10-12 m Picometer Ions, photons Optics, photonics
4 1 x10-15 m Femtometer Subatomic particles QCD/gauge theories
5 1 x10-35 m Planck scale Planck length Planck scale
Atoms Quantum objects:
atoms, ions,
photons
 “Quantum” = anything at the scale of
atomic and subatomic particles (10-9 to 10-15)
 Theme: ability to study and manipulate
physical reality at smaller scales
 Study phenomena (e.g. neurons) in the native
3D structure of physical reality
4 Sep 2022
Quantum Information 9
Basic Concept
What is Quantum Computing?
 Computing: change of state between 0/1
 Move information around and perform a
computation
 Classical computing: serial not parallel
 Quantum computing: treat more than
one status at the same time, compute
all the transactions at the same time
 Fundamentally, a different way of
computing
Source: Fowler, A.G., Mariantoni, M., Martinis, J.M. & Cleland, A.N. (2012). Surface codes: Towards practical large-scale
quantum computation. Phys Rev A. 86(032324).
4 Sep 2022
Quantum Information
 A qubit (quantum bit) is the basic unit of
quantum information, the quantum version
of the classical binary bit
10
What is a Qubit?
Bit exists in a
single binary state
(0 or 1)
Qubit exists in a state of superposition, at
every location with some probability, until
collapsed into a measurement (0/1)
Implication: test more permutations
Classical Bit Quantum Bit (Qubit)
Source: https://www.newsweek.com/quantum-computing-research-computer-flagship-eu-452167
4 Sep 2022
Quantum Information 11
What is a Qudit?
Classical
Bit: 0,1
Qubit: 0,1 Qutrit: 0,1,2
Qutrit stabilizer code on a torus
Source: Imany et al. (2019). High-dimensional optical quantum logic in large operational spaces. npj Quantum Information. 5(59):1-10.
 Qudit (quantum information digit)
 Exists in superposition of 2+ states before
collapsed in measurement
 Qubit (2-values): 0,1
 Qutrit (3-values): 0, 1, 2
 Conducive to 3d error correction
 7-10 qudits have been tested (multi-
dimensional entanglement)
4 Optical Qudits entangled
in time & space (20 qubits)
Bloch sphere: 3D particle
movement in X, Y, Z directions
Particle exists in all positions
until collapsed in measurement
4 Sep 2022
Quantum Information
Quantum: Many Potential Speed-ups
1. Bit (0 or 1)
2. Qubit (0 and 1 in superposition)
3. Qudit (more than 2 values in superposition)
 Microchip generates two entangled qudits each with 10
states, for 100 dimensions total, for more than six
entangled qubits could generate (Imany, 2019 )
4. Optics (time and frequency multiplexing)
 Existing telecommunications infrastructure
 Global network not standalone computers in labs
 Time-frequency binning (20+ states tested)
5. Optics (superposition of inputs and gates)
6. High-dimensional entanglement
12
Classical
Computing
Quantum
Computing
Source: Imany et al. (2019). High-dimensional optical quantum logic in large operational spaces. npj Quantum Information. 5(59):1-10.
4 Sep 2022
Quantum Information
Quantum Error Correction Codes
 Quantum error-correction code: logical
codespace corresponding to a physical
lattice model to manipulate a particle
 Use Pauli matrices to control qubits in the
x, y, z dimensions
13
Code Description
Basic quantum error-correcting code
Stabilizer codes Topology-based Pauli operators (X, Y, Z) correct a bit-flip or a spin flip
Toric code Stabilizer operators defined on a 2D torus-shaped spin lattice
Surface code Stabilizer operators defined on a 2D spin lattice in any shape
Advanced quantum error-correcting code (greater scalability, control)
Bosonic codes Self-contained photon-based oscillator system with bosonic modes
GKP code Squeezed states protect position and amplitude shifts with rotations
Molecular code Rotations performed on any asymmetric body (molecule) in free space
Cat code Superpositioned states (Schrödinger) used as error correction codes
GKP codes (Gottesman, Kitaev, Preskill) (Gottesman et al., 2001)
Source: Swan, M., dos Santos, R.P. & Witte, F. (2022). Quantum Matter Overview. J. 5(2):232-254.
Quantum Error-correcting Codes for Quantum Object Manipulation
Pauli Matrices (x, y, z)
Quantum Circuit
4 Sep 2022
Quantum Information
Quantum Error Correction
 Clifford gates (basic quantum gates)
 Pauli matrices, and the Hadamard, CNOT, and
π/2-phase shift gates; simulated classically
 Non-Clifford gates (complex operations)
 Logical depth (π/8 gate); cannot simulate classically
 Consolidate multiple noisy to few reliable states
 Magic state distillation (computationally costly)
 Gauge fixing stabilizer codes (Majorana fermion
braiding)
 Gauge color fixing (color codes)
 Time-based surface codes
 Replicates the three-dimensional code that performs the
non-Clifford gate functions with three overlapping copies of
the surface code interacting locally over a period of time
14
Source: Fowler, A.G., Mariantoni, M., Martinis, J.M. & Cleland, A.N. (2012). Surface codes: Towards practical large-scale
quantum computation. Phys Rev A. 86(032324).
Time-based surface code
4 Sep 2022
Quantum Information
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 (represented by the Greek letter Ψ)
EΨ(r) = -ћ2/2m ∇2 Ψ(r) + V(r)Ψ(r)
Total Energy = Kinetic Energy + Potential Energy
(motion) (resting)
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
EΨ(r) = -ћ2/2m ∇2 Ψ(r) + V(r)Ψ(r)
Schrödinger
wave equation
4 Sep 2022
Quantum Information
Superconducting Qubit
 Implement by sending current through a small ring
 Create “1” and “0” states as current circulating
clockwise and counterclockwise in the
superconducting loop
 The smallest amount of flux that can be in the loop
corresponds to either +Φ0/2 and - Φ0/2, where Φ0 = ћ/2e
is the magnetic flux quantum
 The two states represent the “0” and “1” values of a
classical bit or the two basis states of a qubit |0> and |1>
 Potential energy wells
 System tunnels back and forth between |0> and |1>
 Can also occupy a superposition state of |0> and |1>
with current simultaneously circulating both clockwise
and counterclockwise
16
Superconducting Tunnel Junction
Image of “0” and “1” states
Source: Smelyanskiy, V.N., Rieffel, E.G., Knysh, S.I. et al. (2012). Near-Term Quantum Computing Approach for Hard Computational
Problems in Space Exploration. arXiv:1204.2821v2.
Single-qubit Hamiltonian
2 x 2 Pauli matrices acting on
single qubit states
Superconducting Qubit Configuration
Qubit Potential Energy Wells
(“1” and “0” states)
Two States: Spin-up/Spin-down
4 Sep 2022
Quantum Information
Moore’s Law
17
Source: Thomasian, N.M., Kamel, I.R. & Bai, H.X. (2021). Machine intelligence in non-invasive endocrine cancer diagnostics. Nat
Rev Endocrinol. 18:81-95. https://ourworldindata.org/uploads/2020/11/Transistor-Count-over-time.png
1. Plateau – sustainable?
2. Already incorporating
quantum effects
4 Sep 2022
Quantum Information
Computing Architecture
End of Moore’s Law Problem
 Large ecosystem of computational platforms
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 Computing
Spiking Neural Networks (SNNs)
Quantum
Computing
18
2500 BC
Abacus
20th Century
Classical
21st Century
Quantum
Abacus -> Logarithm -> Classical -> Quantum
+
4 Sep 2022
Quantum Information
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
19
4 Sep 2022
Quantum Information
Status
Quantum Computing available via Cloud Services
20
Sources: Company press releases, QCWare, Preskill, J. (2021). Quantum computing 40 years later. arXiv:2106.10522,
https://amitray.com/roadmap-for-1000-qubits-fault-tolerant-quantum-computers
https://arstechnica.com/science/2021/11/ibm-clears-the-100-qubit-mark-with-its-new-processor
Era Organization Qubit Method # Qubits Status
1 IBM, academia (factor the number 15) NMR, optical, solid-state superconducting 4-7 Demo (2001-2012)
2a IBM (Almaden CA) Superconducting (gate model) 127 Available (Nov 2021)
2b D-Wave Systems (Vancouver BC) Superconducting (quantum annealing) 2048 Available (May 2019)
2c Rigetti Computing (Berkeley CA) Superconducting (gate model) 80 Available (Dec 2021)
2d IonQ (College Park MD) Trapped Ions 32 Available (Sep 2021)
2c Google (Mountain View CA) Superconducting (gate model) 53 (72) Backend: Google cloud
2e Microsoft (Santa Barbara CA) Majorana Fermions Unknown Backend: Azure cloud
3 Technical breakthrough needed Universal quantum computing 1 million Hypothetical future
 Quantum error correction break-through
needed to scale to million-qubit machines
 Current platforms: NISQ (noisy intermediate-
scale quantum) devices without error correction
 Future platforms: error-corrected FTQC (fault-
tolerant quantum computing)
 Few-qubit (2000s) –> 100-qubit (2021) –> million-qubit
4 Sep 2022
Quantum Information
Quantum Computing
Microsoft
IBM
Rigetti
4 Sep 2022
Quantum Information
Using a Quantum Computer to Factor
22
Source: D-Wave Systems, Inc. https://cloud.dwavesys.com/leap/resources/demos
4 Sep 2022
Quantum Information
Future of Quantum Computing
 Technology is notoriously difficult to predict
 “I think there is a world market for maybe five computers” – Watson, IBM CEO, 1943
 Xerox: “I think we’ll make about four copies a week” – State Street Bank, adopting a xerograph
23
Sources: Ceruzzi, P. (2003). A History of Modern Computing. 2nd Ed. Cambridge: MIT Press; Strohmeyer, R. (2008). The 7 Worst
Tech Predictions of All Time. PCWorld.
D-Wave Systems:
10-feet tall, $15m
Current: Ytterbium-
171 isotopes at 1
Kelvin (-458°F)
Actual room-
temperature
superconductors: ??
70 years
IBM
Quantum
Experience
UNIVAC computer (1950s):
465 multiplications per
second (faster than Hidden
Figures human computers)
Billions of
times faster
4 Sep 2022
Quantum Information
Quantum Information
24
Domain Properties Top Five Properties: Quantum Matter and Quantum Computing Definition
Quantum
Matter
Symmetry Looking the same from different points of view (e.g. a face, cube, laws of physics);
symmetry breaking is phase transition
Topology Geometric structure preserved under deformation (bending, stretching, twisting, and
crumpling, but not cutting or gluing); doughnut and coffee cup both have a hole
Quantum
Computing
Superposition An unobserved particle exists in all possible states simultaneously, but once measured,
collapses to just one state (superpositioned data modeling of all possible states)
Entanglement Particles connected such that their states are related, even when separated by distance
(a “tails-up/tails-down” relationship; one particle in one state, other in the other)
Interference Waves reinforcing or canceling each other out (cohering or decohering)
Source: Swan, M., dos Santos, R.P. & Witte, F. (2022). Quantum Matter Overview. J. 5(2):232-254.
Quantum Information: the
information (physical properties)
of the state of a quantum system
4 Sep 2022
Quantum Information
Quantum Algorithms
 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 (with only √N
queries vs all or at least half N entries classically)
 Floquet circuits: time as engineering problem
 Discrete time crystals (matter phases
not reaching thermal equilibrium)
 Hyperbolic Bloch theorem
 More than four squares connect at
vertices in a hyperbolic lattice
25
Elliptic geometry
(positively-curved)
Hyperbolic geometry
(negatively-curved)
Flat geometry
(no curvature)
Euclidean and beyond spacetimes
Sources: Maciejko, J. & Rayan, S. (2021). Hyperbolic band theory. Sci. Adv. 7:eabe9170. Mi, X. et al. (2021). Observation of Time-
Crystalline Eigenstate Order on a Quantum Processor. arXiv:2107.13571. (Google Quantum AI and collaborators)
Time-crystalline Eigenstate order
Hyperbolic space
4 Sep 2022
Quantum Information
Quantum Algorithms
 VQE: variational quantum eigensolvers
 Finds the ground state of a given problem Hamiltonian
 Finds the eigenvalues of a matrix (Peruzzo, 2014)
 VAE: variational autoencoder (Kingma & Welling, 2014)
 Three-step (compress, analyze, re-encode) neural network
method: nonlinear similarities in high-dimensional unlabeled data
 Example: train autoencoder to minimize the Euclidean distances
(reconstruction errors) between the original and decoded vectors in
a 148-dimensional feature space (Vasylenko,2022)
 QAOA (1): quantum approximate optimization algorithm
 Combinatorial optimization (Farhi, 2014)
 QAOA (2): quantum alternating operator ansatz (guess)
 Alternating Hamiltonians (cost-mixing) model (Hadfield, 2021)
26
Source: McArdle, S., Endo, S., Aspuru-Guzik, A. et al. (2020). Quantum computational chemistry. Reviews of Modern Physics.
92(1):015003, p. 31.
Variational Quantum
Eigensolver (VQE)
4 Sep 2022
Quantum Information
Quantum Walks
 Quadratically faster per ballistic
propagation through lattice walk
environment vs classical diffusive spread
27
Source: Kendon. V. (2020). How to Compute Using Quantum Walks. EPTCS. 315:1-17.
 The walk travels through all paths in superposition
 Application: faster search and cryptography algorithms
 Quantum walk selection parameters
 Coin flip via quantum coin-flip
operator (e.g. Hadamard coin
flipping a qubit to a one or zero)
 Multi-dimensional lattice graph walk
environment
 Quantum walk algorithm
 Time regime (discrete-continuous)
4 Sep 2022
Quantum Information
Quantum Studies in the Academy
28
Digital
Humanities
Arts
Sciences
Quantum
Humanities
computational astronomy,
computational biology
Digital Humanities (literature & painting
analysis, computational philosophy1)
Quantum Humanities
quantum chemistry, quantum finance,
quantum biology, quantum ecology
Apply quantum methods to study field-specific problems e.g. quantum machine learning
Apply data science methods to study field-specific problems e.g. machine learning
 Data science institutes now including quantum
 What are Digital Humanities / Quantum Humanities?
1. Apply digital/quantum methods to research questions
2. Find digital/quantum examples in field subject matter
 (e.g. quantum mechanical formulations in Shakespeare)
3. Open new investigations per digital/quantum conceptualizations
Sources: Miranda, E.R. (2022). Quantum Computing in the Arts and Humanities. London: Springer. Barzen, J. & Leymann, F.
(2020). Quantum Humanities: A First Use Case for Quantum Machine Learning in Media Science. Digitale Welt. 4:102-103.
1Example of computational philosophy: investigate formal axiomatic metaphysics with an automated reasoning environment
Big Data Science
Vermeer imaging (1665-2018)
Textual
analysis
4 Sep 2022
Quantum Information
Quantum Science Fields
29
Source: Swan, M., dos Santos, R.P. & Witte, F. (2020). Quantum Computing: Physics, Blockchains, and Deep Learning Smart
Networks. London: World Scientific.
Quantum Biology
Quantum Neuroscience
Quantum Machine
Learning
€
$
¥
€
Early-adopter fields: space science, biology, chemistry, finance, cryptography, physics
Quantum
Cryptography
Quantum Space
Science Quantum Finance
Foundational
Tools
Advanced
Applications
Quantum
Chemistry
4 Sep 2022
Quantum Information 30
 What are Quantum Technologies?
 Foundational Tools
 Quantum Cryptography
 Quantum Machine Learning
 Quantum Chemistry
 Advanced Applications
 Quantum Space Science
 Quantum Finance
 Quantum Biology
Agenda
4 Sep 2022
Quantum Information
“Y2K of crypto” threat
NIST Post-Quantum Cryptography Project
 Four quantum-resistant algorithms announced (Jul 2022)
 General concept: shift from factoring to lattices (3d+)
 Factoring (number theory); Lattices (group theory, order theory)
 Classical: based on the difficulty of factoring large numbers
 Size of large number: eight 32-bit words (SHA-256)
 Quantum: based on the difficulty of lattice problems
 Lattice: geometric arrangement of points in a space
 Example: find shortest vector to an arbitrary point
31
Module: generalization of vector space in which the field of scalars is replaced by a ring
Hash function: generic structure for converting arbitrary-length input to fixed-size output
Source: https://www.nist.gov/news-events/news/2022/07/nist-announces-first-four-quantum-resistant-cryptographic-algorithms
Application Algorithm Category Based on difficulty of solving
1 Public-key encryption CRYSTALS-Kyber (IBM) Structured lattices Learning-with-errors (LWE)
problem over module lattices
2 Digital signature CRYSTALS-Dilithium (IBM) Structured lattices Lattice problems over module
lattices (Fiat-Shamir with Aborts)
3 Digital signature FALCON (IBM) Structured lattices
(Fast Fourier)
Short integer solution problem
(SIS) over NTRU lattices
(Number Theory Research Unit)
4 Digital signature SPHINCS+ (Eindhoven
University of Technology)
Hash functions Hash functions over lattices (vs.
classical SHA-256 hash functions)
4 Sep 2022
Quantum Information 32
NIST Algorithm Selection
 NIST: 26 of 69 algorithms advance to
post-quantum crypto semifinal (Jan 2019)
 Public-key encryption (17)
 Digital signature schemes (9)
 Approaches: lattice-based,
code-based, multivariate
 Lattice-based: target the Learning with
Errors (LWE) problem with module or ring
formulation (MLWE or RLWE)
 Code-based: error-correcting codes (Low
Density Parity Check (LDPC) codes)
 Multivariate: field equations (hidden fields
and small fields) and algebraic equations
Source: NISTIR 8240: Status Report on the First Round of the NIST Post-Quantum Cryptography Standardization Process, January
2019, https://doi.org/10.6028/NIST.IR.8240.
4 Sep 2022
Quantum Information 33
 What are Quantum Technologies?
 Foundational Tools
 Quantum Cryptography
 Quantum Machine Learning
 Quantum Chemistry
 Advanced Applications
 Quantum Space Science
 Quantum Finance
 Quantum Biology
Agenda
Shine et al., 2021
4 Sep 2022
Quantum Information
Early success in Supervised Learning (2011)
 YouTube: user-classified data
perfect for Supervised Learning
 2 mn cat videos of 800 mn total
YouTube videos (Aug 2022)
34
Source: Google Brain: Le, QV, Dean, Jeff, Ng, Andrew et al. 2012. Building high-level features using large scale unsupervised
learning. https://arxiv.org/abs/1112.6209. https://earthweb.com/
4 Sep 2022
Quantum Information
(Classical) Machine Learning
 Supervised learning (discriminative networks)
 Learn from labeled data (“cat”)
 Unsupervised learning (generative networks)
 Learn the distribution of unlabeled data, create samples
 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
35
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.
4 Sep 2022
Quantum Information
Quantum Machine Learning
 Quantum machine learning
 Implement machine learning algorithms on quantum platforms
 Study quantum problems with machine learning techniques
 QML versions of all three ML architectures
36
Sources: Farhi & Neven. (2018). Classification with quantum neural networks on near term processors. arXiv:1802.06002; Grant et
al. (2018). Hierarchical quantum classifiers. NPJ Quantum Inf. 4(65):1–8; Schuld & Killoran. (2019). Quantum machine learning in
feature Hilbert spaces. Phys. Rev. Lett. 122(4):040504. Chatterjee & Yu. (2017). Generalized coherent states, reproducing kernels,
and quantum support vector machines. Quantum Inf. Commun. 17(15-16):1292–1306.
Architecture Description Application Reference
1 Quantum neural
network
Neural network method based on distilling
information from an input wavefunction into
output qubits
Image classification
(MNIST)
Farhi and
Neven, 2018
2 Quantum tensor
network
Tensor network method based on factoring a
high-order tensor (with a large number of
indices) into a set of low-order tensors whose
indices are summed to form a network defined
by a certain pattern of contractions
Image classification
(MNIST), generate
quantum state data
Grant et al.,
2018
3 Quantum kernel
learning (reusable
structure = “kernel
trick”)
Kernel learning method (pattern analysis) in
which functions in higher-dimensional feature
space are computed on a data kernel using
distance measures (the inner products
between all data pairs in the feature space)
instead of data coordinates;
Quantum finance: trade
identification (support
vector machines and
RKHS (reproducing kernel
Hilbert space)
Schuld &
Killoran, 2019;
Chatterjee &
Yu, 2017
4 Sep 2022
Quantum Information
Born Machine
 In machine learning, an automated energy
function (“machine”) uses a loss function
to assess 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
37
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). RBM: restricted to prohibit intralayer connections for efficient training
Map Restricted Boltzmann
Machine to Born Machine
tensor network
4 Sep 2022
Quantum Information
Neural Operators
 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 2018)
 Neural PDE: NN architecture that uses neural
operators to map between infinite-dimensional spaces
 Fourier neural operator solves all instances of
PDE family in multiple spatial discretizations
 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)
38
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).
4 Sep 2022
Quantum Information
Practical Application
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
39
Source: Iqbal, A., Khan, R. & Karayannis, T. (2019). Developing a brain atlas through deep learning. Nat. Mach. Intell. 1:277-87.
4 Sep 2022
Quantum Information
Status of AI
AI Writes a Paper about Itself
40
Source: Gpt Generative Pretrained Transformer, Almira Osmanovic Thunström, Steinn Steingrimsson. Can GPT-3 write an
academic paper on itself, with minimal human input?. 2022. hhal-03701250 https://hal.archives-ouvertes.fr/hal-03701250
GPT-3 is a machine learning platform that enables developers to train and deploy AI models. It is also
said to be scalable and efficient with the ability to handle large amounts of data. Some have called it a
"game changer" in the field of AI (O'Reilly, 2016). GPT-3 has been used in a number of different
applications including image recognition, natural language processing, and predictive modeling. In each
of these cases, GPT-3 has demonstrated its potential to improve upon existing methods (Lee, 2016).
4 Sep 2022
Quantum Information 41
 What are Quantum Technologies?
 Foundational Tools
 Quantum Cryptography
 Quantum Machine Learning
 Quantum Chemistry
 Advanced Applications
 Quantum Space Science
 Quantum Finance
 Quantum Biology
Agenda
4 Sep 2022
Quantum Information 42
Quantum Chemistry (= Molecular QM)
 Quantum Chemistry: branch of physical chemistry
applying quantum mechanics to chemical systems
 Solve classically-intractable chemistry problems
 High temperature superconductivity, solid-state/condensed matter
physics, transition metal catalysis, new compound discovery
 Biochemical reactions, molecular dynamics, protein folding
 Short-term Objectives
 Computational solutions to Schrödinger equation (approximate)
 Increase size of molecules that can be studied
Sources: Krenn et al. (2020).Self-referencing embedded strings (SELFIES): A 100% robust molecular string representation. Machine
.Learning: Sci. Tech. 1(4):045024; Kmiecik et al. (2020). Coarse-Grained Protein Models and their Applications. Chem. Rev.
116:7898−7936.
4 Sep 2022
Quantum Information
Quantum Chemistry
New Materials Found for Electric Batteries
 Unsupervised machine learning
method identifies new battery
materials for electric vehicles
 Four candidates out of 300
 VAE (variational autoencoder to
compress, analyze, re-encode
high-dimensional data) used to
rank chemical combinations
 Quaternary phase fields containing two
anions (e.g. lithium solid electrolytes)
 Discovery of Li3.3SnS3.3Cl0.7
43
Source: Vasylenko, A., Gamon, J., Duff, B.D. et al. (2021). Element selection for crystalline inorganic solid discovery guided by
unsupervised machine learning of experimentally explored chemistry. Nature Communications. 12:5561.
Ranking of Synthetic Exploration
Probe structure of Li3SnS3Cl predicted
coupled anion and cation order
VAE Analyzes High-Dimensional Data
4 Sep 2022
Quantum Information
Digital Fabrication Methods
Autonomous Robotic Nanofabrication
 Use single molecules to
produce supramolecular
structures
 Control single molecules with
the machine learning agent-
based manipulation of scanning
probe microscope actuators
 Use reinforcement learning (goal-
directed updating) to remove
molecules autonomously from the
structure with a scanning probe
microscope
44
Source: Leinen, P., Esders, M., Schutt, K.T. et al. (2020). Autonomous robotic nanofabrication with reinforcement learning. Sci. Adv.
6:eabb6987.
Subtractive manufacturing with machine
learning: molecules bind to the scanning
microscope tip; bond formation and breaking
increases or decreases the tunneling
current; new molecules are retained in the
monolayer by a network of hydrogen bonds
4 Sep 2022
Quantum Information
Atomically-Precise Manufacturing
 Single atoms positioned to create macroscopic objects
 Applications: molecular electronics, nanomedicine, integrated
circuits, thin films, etch masks, renewable energy materials
45
STM: scanning tunneling microscope; SPM: scanning probe microscope
Source: Randall, J.N. (2021). ZyVector: STM Control System for Atomically Precise Lithography. Zyvex Labs.
https://www.zyvexlabs.com/apm/products/zyvector
Atomically-Precise Writing (Deposition) with an STM
1. Outline the structure of the design
2. Specify crystal lattice vector layout
3. Write (deposit) atoms with the STM tip
4. Finalize atomically-precise pattern
ZyVector: STM Control System
for Atomically Precise
Lithography (Zyvex Labs)
4 Sep 2022
Quantum Information
Molecular Electronics: Quantum Circuit Design
 Molecular circuits for quantum computing, construct
 One-qubit gates using one-electron scattering in molecules
 Two-qubit controlled-phase gates using electron-electron
scattering along metallic leads
46
Source: Jensen, P.W.K., Kristensen, L.B., Lavigne, C. & Aspuru-Guzik, A. (2022). Toward Quantum Computing with Molecular
Electronics. Journal of Chemical Theory and Computation.
Electron transmission magnitude as
a function of incoming kinetic
energy for molecular hydrogen in
the 6-31G basis attached between
one input and two output leads
Electron transmission through molecular hydrogen in
STO-3G basis (the planes intersecting through the
two orbitals indicate the integration limits)
4 Sep 2022
Quantum Information
Quantum Chemistry
System Setup: Quantum Algorithms
 Qubit Hamiltonians
 Quantum algorithm: express Hamiltonian as qubit operator
 Retain fermionic exchange symmetries
 Describe fermionic states in terms of qubit states
 Perform transformations using fermionic-to-qubit mappings (e.g.
Jordan-Wigner transformation)
 Excitation gates as Givens rotations
 Main tool: Variational Quantum Eigensolver (VQE)
 Algorithm to compute approximate system energies
 Optimize the parameters of a
quantum circuit with respect to
the expectation value of a
molecular Hamiltonian
(minimizing a cost function)
47
Source: Arrazola, J.M., Jahangiri, S., Delgado, A. et al. (2021). Differentiable quantum computational chemistry with PennyLane.
arXiv:2111.09967v2
4 Sep 2022
Quantum Information
Quantum Chemistry
Ground and Excited-state Energies
 Ground state energy (GSE)
 Compute Hamiltonian expectation values
 Convert the system Hamiltonian to a sparse matrix
 Use the vector representation of the state to compute the expectation value
using matrix vector multiplication
 Calculate expectation values by performing single-qubit rotations
 Pauli expressions are tensor products of local qubit operators
 Manage complexity by grouping Pauli expressions into sets of mutually-
commuting operators (calculate EV from the same measurement statistics)
 Excited state energy (ESE)
 Compute excited-state energies: add penalty terms to cost function
 The lowest-energy eigenstate of the penalized system is the first
excited state of the original system
 Iterate to find k-th excited state by adjusting penalty parameters
48
Source: Arrazola, J.M., Jahangiri, S., Delgado, A. et al. (2021). Differentiable quantum computational chemistry with PennyLane.
arXiv:2111.09967v2
GSE: Minimize cost function C(θ) = 〈Ψ(θ)|H |Ψ(θ)〉
Exp Value 〈H〉 = 〈 Ψ | H | Ψ 〉
ESE: Minimize cost function C(1)(θ) = 〈Ψ(θ)|H(1) |Ψ(θ)〉
Exp Value H(1) = H + β |Ψ0 > <Ψ0|
Qubit Rotation
4 Sep 2022
Quantum Information
Quantum Chemistry
Total System Energy
 Study total energy gradients with energy
derivatives
 Nuclear forces and geometry optimization
 Force experienced each nuclei is given by the
gradient of the total energy with respect to the
nuclear coordinates (Hellman-Feynman
theorem)
 Vibrational normal modes and frequencies in
the harmonic approximation
 Compute Hessians and vibrational modes
with expressions for higher-order energy
derivatives
49
Sources: Arrazola, J.M., Jahangiri, S., Delgado, A. et al. (2021). Differentiable quantum computational chemistry with PennyLane.
arXiv:2111.09967v2; McArdle, S., Endo, S., Aspuru-Guzik, A. et al. (2020). Quantum computational chemistry. Reviews of Modern
Physics. 92(1):015003.
Fermion to qubit mapping
for Lithium Hydride (LiH)
4 Sep 2022
Quantum Information 50
 What are Quantum Technologies?
 Foundational Tools
 Quantum Cryptography
 Quantum Machine Learning
 Quantum Chemistry
 Advanced Applications
 Quantum Space Science
 Quantum Finance
 Quantum Biology
Agenda
4 Sep 2022
Quantum Information
35 International Spaceports (Aug 2022)
51
Source: https://www.go-astronomy.com/space-ports.php
Newest Spaceport:
ESRANGE (Sweden)
 14 U.S., 21 international
4 Sep 2022
Quantum Information
14 FAA-Permitted U.S. Spaceports (May 2022)
52
Source: https://www.faa.gov/space/spaceports_by_state
 Military, commercial, private space entrepreneurship
SpaceX: 155
successful
rocket launches
(Jun 2022)
4 Sep 2022
Quantum Information
Space-based Arctic Control
 Melting polar ice
opens up
shipping lanes
and geopolitical
control
53
Northwest
Passage
(Canada)
Northeast
Passage
(Russia)
Northern Sea Route
4 Sep 2022
Quantum Information
Space-based Arctic Communications
 Sustainable development of the Arctic
 Isolated fragile environment
 Provide communications infrastructure
from space via satellite-based services
 Connectivity, environmental protection, weather
and climate monitoring, illegal activity detection
 Pentagon (Air Force) expands
satellite-based command and control
capability in the Arctic (May 2022)
 OneWeb, Starlink
 LEO voice and data services
 Ease of switching space internet providers
54
Source: https://www.airforcemag.com/a-space-internet-experiment-for-the-arctic-is-among-vanhercks-priorities
Secure Communication
Space Internet Service
Icebreaker
4 Sep 2022
Quantum Information
Quantum Space Warfare
 Precision weaponization in space
 LEO/GEO communications, sensing, lidar/radar
55
Sources: Krelina, M. (2021). Quantum Warfare: Definitions, Overview and Challenges. arXiv:2103.12548v1.
Farnborough International Airshow announcement Jul 2022 https://www.bbc.com/news/technology-62177614
UK: 164 mile drone
superhighway planned
for security, monitoring,
automated mail and
prescription delivery
4 Sep 2022
Quantum Information
Why Quantum and Space?
 Automated decision-making required
 Autonomous rovers, unmanned spacecraft, remote
space habitats require intelligent decision-making
with little or no human guidance
56
Sources: Smelyanskiy, V.N., Rieffel, E.G., Knysh, S.I. et al. (2012). Near-Term Quantum Computing Approach for Hard Computational
Problems in Space Exploration. arXiv:1204.2821v2; NASA Space Communications Plan. (2007). http://tinyurl.com/spacecomm
NASA Space Communications Networks
 Combinatorial
problems
 NP-hard, would like to
solve autonomously
in space
 Secure
asynchronous
communications
Deep Space Network (DSN)
Near Earth Network (NEN)
Space Network (SN)
Earth-Mars roundtrip :
10-40 minutes
4 Sep 2022
Quantum Information
Deep Space Quantum Computing
 NASA managing deep space communications with
quantum computing (Azure Quantum) (Jan 2022)
 Jet Propulsion Lab (JPL) coordinates space missions through
the Deep Space Network (DSN)
 Global network of large radio antennae (California, Spain, Australia)
in constant communication with spacecraft as the earth rotates
 Missions make several hundred requests per week when
spacecraft is visible to the antenna
 Especially high-fidelity data operations: Perseverance Rover
(2020) and James Webb Space Telescope (2021)
 Quantum-inspired optimization algorithms
 Reduced runtime to produce a mission schedule
from two hours to 2-16 minutes
57
Sources: https://quantumzeitgeist.com/nasa-now-manages-its-space-missions-through-quantum-computing
https://cloudblogs.microsoft.com/quantum/2022/01/27/nasas-jpl-uses-microsofts-azure-quantum-to-manage-communication-with-
space-missions/
4 Sep 2022
Quantum Information
Space Automation Technology
Remote Quantum Monitoring
 Remote monitoring system developed
for inaccessible quantum devices
 Autonomous quantum devices operating in secure remote
environments: space, volcanoes, hospitals, energy plants
 Due to the high sensitivity of quantum apparatus, a stable
environment is essential
 Use remote monitoring technology to access
 Temperature
 Pressure
 Laser beams
 Magnetic fields
 Test setup
 Quantum monitoring network
 Across cold atom laboratories with a shared laser system
58
Source: Barrett, T.J., Evans, W., Gadge, A. et al. (2022). An environmental monitoring network for quantum gas experiments and
devices. Quantum Sci. Technol. 7:025001.
Quantum sensors assess the
safety of electric vehicle batteries
4 Sep 2022
Quantum Information
Practical Application
Time on Mars
59
Sources: https://www.giss.nasa.gov/tools/mars24, https://marsclock.com
 15-minute communications
delay (10-40 minute), hence
 Rover-helicopter coordination
 Mars24 Sunclock
 Earth-day and Martian-sol
 Asynchronous
time-tech
4 Sep 2022
Quantum Information
Planetary Surfaces
 Remarkable similarity
 Automated data registration
60
Surface of Mars (NASA) Surface of Venus (Russian
Academy of Sciences)
Source: Smelyanskiy, V.N., Rieffel, E.G., Knysh, S.I. et al. (2012). Near-Term Quantum Computing Approach for Hard Computational
Problems in Space Exploration. arXiv:1204.2821v2.
4 Sep 2022
Quantum Information
ISS and Quantum
61
Source: https://www.issnationallab.org/ispa-quantum-technologies
Astronaut Christina Koch unloads new hardware for the Cold
Atom Lab - International Space Station (week of 9 Dec 2019)
 Cold atom lab (2019)
 Study Bose-Einstein condensates
 Test states of matter not available on Earth
 Viscosity, conductivity, mechanical motion properties
 Describe unique quantum mechanical behavior
 Benefit of space-
based research
 Vacuum of space
 Low-interference
 Microgravity
4 Sep 2022
Quantum Information 62
QC and ISS: SEAQUE mission (est. launch 2022)
 ISS to host quantum communications test
 SEAQUE space entanglement and annealing quantum experiment
Source: https://www.jpl.nasa.gov/news/space-station-to-host-self-healing-quantum-communications-tech-demo
1. Produce and detect pairs of
entangled photons
 Entanglement source based on
integrated optics
 Automated alignment in space
without operator intervention
2. Self-heal from radiation damage
 Accumulated defects manifest as
“dark counts” in detector output,
overwhelming signal
 Periodically repair radiation-
induced damage with a bright
laser to maintain detector array
Milk carton-sized quantum
experiment to sit outside the
ISS (Nanoracks Bishop airlock)
4 Sep 2022
Quantum Information
QC and CERN
 IBM quantum 27-qubit Falcon processor
 Use QSVM (quantum support vector machine) with
quantum kernel estimator algorithms to identify Higgs
boson-producing collisions
63
Source: Nellist, C. on behalf of the ATLAS Collaboration (2021). tt + Z / W / tt at ATLAS. SNSN-323-63. arXiv:1902.00118v1.
CERN is one IBM Quantum Network hub (2021)
 Simulation frameworks:
 Google TensorFlow Quantum, IBM
Quantum, Amazon Braket
 20-qubit analysis of 50,000 events
 Hardware platform: ibmq-
paris (superconducting)
 15-qubit analysis of 100 events
4 Sep 2022
Quantum Information
QC and CERN: Dark Matter/Dark Energy
 LHC top quark + Higgs boson production
 Top quark: attractive (“bare quark”) is not bound
 Dark matter/dark energy experiments
 Direct observation of Higgs boson production
associated to top-quark pairs
 Use machine learning for improved classification
of events (signal against background noise)
 Quantum computing: exploit exponentially
large qubit Hilbert space
 Identify quantum correlations in particle collision
datasets more efficiently than classically
 Use quantum classifier to distinguish events
associated with Higgs particle production
64
Sources: Carminati, F. (2018). Quantum thinking required. Cern Courier. 58(9):5. https://research.ibm.com/blog/cern-lhc-qml#fn-1.
4 Sep 2022
Quantum Information
Quantum Astronomy
65
GHZ: Greenberger-Horne-Zeilinger
Source: Khabiboulline, E.T., Borregaard, J., De Greve, D. & Lukin, M.D. (2019). Optical Interferometry with Quantum Networks.
Physical Review Letters. 123(7):070504.
 Optical interferometry network
 Collect and store distant source light
 Qubit codes in quantum memory
 Retrieve quantum state nonlocally via
entanglement-assisted parity checks
 Extract phase difference without loss
 Quantum teleport quantum states
 GHZ states (3+ qubits) to preserve
coherence across the quantum network
 Quantum teleport memory (qubit states)
 Apply quantum Fourier transform
 Obtain intensity distribution as the
probabilities of measurement outcome
Collect and Store Light in
Quantum Memory
Quantum Teleportation
European Southern Observatory’s
Very Large Telescope (Chile): four
8.2-meter telescopes
4 Sep 2022
Quantum Information 66
 What are Quantum Technologies?
 Foundational Tools
 Quantum Cryptography
 Quantum Machine Learning
 Quantum Chemistry
 Advanced Applications
 Quantum Space Science
 Quantum Finance
 Quantum Biology
Agenda
4 Sep 2022
Quantum Information
Quantum Finance
 Optimize complexity
 Portfolio allocation
 Trading and arbitrage opportunities
 Capital allocation
 Credit scoring (feature selection)
 Risk assessment
 Risk-return optimization – combinatorial explosion
 Four years of analysis of an eight-asset portfolio with monthly
transactions already a number of configurations greater than
the number of atoms in the known universe
67
Source: D-Wave Systems: Quantum in Financial Services. https://www.dwavesys.com/solutions-and-products/financial-services
Case Study: BBVA (European bank)
Aim: find management strategies with the
highest Sharpe ratio (a metric reflecting
the rate of return at a given level of risk)
Result: evaluated 10382 possible portfolios
in 171 seconds to identify a portfolio with a
Sharpe ratio of 12.16
4 Sep 2022
Quantum Information
Quantum blockchains application
Quantum finance and econophysics
68
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
1Quantum amplitude estimation: technique used to estimate the properties of random distributions
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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
estimation1
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
4 Sep 2022
Quantum Information
Quantum finance (references)
69
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).
4 Sep 2022
Quantum Information 70
 What are Quantum Technologies?
 Foundational Tools
 Quantum Cryptography
 Quantum Machine Learning
 Quantum Chemistry
 Advanced Applications
 Quantum Space Science
 Quantum Finance
 Quantum Biology
Agenda
4 Sep 2022
Quantum Information
Quantum Biology
 Quantum Biology: application of quantum methods to
investigate the complexities of biology and the role of
quantum effects in biology (e.g. magneto-navigation)
71
Sources: Swan, M., dos Santos, R.P. & Witte, F. (2022). Quantum Neurobiology. Quantum Reports. 4(1):107-127.
Ball, P. (2011). The dawn of quantum biology. Nature. 474:272-74. https://qubbe.uchicago.edu/research/imaging.html
Imaging and Sensors
In-cell Targeting
Neural Sequencing (BIOS.health)
Clinical Translation
Connectome Parcellation
Schrödinger
What is
Life?
4 Sep 2022
Quantum Information
The Human Brain
72
 86 billion neurons, 242 trillion synapses
 ~10,000 incoming signals to each neuron
 Not “big numbers” in the big data era
 But all-to-all connectivity possibilities complex to model, but
formerly intractable projects coming into reach
 Quantum BCI and whole-brain modeling
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
Source: Swan, M., dos Santos, R.P., Lebedev, M.A. & Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific.
Neural Entities and Quantum Computation
4 Sep 2022
Quantum Information 73
Connectome Project Status
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
4 Sep 2022
Quantum Information
Levels of Organization in the Brain
74
 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.
4 Sep 2022
Quantum Information
Multiscalar Neuroscience
75
Source: Cook, S.J. et al. (2019). Whole-animal connectomes of both Caenorhabditis elegans sexes. Nature. (571):63-89.
 C. elegans motor neuron mapping (completed 2019)
 302 neurons and 7500 synapses (25:1)
 Human: 86 bn neurons 242 tn synapses (2800:1)
 Functional map of neuronal connections
4 Sep 2022
Quantum Information
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
76
Implicated in neuropathologies of Alzheimer’s, Parkinson’s, stroke, cancer
Synaptic Integration
Math: PDE (Partial Differential
Equation: multiple unknowns)
4 Sep 2022
Quantum Information
Dendritic Spike Integration
 Two kinds of neuronal spiking
 Somatic (axon) spikes
 Dendritic spikes
 (a) Dendritic spine receives EPSP
 (b) Local spiking activity along dendrite
 (c ) Aggregate dendritic spikes at axon
77
EPSP: excitatory postsynaptic potential (contrast with IPSP: inhibitory postsynaptic potential)
Source: Williams, S.R. & Atkinson, S.E. (2008). Dendritic Synaptic Integration in Central Neurons. Curr. Biol. 18(22). R1045-R1047.
(a)
(b)
(c)
4 Sep 2022
Quantum Information
Alzheimer’s Disease Proteome
 Cluster analysis of protein changes
 1,532 proteins changed more than 20% in Alzheimer’s disease
 Upregulation: immune response and cellular signaling pathways
 Downregulation: synaptic function pathways including long term
potentiation, glutamate signaling, and calcium signaling
78
“Omics” 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
Hotspot Clustering Analysis
Sources: Hesse 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). Minehart et al. (2021). Developmental Connectomics of Targeted Microcircuits.
Front Synaptic Neuroscience. 12(615059).
4 Sep 2022
Quantum Information
Glutamate (excitatory) and GABA (inhibitory)
 Post-synaptic density (PSD) proteins
79
Sources: Sheng, M. & Kim, E. (2011). The Postsynaptic Organization of Synapses. Cold Spring Harb Perspect Biol. 3(a005678):1-
20. Image: presynaptic terminal – post-synaptic density: Shine, J.M., Muller, E.J., Munn, B. et al. (2021). Computational models link
cellular mechanisms of neuromodulation to large-scale neural dynamics. Nat Neuro. 24(6):765-776.
Glutamate (Excitatory) Receptor GABA (Inhibitory) Receptor
Major proteins at Glutaminergic and GABAergic synapses
4 Sep 2022
Quantum Information
Waves and Neural Field Theory
80
Source: Complete References: Swan et al. (2022). Quantum Computing for the Brain, Swan et al. (2022) Quantum Neurobiology,
https://www.slideshare.net/lablogga/quantum-neuroscience-crispr-for-alzheimers-connectomes-quantum-bcis
Area What is the Math? Reference
Quantum image reconstruction (via quantum algorithms) Kiani et al., 2020
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)
EEG QML Variational quantum classifier (VQE) Aishwarya et al., 2020
EEG QML Quantum wavelet neural networks (RNNs) Taha & Taha, 2018
EEG QML: Parkinson’s Feature extraction (794 features/21 EEG channels) DBS Koch et al., 2019
EEG/fMRI integration Epilepsy: bifurcation; Resting State: bistability Shine et al., 2021
Single neuron Hodgkin-Huxley, integrate-and-fire, theta neurons Swan et al., 2022
Local ensemble FitzHugh-Nagumo, Hindmarsh-Rose, Morris-Lecor Swan et al., 2022
Neural field theory Jansen-Rit, Wilson-Cowan, Floquet, Kuramoto oscillator, FPE Breakspear, 2017
Swan et al., 2022
Synchrony as a bulk
property of the brain
Columnar microscale current (local field potentials) integrated by
magnitude, distribution of simultaneously-arriving signals
Nunez et al., 2015
 Imaging waveform reconstruction
 Field theory for collective behavior of neurons
4 Sep 2022
Quantum Information
 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)
81
Sources: Maldacena, J. (1999). The large N limit of superconformal field theories and supergravity. Intl. J. Theor. Phys.
38(4):1113-33. 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
4 Sep 2022
Quantum Information
AdS/CFT Studies
82
Category 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/Mathematics AdS/Thermal Systems; AdS/Geometry Shenker & Stanford, 2014; Hazboun 2018
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 AdS/Brain/Cloud Interface Swan, 2023
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., 2018; Cottrell et al., 2019
 Describe a complex bulk volume with a
boundary theory in one less dimension
Sources: Maldacena, J.M. (1999). The large N limit of superconformal field theories and supergravity. Intl. J. Theor. Phys.
38(4):1113–33; Swan et al. (2022). Quantum Computing for the Brain. London: World Scientific.
4 Sep 2022
Quantum Information
AdS/Neuroscience
 AdS/CFT Correspondence
 Mathematics to compute physical system
with a bulk volume and a boundary surface
 AdS/Brain (Neural Signaling)
 Multiscalar phase transitions
 Floquet periodicity-based dynamics
 bMERA tensor networks and matrix
quantum mechanics for renormalization
 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. & 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. 83
Tier Scale Signal
1 Network 10-2 Local field potential
2 Neuron 10-4 Action potential
3 Synapse 10-6 Dendritic spike
4 Molecule 10-10 Ion charge
4 Sep 2022
Quantum Information
Neuroscience Physics
84
Neuroscience Physics Neurobiological Description Reference
1 AdS/Neuroscience
AdS/Brain
AdS/Memory
Bulk-boundary relationship describes complicated volume from
surface in one fewer dimensions: multiscalar neural signaling
(network-neuron-synapse-ion); excited state memory capture
Swan et al., 2022
Dvali, 2017
2 Chern-Simons Neuroscience Topological invariance: geometrical curve min-max indicates
exception (genetic mutation, protein folding, molecular docking)
Bajardi et al., 2021
3 Neural Dynamics (chaos-based)
(multiscalar space-time regimes)
Bifurcation explains epileptic seizure
Bistability explains healthy resting state
Wang et al., 2022
Breakspear, 2017
4 Network Neuroscience Graph-theoretic multiscalar structure-function link in brains Bassett et al., 2018
5 Neuronal Gauge Theories Gauge fields reset universal symmetry (free energy) in signaling Sengupta-Friston, 2016
6 Molecular Knotting DNA compaction, histone spooling, DNA chirality inversion Leigh et al., 2021
7 Topological Materials
(novel matter phases)
Quantum spin liquids (QSL) and fractional quantum Hall state
(FQHE) per disordered spins: signaling as emergence
Winter & Valenti, 2021
Frenkel & Hartnoll, 2021
8 Potential quantum effects in the brain Higher-order cognition, memory, attention, consciousness Craddock et al., 2019
Source: Swan, M. et al. (2022). Quantum Computing for the Brain. London: World Scientific.
 Neuroscience physics:
neuroscience interpretation of
foundational physics findings
4 Sep 2022
Quantum Information
Chern-Simons Biology
Genome Physics
 Model DNA and RNA as knot polynomial
 Chiral molecule twisted left-to-right in supersymmetry
breaking as knot polynomial
 t-RNA anti-codon also in knot structure
85
Right-hand nucleic acid modeled as
Hopf fibration with S3 group action to
projective space of genetic code
 Gauge group
 Gauge group of gene geometric translation
is group action of transcription process
 Genetic code as brane Wilson loop EV
 Genetic code is average expectation value
of Wilson loop operator of coupling
between hidden state and twist D-brane
and anti-D-brane over superspace of cell
membrane
Source: Capozziello, S., Pincak, R., Kanjamapornkul, K. & Saridakis, E.N. (2018). The Chern-Simons current in systems of DNA-
RNA transcriptions. Annalen der Physik. 530(4): 1700271.
4 Sep 2022
Quantum Information
Genome Physics
 Dynamics of chromatin looping
 Genomes folded into loops and
topologically associating domains
(TADs) by CTCF (CCCTC-
binding factor) and cohesin (loop
lifecycle (10-30 min)
 DNA Matter Phases
 Spatial organization of
chromosomes leads to
heterogeneous chromatin motion
and drives the liquid- or gel-like
dynamical behavior of chromatin
86
Sources: Gabriele et al. (2022). Dynamics of CTCF- and cohesin-mediated chromatin looping revealed by live-cell imaging. Science.
376(6592):496-501. Salari et al. (2021). Spatial organization of chromosomes leads to heterogeneous chromatin motion and drives
the liquid- or gel-like dynamical behavior of chromatin. bioRxiv preprint doi: https://doi.org/10.1101/2021.05.10.443375.
Topologically-associating domains (TADs)
4 Sep 2022
Quantum Information
Genome Physics
 DNA Sol-Gel phase transition
 Role of gelation (CTCF site
anchoring) in orchestrating
genetic locus rearrangement
without loops or crosslinks
 DNA condensation and
damage repair
 Chromatin manipulation and
DNA damage detection
87
Sources: Takata et al. (2013). Chromatin Compaction Protects Genomic DNA from Radiation Damage. PLoS ONE. 8(10):75622.
Khanna et al. (2019). Chromosome dynamics near the sol-gel phase transition dictate the timing of remote genomic interactions.
Nature Communications. 10:2771.
4 Sep 2022
Quantum Information
Genome Physics
Molecular Knotting
88
Sources: Lim, N.C.H. & Jackson, S.E. (2015). Molecular knots in biology and chemistry. Journal of Physics: Condensed Matter.
27:354101. Leigh, D.A. et al. (2021). A molecular endless (74) knot. Nature Chemistry. 13:117–122. Lewandowska et al., 2017.
 Alexander polynomial knot classification
 Number = crossing (complexity measure)
 Index subscript = order within that crossing
 Ex: trefoil knot with three crossings (31)
 DNA (long biopolymer) forms chiral, achiral,
torus, twist knots
 Simple trefoil (31) knots to 9+ crossings
 Viral genomic DNA: chiral and torus knots
 Molecular nanoweaving
 Zinc and iron ions used to weave ligand strands to
form a molecular endless 74 knot
 Organic molecule (collagen peptide) nanoweaving
in 90-degree kagome lattices of weft-warp threads
Molecular
trefoil knot
4 Sep 2022
Quantum Information
DNA Chirality Inversion
89
DNA Chirality Inversion
Liquid Crystal
 Add chiral dopant (LuIII) to solution
 Liquid-crystal DNA unfolds and
refolds into opposite chirality
 Remove dopant
 Initial chirality returns
 Result: low-cost alternative to
covalent bond breaking
 Liquid crystal: matter state
between liquid and crystal
 Attractive to manipulate: flows
like a liquid with molecules
arranged in a lattice (crystal)
Source: Leigh Laboratory: Katsonis, N. et al. (2020). Knotting a molecular strand can invert macroscopic effects of chirality. Nature
Chemistry. 12:939-944.
Dopant: Lanthanide ions LuIII
4 Sep 2022
Quantum Information
Ice
Phytoplankton
Whales
Krill swarm
Krill distribution
Whale distribution
Phytoplankton distribution
Multiscalar System: Food-Web Ecosystem
Southern Ocean: Phytoplankton – Krill Swarm – Whale
Primary factors: light, nutrients
Secondary factors: temperature
Primary factors: daylight (solar elevation, radiation),
proximity to Antarctic continental slope
Secondary factors: current velocities and gradients
Primary factors: foraging
availability, distance to neighbors
Secondary factors: predation, light,
physiological stimuli, reproduction
HSO = f (P1, K1, W1, s, )
∂s
∂P1
∂s
∂K1
∂s
∂W1
, ,
f (P, K, W, s) + g (P, K, W, s) + h (P, K, W, s) = i (P, K, W, s)
∂s
∂W
∂s
∂K
∂s
∂P
Krill swarm mathematical modeling (03/28/22)
Mathematical Model by Ecosystem Tier
 Phytoplankton: Reaction-diffusion-advection per light spectrum
differentiation, coupled plankton-oxygen dynamics, fluid
dynamics and Brownian motion (Heggerud, 2021)
 Krill swarm: Lagrangian (Brownian motion, spatial distribution)
(Hofmann, 2004); hydrodynamic signal per drafting within front
neighbor propulsion jet (Murphy, 2019); Kuramoto oscillator for
time and space synchrony (O’Keeffe, 2022)
 Krill-whale relation: hotspot clustering, statistical field theory
(Miller, 2019)
Light Spectrum Differentiation
4 Sep 2022
Quantum Information
Order, Disorder, Chaos
 Order (arrangement), disorder (confusion), chaos
(self-organization: confusion gives way to order)
 Flocking: 3D orientation vis-à-vis 5-10 neighbors
 Swarmalators: self-synchronization in time and space
 Krill self-position in propulsion jet of nearest front neighbor (draft) as
a hydrodynamic communication channel that structures the school
(via metachronal stimulation of individual krill pleopods (~fins))
91
Source: Murphy et al. (2019). The Three-Dimensional Spatial Structure of Antarctic Krill Schools in the Laboratory. Scientific
Reports. 9(381):1-12.
Krill swarm: 30,000 individuals per square meter
(largest known aminal aggregations)
Flocking: 3D orientation vis-a-vis 5-10 nearest neighbors
Black holes, quasi-
particles, quantum
spin liquids,
schooling, flocking,
swarming
4 Sep 2022
Quantum Information
Practical Application
Quantum Life Sciences
 Computer-aided drug design
for small-molecule drugs
 Accelerate discovery of
selectively-binding chemical
compounds with minimal off-
target effects
 Protein structure prediction,
engineering, and design
 Predict protein structure from
amino acid sequence
 Generate complex biomolecules
 Precision medicine, pathology,
and imaging analysis
92
Case Study: GlaxoSmithKline and Menton AI
Aim: identify antiviral peptides that block
infection. Create a fixed chemical backbone
as a peptide scaffold, and explore the
combinatorial space of possible amino acid
compositions specific to the scaffold
Result: identify several promising peptide
designs of natural and synthetic amino acids
Source: D-Wave Systems: Quantum in Life Sciences. https://www.dwavesys.com/solutions-and-products/life-sciences
 90% of new drug development efforts ineffective
4 Sep 2022
Quantum Information
Galleri Blood Test
Cancer Blood Test for over 50 Cancer Types
93
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
 Concierge availability online ($995)
4 Sep 2022
Quantum Information
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)
94
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
4 Sep 2022
Quantum Information
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)
95
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
CRISPR/Cas9 therapeutic strategies are being evaluated
on pre-clinical Alzheimer’s disease models (Hanafy, 2020)
4 Sep 2022
Quantum Information
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
96
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
4 Sep 2022
Quantum Information
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
97
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).
4 Sep 2022
Quantum Information
Glia and Calcium Signaling
98
 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.
4 Sep 2022
Quantum Information
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
99
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.
4 Sep 2022
Quantum Information
Alzheimer’s Disease
100
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.
 Patient case:
 Left: Subject with protective Christchurch APOE3R136S
mutation (rs121918393) A not C: heavy Aβ plaque burden
(top), but limited tau tangles (bottom), and no early onset
Alzheimer’s disease
 Right: Control case with Paisa mutation Presenilin 1
(rs63750231): low Aβ plaque burden (top), substantial tau
tangles (bottom), and early-onset Alzheimer’s
 Implication: CRISPR-based genetic cut-paste study
Plaques (top red): No
Early-onset Alzheimer’s
Tangles (bottom red):
Early-onset Alzheimer’s
 Contra indicating
plaques and
tangles
4 Sep 2022
Quantum Information
Personalized Genomics for Brain Disease
 Personalized genomic screening for brain disease
 Synaptome analysis + genomic data
 133 brain diseases caused by mutations
 Neurological (AD, PD), motor, affective, metabolic disease
 1,461 proteins human neocortex postsynaptic density
 PSD, CaMKIIa, App, Syngap, GluA, Plp1, Vcan, Hapln1, CRMP,
Ras, Sh3gl, PKA, Shank3
101
Sources: Grant, S.G.N. (2019). Synapse diversity and synaptome architecture in human genetic disorders. Hum Mol Gen.
28(R2):R219-25. A. Heo, S., Diering, G.H., Na, C.H. et al. (2018). Identification of long-lived synaptic proteins by proteomic analysis
of synaptosome protein turnover. PNAS. 115(16):E3827-36. B. Bayes, A., van de Lagemaat, L.N., Collins, M.O. et al. (2011).
Characterization of the proteome, diseases and evolution of the human postsynaptic density. Nat. Neurosci. 14:19-21.
B. 133 Brain Diseases per ICD-10 Classification caused
by genetic mutation and faulty proteins
A. 1,461 Synapse Proteins influencing
molecular and cellular function
4 Sep 2022
Quantum Information
Aging Brain: Synaptic Decline
 Brainwide atlas of synapses across mouse lifespan
 Whole-brain data of 12 regions and 109 anatomical subregions
 Isocortex, olfaction, hippocampus, cortical subplate, striatum, pons,
pallidum, thalamus, hypothalamus, midbrain, medulla, cerebellum
 Lifespan changes in three phases
 Phase 1 (0-2 mos): number of puncta increase rapidly
 Phase 2 (2-12 mos): rate of increase in puncta density slows and
characterized by relative stability (adulthood is reached at 6 mos)
 Phase 3 (12-18 mos): puncta density decline, synapse size increase
102
Source: Cizeron, M., Qiu, Z., Koniaris, B. et al. (2020). A brainwide atlas of synapses across the mouse life span. Science. 369:270-
75.
Two scaffolding proteins (PSD95: green; SAP102: magenta) across 18-month mouse lifespan: in
older age, the protein density declines for both, and the size of the SAP proteome inflates
4 Sep 2022
Quantum Information 103
 What are Quantum Technologies?
 Foundational Tools
 Quantum Cryptography
 Quantum Machine Learning
 Quantum Chemistry
 Advanced Applications
 Quantum Space Science
 Quantum Finance
 Quantum Biology
Agenda
4 Sep 2022
Quantum Information 104
The fast pace of quantum information study is
enabling a new tier of scientific problem-solving
Early-adopter fields: space science, biology, chemistry,
finance, cryptography, physics
Thesis
4 Sep 2022
Quantum Information 105
Next-generation Materials
 New forms of Consumer Electronics
 Continue trend of miniaturization and
functionality improvement
 Metamaterial plasmonics
 Replace lasers with near field optics
 More efficient field generator
Source: Oka & Kitamura. (2019). Floquet engineering of quantum materials. Ann. Rev. Cond. Matt. Phys. 0:387–408 Ma et al.
(2021). Topology and geometry under the nonlinear electromagnetic spotlight. Nature Materials. 20:1601–1614.
Novel Quantum Materials (Ma, 2021)
 Nonlinear quantum phase
materials
 Use topology and quantum
geometry methods to detect
new electromagnetic
responses in quantum
materials
Novel Materials
4 Sep 2022
Quantum Information 106
Quantum Math
Quantum Science
Classical Mindset Quantum Mindset
Quantum Mindset
Classical Mind Quantum Mind
The self-knowing time series
Classical Math
Classical Science
Mindset progression
 All physics and mathematics ever developed
until recently was with the Classical Mindset
5 properties: symmetry,
topology, superposition,
entanglement, interference
Hyperbolic band theory (Bloch
theorem), quantum statistics
Quantum machine learning (Born
machine, neural operators)
4 Sep 2022
Quantum Information
Quantum Mind as Self-knowing Time Series
 Thinking in the mode of physics concepts
 Time series as the foundational clue
 Ideal-real tiers, integration of diverse scale domains
 Time dilation in thought
 Radical uncertainty, all events are probabilistic
 Knowability trade-offs (time-location, speed-energy, etc.)
 Superpositioned thinking
 Holding multiple positions in mind simultaneously
before collapsing to a measurement
107
Quantum microscopy
Schrödinger cat states Hyperbolic space
Source: https://www.slideshare.net/lablogga/critical-theory-of-silence
4 Sep 2022
Quantum Information
Quantum Science Fields
108
Source: Swan, M., dos Santos, R.P. & Witte, F. (2020). Quantum Computing: Physics, Blockchains, and Deep Learning Smart
Networks. London: World Scientific.
Quantum Biology
Quantum Neuroscience
Quantum Machine
Learning
€
$
¥
€
Early-adopter fields: space science, biology, chemistry, finance, cryptography, physics
Quantum
Cryptography
Quantum Space
Science Quantum Finance
Foundational
Tools
Advanced
Applications
Quantum
Chemistry
4 Sep 2022
Quantum Information
Quantum Mathematics by Field
109
Source: Swan, M., dos Santos, R.P. & Witte, F. (2022). Quantum Information Science. IEEE Internet Computing. Special Journal
Issue: Quantum and Post-Moore’s Law Computing. January/February 2022.
Quantum Discipline What is the Math?
1 Quantum Cryptography Lattice problems (group theory)
difficulty of learning with errors, shortest vector, the other thing
Difficulty of lattice problems (finding shortest vector to an arbitrary point); learning-with-errors and Fiat-
Shamir with Aborts over module lattices, short integer solutions over NTRU lattices and has functions over
lattices
2 Quantum Machine
Learning
Variational algorithms, Neural ODE, Neural PDE (neural operators), QGANs
QNN, TN, QSVM/Q RKHS Q Kernel Learning
3 Quantum Chemistry Waves: atomic wavefunction (approximation)
Ground-state excited-state energy functions, total system energy
Qubit Hamiltonians, VQE
4 Quantum Space
Science
Quantum optimization algorithms (Azure); optics; QAOA; AdS/CFT, BH, chaos, TN, MERA, RG
5 Quantum Finance Quantum estimation algorithm
Quantum amplitude estimation: technique used to estimate the properties of random distributions
Chern-Simons (topological invariance)
6 Quantum Biology Waves: Fourier transform, Fourier slice theorem & Radon transform; QML (VQE)
Single-neuron: Hodgkin-Huxley, integrate-and-fire, theta neuron
Local ensemble: FitzHugh-Nagumo, Hindmarsh-Rose, Morris-Lecor
Neural field theory: Jansen-Rit, Wilson-Cowan, Floquet, Kuramoto oscillators, Fokker-Planck equations
Neuroscience Physics: AdS/CFT, Chern-Simons, gauge theory, bifurcation & bistability
Swarmalator: phytoplankton (diffusion); krill (Brownian motion, Kuramoto oscillator); whale (clustering)
 Mainly heterogeneous (recurrence: Chern-Simons)
4 Sep 2022
Quantum Information
Risks and Limitations
110
 Quantum domain is hard to understand
 Complex, non-intuitive
 Human-Technology Relation
 Personal data monopoly domination
 Google, Apple, Facebook, Microsoft
 Digital divide widens (cost, accessibility)
 Overwhelm (right to non-adoption in increasingly
technologized world)
 Lack of empowering relation with technology
 Humans willingly enframed as standing reserve
instead of technology as background enabler
 Alienation (one-way panopticon video
surveillance via biometrics, drones)
Heidegger, The Question
Concerning Technology
+
-
Santa Ana CA, 4 Sep 2022
Slides: http://slideshare.net/LaBlogga
Melanie Swan, PhD
Quantum Technologies
University College London
Quantum Information
Space, Biology, and Computation
Thank you!
Questions?
“Outside there was silence, as there is and has been and
always should be. The perfect silence of the spheres.”
- Elizabeth Bear, Ancestral Night, 2019, p. 384
4 Sep 2022
Quantum Information
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
The Fountain, Monto, 2018
Elastic: Flexible Thinking in a Time
of Change, Mlodinow, 2018
The new skillset: elastic
thinking includes neophilia
(affinity for novelty),
schizotypy (perceiving the
unusual), imagination, and
integrative thinking
Exercise means that 60 really
is the new 30, releasing anti-
inflammatory IL-6 which
enhances cognitive
performance through
telomere lengthening and
mitochondrial genesis
112
Livewired: The Inside Story of the Ever-
Changing Brain, Eagleman, 2020
More than simple
neural plasticity, the
brain is “livewired” to
constantly absorb
changes by interacting
with its environment
Neocortex learns a model of the
world and constantly updates it;
no centralized control mechanism;
cortical columns make predictions;
aggregate neuron strength wins
A Thousand
Brains,
Hawkins, 2021
Question what we think we
know. Conversations are
for being open-minded not
for convincing. Be humble,
curious, and open
Think Again, Grant, 2021
Human intelligence is based on
abductive inference which is not
fully understood; it cannot be
reduced to induction or deduction,
or encoded and programed, hence
at present, computers cannot be
trained to think as humans
The Myth of Artificial
Intelligence, Larson, 2021
4 Sep 2022
Quantum Information
Space Quiz (as of 1 Sep 2022)
113
1. Number of humans who have been to space? (Jun 2022)
 (LEO, GEO, ISS, 90-seconds of 0-g space flight)
2. Number of confirmed exoplanet discoveries?
3. Number of international spaceports?
4. Number of FAA-permitted U.S. spaceports?
5. Number of countries in Africa? (calibration question)
4 Sep 2022
Quantum Information
Jokes
114
 Why was the amoeba
moving in the microscope?
 To get to the other slide
 Which side of the brain has
the most neurons?
 The inside
 What did the EEG say to
the neuroscientist?
 Nothing, it just waved
 What do glial cells see at
the ballet?
 Schwann Lake
 What is a cat's favorite type
of neuron?
 Purr-kinje cells (Purkinje cell)
Quantum Mechanics and Space
 Police officer: “Sir, did you know
there’s a dead cat in your trunk?”
 Schrödinger: “Well, now I do~!”
 A neutron walks into a bar
 For you, no charge
 A quantum particle walks into two bars
 How many astronomers does it take to
change a light bulb?
 3 plus or minus 75
 How was the restaurant on the moon?
 Good food but not much atmosphere
 The new gravity book
 I just can’t put it down
 Astronomy
 One star is easy to find, but you have to wait
until daytime
Biology and Neuroscience
Coffee and doughnuts are the
same to a topologist
4 Sep 2022
Quantum Information 115
Appendix
Quantum
Chemistry
Quantum
Computing
Quantum
Finance
Quantum
Medicine
Laser Microscopy:
six pairs of atoms
4 Sep 2022
Quantum Information
Mathematical Approaches to Neuroscience
116
Behavioral tier Classical approach Quantum approach
1 Network-neuron
Behavior: neuronal firing
Task: integrate empirical
data (EEG, MEG, fMRI,
tractography etc.)
• Orbit and bifurcation: Turing
instability to Hopf instability
and Bogdanov-Takens
bifurcation (codimensionality
>1), piecewise functions,
Floquet periodicity
• Criticality-triggered phase
transition: various models
• QAOA: MaxCut partition
functions, MaxSET max
independent set, graph
coloring, Hamiltonians
• AdS/Brain and bMERA
• Quantum kernel learning
• Quantum control theory
2 Neuron-synapse
Behavior: action potential
to neurotransmitter to
action potential
Task: Signal transduction:
E-to-C and C-to-E
(E: electrical, C: chemical)
• Synaptic integration: ODE but
need PDE (radial-longitudinal
reaction-diffusion of calcium)
• Near-far fast-slow space-time
based signal attenuation
• Charge-voltage differentials
• Lateral-dorsal (in pyramidal)
• MPS spin-state criticality
scattering model
• Anharmonic oscillators
• Amplitude estimation
• Continuous-time quantum
walks and UV-IR correlations
• Quasicrystal non-Fermi
liquid phase transitions
3 Synapse-ion
Behavior: ion reception
Task: molecular dynamics
model of ion docking
• Topology, elliptical geometry
• Bayesian, ANOVA analysis
• Microscopy data acquisition
(behaving brain, etc.)
• VQE (molecular energies)
• QBism (quantum Bayesian)
• GBS (femtochemistry)
• QML (GAN feeds QNN)
Source: Swan, M., dos Santos, R.P., Lebedev, M.A. & Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific.
4 Sep 2022
Quantum Information
Mathematic Problem Reformulation
117
Neuroscience problem Classical requirements Quantum reframe
1 Network-neuron
Empirical datastream
integration (EEG, MEG,
fMRI, tractography,
connectome, synaptome)
• Multiscalar integration of
diverse space-time and
dynamics regimes
• Unknown statistical
distributions (apply partial
Fokker-Planck equations
and mean-field, Jansen-Rit,
oscillatory neural dynamics)
• Scale renormalization as a
feature (MERA tensor
networks and quantum
kernel learning RKHS)
• Advanced probabilistic
methods (Born machine) find
statistical distributions and
generate new data
2 Neuron-synapse
Synaptic integration
• Radial-longitudinal reaction-
diffusion PDEs
• Superpositioned quantum
information state modeling
3 Synapse-ion
a. Electrical-chemical
signal conversion
b. Astrocyte calcium
signaling
c. Ion transfer
d. Excitatory-inhibitory
(GLUT-GABA) at
dendritic arbors
• Synaptogamin vesicles
• EPSP (head)/IPSP (spine)
• Dendritic head ellipses
• Piecewise functions
• Floquet periodicity
• Orbit-instability
• Bifurcation
• Chaotic neural dynamics
• Holographic partitions
• Scrambling Hamiltonian:
information spread
• SYK model: bosonic-
fermionic operators of
strongly correlated system
• Superconducting
condensate
Source: Swan, M., dos Santos, R.P., Lebedev, M.A. & Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific.
4 Sep 2022
Quantum Information
Quantum Information Science techniques
Tackle New Problem Classes
118
High-
dimensionality
quantum platforms
Quantum mathematics Practical advance:
quantum computation
Theoretical advance:
foundational physics
• Ion trap
• Rydberg arrays
• Cold atom
arrays
• Neutral atoms
• GBS
(Gaussian
boson
sampling)
• Optical
platforms
• Random tensors
(1/N expansion,
melonic diagrams,
large D branching
polymers)
• QAOA alternating
cost-mixing
Hamiltonians
• Partition functions
• Variational quantum
eigensolver (VQE)
• Graph coloring
• Max independent
set and MaxSAT
• Superpositioned
quantum information
state modeling
• Ladder operators
Continuous-time
quantum walks
• GHZ-states
• GBS/graph theory
• Quantum kernel
learning (RKHS)
• Global timekeeping:
quantum clock
network
• Materials:
superconductivity
• Materials: new
topological matter
phases not reaching
thermal equilibrium
• Operators: winding-
unwinding distribution
growth
• SYK operators
• Quantum Bayesian
updating (QBism)
Quantum Theory (Quantum Information Science canon)
Source: Swan, M., dos Santos, R.P., Lebedev, M.A. & Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific.

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Quantum Technologies Research Program

  • 1. Santa Ana CA, 4 Sep 2022 Slides: http://slideshare.net/LaBlogga Melanie Swan, PhD Quantum Technologies University College London Quantum Information Space, Biology, and Computation “Outside there was silence, as there is and has been and always should be. The perfect silence of the spheres.” - Elizabeth Bear, Ancestral Night, 2019, p. 384
  • 2. 4 Sep 2022 Quantum Information 1 The fast pace of quantum information study is enabling a new tier of scientific problem-solving Early-adopter fields: space science, biology, chemistry, finance, cryptography, physics Thesis
  • 3. 4 Sep 2022 Quantum Information 2 Quantum Technologies Research Program 2015 2019 2020 Blockchain Blockchain Economics Quantum Computing Quantum Computing for the Brain 2022
  • 4. 4 Sep 2022 Quantum Information 3  What are Quantum Technologies?  Foundational Tools  Quantum Cryptography  Quantum Machine Learning  Quantum Chemistry  Advanced Applications  Quantum Space Science  Quantum Finance  Quantum Biology Agenda
  • 5. 4 Sep 2022 Quantum Information Space: We are Here~! 4 Source: Tully, R.B., Courtois, H., Hoffman, Y. & Pomarede, D. (2014). The Laniakea supercluster of galaxies. Nature. 513(7516):71. Distribution of Galaxies Location of the Milky Way Galaxy (Virgo Supercluster) within the Laniakea Supercluster  Decentered in the supercluster, the local group, the galaxy, and the solar system Laniakea Supercluster Milky Way Galaxy Novel method: analyze relative velocities of galaxies as watershed divides (turbulence)
  • 6. 4 Sep 2022 Quantum Information Time: Seeing farther back into the Big Bang 5 Source: https://www.jwst.nasa.gov/content/about/comparisonWebbVsHubble.html Hubble (HST) can see “toddler galaxies” Webb (JWST) can see “baby galaxies” 6.25x larger collecting area than Hubble  James Webb Space Telescope (launched Dec 2021)  “See” farther back in time with infrared spectrum
  • 7. 4 Sep 2022 Quantum Information Other Potential Life 5,125+ Exoplanets Discovered (Aug 2022)  1/3 each super-earths, neptunes, jupiters  Over 800 with more than one planet  Atmosphere, volcanism, sun-planet relation  Habitable zone (CHON carbon-hydrogen-oxygen-nitrogen) 6 Source: https://www.jwst.nasa.gov/content/about/comparisonWebbVsHubble.html Radial Velocity (Yellow: Kepler, Pink: Terrestrial) Transit (Blue: space-based telescopes) Detection Method:
  • 8. 4 Sep 2022 Quantum Information The Large and Small Scale Universe 7 Scale Measure Comment 1 5.1 x 1096 Planck density Kg/Meter3 Density of the universe immediately after the Big Bang 2 1 x 1080 Particles Total particles in the observable universe (est.) 3 1 x 1014 Cells Cells in the human body (9 out of 10 are bacteria) 4 8 x 1010 Stars Number of stars in the Milky Way galaxy (est.) 5 1 x 102 Meter Earth Earth’s atmosphere: 10,000 ft life support, 62 mi to space 6 1 x 101 Meter Human Human-scale: Classical Mechanics 7 1 x 10-9 Nanometer Atoms Quantum mechanics (nanotechnology) 8 1 x 10-12 Picometer Ions, photons Optics, photonics 9 1 x 10-15 Femtometer Subatomic Gauge theories 10 1 x 10-35 Planck scale Meters Smallest known length scale 11 5.4 x 10-44 Planck time Seconds Shortest meaningful interval of time Source: The Universe by Numbers. https://www.physicsoftheuniverse.com/numbers.html Large-scale: General Relativity (GR) Small-scale: Quantum Mechanics (QM) Human-scale: Classical Mechanics  Quantum mechanics, classical mechanics, general relativity  Quantum effects visible at 10-9 m  Relativistic effects present at any speed (matter of precision)
  • 9. 4 Sep 2022 Quantum Information Quantum Scale 8 QCD: Quantum Chromodynamics Subatomic particles Matter particles: fermions (quarks) Force particles: bosons (gluons) Scale Entities Physical Theory 1 1 x101 m Meter Humans Newtonian mechanics 2 1 x10-9 m Nanometer Atoms Quantum mechanics (nanotechnology) 3 1 x10-12 m Picometer Ions, photons Optics, photonics 4 1 x10-15 m Femtometer Subatomic particles QCD/gauge theories 5 1 x10-35 m Planck scale Planck length Planck scale Atoms Quantum objects: atoms, ions, photons  “Quantum” = anything at the scale of atomic and subatomic particles (10-9 to 10-15)  Theme: ability to study and manipulate physical reality at smaller scales  Study phenomena (e.g. neurons) in the native 3D structure of physical reality
  • 10. 4 Sep 2022 Quantum Information 9 Basic Concept What is Quantum Computing?  Computing: change of state between 0/1  Move information around and perform a computation  Classical computing: serial not parallel  Quantum computing: treat more than one status at the same time, compute all the transactions at the same time  Fundamentally, a different way of computing Source: Fowler, A.G., Mariantoni, M., Martinis, J.M. & Cleland, A.N. (2012). Surface codes: Towards practical large-scale quantum computation. Phys Rev A. 86(032324).
  • 11. 4 Sep 2022 Quantum Information  A qubit (quantum bit) is the basic unit of quantum information, the quantum version of the classical binary bit 10 What is a Qubit? Bit exists in a single binary state (0 or 1) Qubit exists in a state of superposition, at every location with some probability, until collapsed into a measurement (0/1) Implication: test more permutations Classical Bit Quantum Bit (Qubit) Source: https://www.newsweek.com/quantum-computing-research-computer-flagship-eu-452167
  • 12. 4 Sep 2022 Quantum Information 11 What is a Qudit? Classical Bit: 0,1 Qubit: 0,1 Qutrit: 0,1,2 Qutrit stabilizer code on a torus Source: Imany et al. (2019). High-dimensional optical quantum logic in large operational spaces. npj Quantum Information. 5(59):1-10.  Qudit (quantum information digit)  Exists in superposition of 2+ states before collapsed in measurement  Qubit (2-values): 0,1  Qutrit (3-values): 0, 1, 2  Conducive to 3d error correction  7-10 qudits have been tested (multi- dimensional entanglement) 4 Optical Qudits entangled in time & space (20 qubits) Bloch sphere: 3D particle movement in X, Y, Z directions Particle exists in all positions until collapsed in measurement
  • 13. 4 Sep 2022 Quantum Information Quantum: Many Potential Speed-ups 1. Bit (0 or 1) 2. Qubit (0 and 1 in superposition) 3. Qudit (more than 2 values in superposition)  Microchip generates two entangled qudits each with 10 states, for 100 dimensions total, for more than six entangled qubits could generate (Imany, 2019 ) 4. Optics (time and frequency multiplexing)  Existing telecommunications infrastructure  Global network not standalone computers in labs  Time-frequency binning (20+ states tested) 5. Optics (superposition of inputs and gates) 6. High-dimensional entanglement 12 Classical Computing Quantum Computing Source: Imany et al. (2019). High-dimensional optical quantum logic in large operational spaces. npj Quantum Information. 5(59):1-10.
  • 14. 4 Sep 2022 Quantum Information Quantum Error Correction Codes  Quantum error-correction code: logical codespace corresponding to a physical lattice model to manipulate a particle  Use Pauli matrices to control qubits in the x, y, z dimensions 13 Code Description Basic quantum error-correcting code Stabilizer codes Topology-based Pauli operators (X, Y, Z) correct a bit-flip or a spin flip Toric code Stabilizer operators defined on a 2D torus-shaped spin lattice Surface code Stabilizer operators defined on a 2D spin lattice in any shape Advanced quantum error-correcting code (greater scalability, control) Bosonic codes Self-contained photon-based oscillator system with bosonic modes GKP code Squeezed states protect position and amplitude shifts with rotations Molecular code Rotations performed on any asymmetric body (molecule) in free space Cat code Superpositioned states (Schrödinger) used as error correction codes GKP codes (Gottesman, Kitaev, Preskill) (Gottesman et al., 2001) Source: Swan, M., dos Santos, R.P. & Witte, F. (2022). Quantum Matter Overview. J. 5(2):232-254. Quantum Error-correcting Codes for Quantum Object Manipulation Pauli Matrices (x, y, z) Quantum Circuit
  • 15. 4 Sep 2022 Quantum Information Quantum Error Correction  Clifford gates (basic quantum gates)  Pauli matrices, and the Hadamard, CNOT, and π/2-phase shift gates; simulated classically  Non-Clifford gates (complex operations)  Logical depth (π/8 gate); cannot simulate classically  Consolidate multiple noisy to few reliable states  Magic state distillation (computationally costly)  Gauge fixing stabilizer codes (Majorana fermion braiding)  Gauge color fixing (color codes)  Time-based surface codes  Replicates the three-dimensional code that performs the non-Clifford gate functions with three overlapping copies of the surface code interacting locally over a period of time 14 Source: Fowler, A.G., Mariantoni, M., Martinis, J.M. & Cleland, A.N. (2012). Surface codes: Towards practical large-scale quantum computation. Phys Rev A. 86(032324). Time-based surface code
  • 16. 4 Sep 2022 Quantum Information 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 (represented by the Greek letter Ψ) EΨ(r) = -ћ2/2m ∇2 Ψ(r) + V(r)Ψ(r) Total Energy = Kinetic Energy + Potential Energy (motion) (resting) 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 EΨ(r) = -ћ2/2m ∇2 Ψ(r) + V(r)Ψ(r) Schrödinger wave equation
  • 17. 4 Sep 2022 Quantum Information Superconducting Qubit  Implement by sending current through a small ring  Create “1” and “0” states as current circulating clockwise and counterclockwise in the superconducting loop  The smallest amount of flux that can be in the loop corresponds to either +Φ0/2 and - Φ0/2, where Φ0 = ћ/2e is the magnetic flux quantum  The two states represent the “0” and “1” values of a classical bit or the two basis states of a qubit |0> and |1>  Potential energy wells  System tunnels back and forth between |0> and |1>  Can also occupy a superposition state of |0> and |1> with current simultaneously circulating both clockwise and counterclockwise 16 Superconducting Tunnel Junction Image of “0” and “1” states Source: Smelyanskiy, V.N., Rieffel, E.G., Knysh, S.I. et al. (2012). Near-Term Quantum Computing Approach for Hard Computational Problems in Space Exploration. arXiv:1204.2821v2. Single-qubit Hamiltonian 2 x 2 Pauli matrices acting on single qubit states Superconducting Qubit Configuration Qubit Potential Energy Wells (“1” and “0” states) Two States: Spin-up/Spin-down
  • 18. 4 Sep 2022 Quantum Information Moore’s Law 17 Source: Thomasian, N.M., Kamel, I.R. & Bai, H.X. (2021). Machine intelligence in non-invasive endocrine cancer diagnostics. Nat Rev Endocrinol. 18:81-95. https://ourworldindata.org/uploads/2020/11/Transistor-Count-over-time.png 1. Plateau – sustainable? 2. Already incorporating quantum effects
  • 19. 4 Sep 2022 Quantum Information Computing Architecture End of Moore’s Law Problem  Large ecosystem of computational platforms 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 Computing Spiking Neural Networks (SNNs) Quantum Computing 18 2500 BC Abacus 20th Century Classical 21st Century Quantum Abacus -> Logarithm -> Classical -> Quantum +
  • 20. 4 Sep 2022 Quantum Information 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 19
  • 21. 4 Sep 2022 Quantum Information Status Quantum Computing available via Cloud Services 20 Sources: Company press releases, QCWare, Preskill, J. (2021). Quantum computing 40 years later. arXiv:2106.10522, https://amitray.com/roadmap-for-1000-qubits-fault-tolerant-quantum-computers https://arstechnica.com/science/2021/11/ibm-clears-the-100-qubit-mark-with-its-new-processor Era Organization Qubit Method # Qubits Status 1 IBM, academia (factor the number 15) NMR, optical, solid-state superconducting 4-7 Demo (2001-2012) 2a IBM (Almaden CA) Superconducting (gate model) 127 Available (Nov 2021) 2b D-Wave Systems (Vancouver BC) Superconducting (quantum annealing) 2048 Available (May 2019) 2c Rigetti Computing (Berkeley CA) Superconducting (gate model) 80 Available (Dec 2021) 2d IonQ (College Park MD) Trapped Ions 32 Available (Sep 2021) 2c Google (Mountain View CA) Superconducting (gate model) 53 (72) Backend: Google cloud 2e Microsoft (Santa Barbara CA) Majorana Fermions Unknown Backend: Azure cloud 3 Technical breakthrough needed Universal quantum computing 1 million Hypothetical future  Quantum error correction break-through needed to scale to million-qubit machines  Current platforms: NISQ (noisy intermediate- scale quantum) devices without error correction  Future platforms: error-corrected FTQC (fault- tolerant quantum computing)  Few-qubit (2000s) –> 100-qubit (2021) –> million-qubit
  • 22. 4 Sep 2022 Quantum Information Quantum Computing Microsoft IBM Rigetti
  • 23. 4 Sep 2022 Quantum Information Using a Quantum Computer to Factor 22 Source: D-Wave Systems, Inc. https://cloud.dwavesys.com/leap/resources/demos
  • 24. 4 Sep 2022 Quantum Information Future of Quantum Computing  Technology is notoriously difficult to predict  “I think there is a world market for maybe five computers” – Watson, IBM CEO, 1943  Xerox: “I think we’ll make about four copies a week” – State Street Bank, adopting a xerograph 23 Sources: Ceruzzi, P. (2003). A History of Modern Computing. 2nd Ed. Cambridge: MIT Press; Strohmeyer, R. (2008). The 7 Worst Tech Predictions of All Time. PCWorld. D-Wave Systems: 10-feet tall, $15m Current: Ytterbium- 171 isotopes at 1 Kelvin (-458°F) Actual room- temperature superconductors: ?? 70 years IBM Quantum Experience UNIVAC computer (1950s): 465 multiplications per second (faster than Hidden Figures human computers) Billions of times faster
  • 25. 4 Sep 2022 Quantum Information Quantum Information 24 Domain Properties Top Five Properties: Quantum Matter and Quantum Computing Definition Quantum Matter Symmetry Looking the same from different points of view (e.g. a face, cube, laws of physics); symmetry breaking is phase transition Topology Geometric structure preserved under deformation (bending, stretching, twisting, and crumpling, but not cutting or gluing); doughnut and coffee cup both have a hole Quantum Computing Superposition An unobserved particle exists in all possible states simultaneously, but once measured, collapses to just one state (superpositioned data modeling of all possible states) Entanglement Particles connected such that their states are related, even when separated by distance (a “tails-up/tails-down” relationship; one particle in one state, other in the other) Interference Waves reinforcing or canceling each other out (cohering or decohering) Source: Swan, M., dos Santos, R.P. & Witte, F. (2022). Quantum Matter Overview. J. 5(2):232-254. Quantum Information: the information (physical properties) of the state of a quantum system
  • 26. 4 Sep 2022 Quantum Information Quantum Algorithms  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 (with only √N queries vs all or at least half N entries classically)  Floquet circuits: time as engineering problem  Discrete time crystals (matter phases not reaching thermal equilibrium)  Hyperbolic Bloch theorem  More than four squares connect at vertices in a hyperbolic lattice 25 Elliptic geometry (positively-curved) Hyperbolic geometry (negatively-curved) Flat geometry (no curvature) Euclidean and beyond spacetimes Sources: Maciejko, J. & Rayan, S. (2021). Hyperbolic band theory. Sci. Adv. 7:eabe9170. Mi, X. et al. (2021). Observation of Time- Crystalline Eigenstate Order on a Quantum Processor. arXiv:2107.13571. (Google Quantum AI and collaborators) Time-crystalline Eigenstate order Hyperbolic space
  • 27. 4 Sep 2022 Quantum Information Quantum Algorithms  VQE: variational quantum eigensolvers  Finds the ground state of a given problem Hamiltonian  Finds the eigenvalues of a matrix (Peruzzo, 2014)  VAE: variational autoencoder (Kingma & Welling, 2014)  Three-step (compress, analyze, re-encode) neural network method: nonlinear similarities in high-dimensional unlabeled data  Example: train autoencoder to minimize the Euclidean distances (reconstruction errors) between the original and decoded vectors in a 148-dimensional feature space (Vasylenko,2022)  QAOA (1): quantum approximate optimization algorithm  Combinatorial optimization (Farhi, 2014)  QAOA (2): quantum alternating operator ansatz (guess)  Alternating Hamiltonians (cost-mixing) model (Hadfield, 2021) 26 Source: McArdle, S., Endo, S., Aspuru-Guzik, A. et al. (2020). Quantum computational chemistry. Reviews of Modern Physics. 92(1):015003, p. 31. Variational Quantum Eigensolver (VQE)
  • 28. 4 Sep 2022 Quantum Information Quantum Walks  Quadratically faster per ballistic propagation through lattice walk environment vs classical diffusive spread 27 Source: Kendon. V. (2020). How to Compute Using Quantum Walks. EPTCS. 315:1-17.  The walk travels through all paths in superposition  Application: faster search and cryptography algorithms  Quantum walk selection parameters  Coin flip via quantum coin-flip operator (e.g. Hadamard coin flipping a qubit to a one or zero)  Multi-dimensional lattice graph walk environment  Quantum walk algorithm  Time regime (discrete-continuous)
  • 29. 4 Sep 2022 Quantum Information Quantum Studies in the Academy 28 Digital Humanities Arts Sciences Quantum Humanities computational astronomy, computational biology Digital Humanities (literature & painting analysis, computational philosophy1) Quantum Humanities quantum chemistry, quantum finance, quantum biology, quantum ecology Apply quantum methods to study field-specific problems e.g. quantum machine learning Apply data science methods to study field-specific problems e.g. machine learning  Data science institutes now including quantum  What are Digital Humanities / Quantum Humanities? 1. Apply digital/quantum methods to research questions 2. Find digital/quantum examples in field subject matter  (e.g. quantum mechanical formulations in Shakespeare) 3. Open new investigations per digital/quantum conceptualizations Sources: Miranda, E.R. (2022). Quantum Computing in the Arts and Humanities. London: Springer. Barzen, J. & Leymann, F. (2020). Quantum Humanities: A First Use Case for Quantum Machine Learning in Media Science. Digitale Welt. 4:102-103. 1Example of computational philosophy: investigate formal axiomatic metaphysics with an automated reasoning environment Big Data Science Vermeer imaging (1665-2018) Textual analysis
  • 30. 4 Sep 2022 Quantum Information Quantum Science Fields 29 Source: Swan, M., dos Santos, R.P. & Witte, F. (2020). Quantum Computing: Physics, Blockchains, and Deep Learning Smart Networks. London: World Scientific. Quantum Biology Quantum Neuroscience Quantum Machine Learning € $ ¥ € Early-adopter fields: space science, biology, chemistry, finance, cryptography, physics Quantum Cryptography Quantum Space Science Quantum Finance Foundational Tools Advanced Applications Quantum Chemistry
  • 31. 4 Sep 2022 Quantum Information 30  What are Quantum Technologies?  Foundational Tools  Quantum Cryptography  Quantum Machine Learning  Quantum Chemistry  Advanced Applications  Quantum Space Science  Quantum Finance  Quantum Biology Agenda
  • 32. 4 Sep 2022 Quantum Information “Y2K of crypto” threat NIST Post-Quantum Cryptography Project  Four quantum-resistant algorithms announced (Jul 2022)  General concept: shift from factoring to lattices (3d+)  Factoring (number theory); Lattices (group theory, order theory)  Classical: based on the difficulty of factoring large numbers  Size of large number: eight 32-bit words (SHA-256)  Quantum: based on the difficulty of lattice problems  Lattice: geometric arrangement of points in a space  Example: find shortest vector to an arbitrary point 31 Module: generalization of vector space in which the field of scalars is replaced by a ring Hash function: generic structure for converting arbitrary-length input to fixed-size output Source: https://www.nist.gov/news-events/news/2022/07/nist-announces-first-four-quantum-resistant-cryptographic-algorithms Application Algorithm Category Based on difficulty of solving 1 Public-key encryption CRYSTALS-Kyber (IBM) Structured lattices Learning-with-errors (LWE) problem over module lattices 2 Digital signature CRYSTALS-Dilithium (IBM) Structured lattices Lattice problems over module lattices (Fiat-Shamir with Aborts) 3 Digital signature FALCON (IBM) Structured lattices (Fast Fourier) Short integer solution problem (SIS) over NTRU lattices (Number Theory Research Unit) 4 Digital signature SPHINCS+ (Eindhoven University of Technology) Hash functions Hash functions over lattices (vs. classical SHA-256 hash functions)
  • 33. 4 Sep 2022 Quantum Information 32 NIST Algorithm Selection  NIST: 26 of 69 algorithms advance to post-quantum crypto semifinal (Jan 2019)  Public-key encryption (17)  Digital signature schemes (9)  Approaches: lattice-based, code-based, multivariate  Lattice-based: target the Learning with Errors (LWE) problem with module or ring formulation (MLWE or RLWE)  Code-based: error-correcting codes (Low Density Parity Check (LDPC) codes)  Multivariate: field equations (hidden fields and small fields) and algebraic equations Source: NISTIR 8240: Status Report on the First Round of the NIST Post-Quantum Cryptography Standardization Process, January 2019, https://doi.org/10.6028/NIST.IR.8240.
  • 34. 4 Sep 2022 Quantum Information 33  What are Quantum Technologies?  Foundational Tools  Quantum Cryptography  Quantum Machine Learning  Quantum Chemistry  Advanced Applications  Quantum Space Science  Quantum Finance  Quantum Biology Agenda Shine et al., 2021
  • 35. 4 Sep 2022 Quantum Information Early success in Supervised Learning (2011)  YouTube: user-classified data perfect for Supervised Learning  2 mn cat videos of 800 mn total YouTube videos (Aug 2022) 34 Source: Google Brain: Le, QV, Dean, Jeff, Ng, Andrew et al. 2012. Building high-level features using large scale unsupervised learning. https://arxiv.org/abs/1112.6209. https://earthweb.com/
  • 36. 4 Sep 2022 Quantum Information (Classical) Machine Learning  Supervised learning (discriminative networks)  Learn from labeled data (“cat”)  Unsupervised learning (generative networks)  Learn the distribution of unlabeled data, create samples  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 35 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.
  • 37. 4 Sep 2022 Quantum Information Quantum Machine Learning  Quantum machine learning  Implement machine learning algorithms on quantum platforms  Study quantum problems with machine learning techniques  QML versions of all three ML architectures 36 Sources: Farhi & Neven. (2018). Classification with quantum neural networks on near term processors. arXiv:1802.06002; Grant et al. (2018). Hierarchical quantum classifiers. NPJ Quantum Inf. 4(65):1–8; Schuld & Killoran. (2019). Quantum machine learning in feature Hilbert spaces. Phys. Rev. Lett. 122(4):040504. Chatterjee & Yu. (2017). Generalized coherent states, reproducing kernels, and quantum support vector machines. Quantum Inf. Commun. 17(15-16):1292–1306. Architecture Description Application Reference 1 Quantum neural network Neural network method based on distilling information from an input wavefunction into output qubits Image classification (MNIST) Farhi and Neven, 2018 2 Quantum tensor network Tensor network method based on factoring a high-order tensor (with a large number of indices) into a set of low-order tensors whose indices are summed to form a network defined by a certain pattern of contractions Image classification (MNIST), generate quantum state data Grant et al., 2018 3 Quantum kernel learning (reusable structure = “kernel trick”) Kernel learning method (pattern analysis) in which functions in higher-dimensional feature space are computed on a data kernel using distance measures (the inner products between all data pairs in the feature space) instead of data coordinates; Quantum finance: trade identification (support vector machines and RKHS (reproducing kernel Hilbert space) Schuld & Killoran, 2019; Chatterjee & Yu, 2017
  • 38. 4 Sep 2022 Quantum Information Born Machine  In machine learning, an automated energy function (“machine”) uses a loss function to assess 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 37 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). RBM: restricted to prohibit intralayer connections for efficient training Map Restricted Boltzmann Machine to Born Machine tensor network
  • 39. 4 Sep 2022 Quantum Information Neural Operators  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 2018)  Neural PDE: NN architecture that uses neural operators to map between infinite-dimensional spaces  Fourier neural operator solves all instances of PDE family in multiple spatial discretizations  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) 38 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).
  • 40. 4 Sep 2022 Quantum Information Practical Application 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 39 Source: Iqbal, A., Khan, R. & Karayannis, T. (2019). Developing a brain atlas through deep learning. Nat. Mach. Intell. 1:277-87.
  • 41. 4 Sep 2022 Quantum Information Status of AI AI Writes a Paper about Itself 40 Source: Gpt Generative Pretrained Transformer, Almira Osmanovic Thunström, Steinn Steingrimsson. Can GPT-3 write an academic paper on itself, with minimal human input?. 2022. hhal-03701250 https://hal.archives-ouvertes.fr/hal-03701250 GPT-3 is a machine learning platform that enables developers to train and deploy AI models. It is also said to be scalable and efficient with the ability to handle large amounts of data. Some have called it a "game changer" in the field of AI (O'Reilly, 2016). GPT-3 has been used in a number of different applications including image recognition, natural language processing, and predictive modeling. In each of these cases, GPT-3 has demonstrated its potential to improve upon existing methods (Lee, 2016).
  • 42. 4 Sep 2022 Quantum Information 41  What are Quantum Technologies?  Foundational Tools  Quantum Cryptography  Quantum Machine Learning  Quantum Chemistry  Advanced Applications  Quantum Space Science  Quantum Finance  Quantum Biology Agenda
  • 43. 4 Sep 2022 Quantum Information 42 Quantum Chemistry (= Molecular QM)  Quantum Chemistry: branch of physical chemistry applying quantum mechanics to chemical systems  Solve classically-intractable chemistry problems  High temperature superconductivity, solid-state/condensed matter physics, transition metal catalysis, new compound discovery  Biochemical reactions, molecular dynamics, protein folding  Short-term Objectives  Computational solutions to Schrödinger equation (approximate)  Increase size of molecules that can be studied Sources: Krenn et al. (2020).Self-referencing embedded strings (SELFIES): A 100% robust molecular string representation. Machine .Learning: Sci. Tech. 1(4):045024; Kmiecik et al. (2020). Coarse-Grained Protein Models and their Applications. Chem. Rev. 116:7898−7936.
  • 44. 4 Sep 2022 Quantum Information Quantum Chemistry New Materials Found for Electric Batteries  Unsupervised machine learning method identifies new battery materials for electric vehicles  Four candidates out of 300  VAE (variational autoencoder to compress, analyze, re-encode high-dimensional data) used to rank chemical combinations  Quaternary phase fields containing two anions (e.g. lithium solid electrolytes)  Discovery of Li3.3SnS3.3Cl0.7 43 Source: Vasylenko, A., Gamon, J., Duff, B.D. et al. (2021). Element selection for crystalline inorganic solid discovery guided by unsupervised machine learning of experimentally explored chemistry. Nature Communications. 12:5561. Ranking of Synthetic Exploration Probe structure of Li3SnS3Cl predicted coupled anion and cation order VAE Analyzes High-Dimensional Data
  • 45. 4 Sep 2022 Quantum Information Digital Fabrication Methods Autonomous Robotic Nanofabrication  Use single molecules to produce supramolecular structures  Control single molecules with the machine learning agent- based manipulation of scanning probe microscope actuators  Use reinforcement learning (goal- directed updating) to remove molecules autonomously from the structure with a scanning probe microscope 44 Source: Leinen, P., Esders, M., Schutt, K.T. et al. (2020). Autonomous robotic nanofabrication with reinforcement learning. Sci. Adv. 6:eabb6987. Subtractive manufacturing with machine learning: molecules bind to the scanning microscope tip; bond formation and breaking increases or decreases the tunneling current; new molecules are retained in the monolayer by a network of hydrogen bonds
  • 46. 4 Sep 2022 Quantum Information Atomically-Precise Manufacturing  Single atoms positioned to create macroscopic objects  Applications: molecular electronics, nanomedicine, integrated circuits, thin films, etch masks, renewable energy materials 45 STM: scanning tunneling microscope; SPM: scanning probe microscope Source: Randall, J.N. (2021). ZyVector: STM Control System for Atomically Precise Lithography. Zyvex Labs. https://www.zyvexlabs.com/apm/products/zyvector Atomically-Precise Writing (Deposition) with an STM 1. Outline the structure of the design 2. Specify crystal lattice vector layout 3. Write (deposit) atoms with the STM tip 4. Finalize atomically-precise pattern ZyVector: STM Control System for Atomically Precise Lithography (Zyvex Labs)
  • 47. 4 Sep 2022 Quantum Information Molecular Electronics: Quantum Circuit Design  Molecular circuits for quantum computing, construct  One-qubit gates using one-electron scattering in molecules  Two-qubit controlled-phase gates using electron-electron scattering along metallic leads 46 Source: Jensen, P.W.K., Kristensen, L.B., Lavigne, C. & Aspuru-Guzik, A. (2022). Toward Quantum Computing with Molecular Electronics. Journal of Chemical Theory and Computation. Electron transmission magnitude as a function of incoming kinetic energy for molecular hydrogen in the 6-31G basis attached between one input and two output leads Electron transmission through molecular hydrogen in STO-3G basis (the planes intersecting through the two orbitals indicate the integration limits)
  • 48. 4 Sep 2022 Quantum Information Quantum Chemistry System Setup: Quantum Algorithms  Qubit Hamiltonians  Quantum algorithm: express Hamiltonian as qubit operator  Retain fermionic exchange symmetries  Describe fermionic states in terms of qubit states  Perform transformations using fermionic-to-qubit mappings (e.g. Jordan-Wigner transformation)  Excitation gates as Givens rotations  Main tool: Variational Quantum Eigensolver (VQE)  Algorithm to compute approximate system energies  Optimize the parameters of a quantum circuit with respect to the expectation value of a molecular Hamiltonian (minimizing a cost function) 47 Source: Arrazola, J.M., Jahangiri, S., Delgado, A. et al. (2021). Differentiable quantum computational chemistry with PennyLane. arXiv:2111.09967v2
  • 49. 4 Sep 2022 Quantum Information Quantum Chemistry Ground and Excited-state Energies  Ground state energy (GSE)  Compute Hamiltonian expectation values  Convert the system Hamiltonian to a sparse matrix  Use the vector representation of the state to compute the expectation value using matrix vector multiplication  Calculate expectation values by performing single-qubit rotations  Pauli expressions are tensor products of local qubit operators  Manage complexity by grouping Pauli expressions into sets of mutually- commuting operators (calculate EV from the same measurement statistics)  Excited state energy (ESE)  Compute excited-state energies: add penalty terms to cost function  The lowest-energy eigenstate of the penalized system is the first excited state of the original system  Iterate to find k-th excited state by adjusting penalty parameters 48 Source: Arrazola, J.M., Jahangiri, S., Delgado, A. et al. (2021). Differentiable quantum computational chemistry with PennyLane. arXiv:2111.09967v2 GSE: Minimize cost function C(θ) = 〈Ψ(θ)|H |Ψ(θ)〉 Exp Value 〈H〉 = 〈 Ψ | H | Ψ 〉 ESE: Minimize cost function C(1)(θ) = 〈Ψ(θ)|H(1) |Ψ(θ)〉 Exp Value H(1) = H + β |Ψ0 > <Ψ0| Qubit Rotation
  • 50. 4 Sep 2022 Quantum Information Quantum Chemistry Total System Energy  Study total energy gradients with energy derivatives  Nuclear forces and geometry optimization  Force experienced each nuclei is given by the gradient of the total energy with respect to the nuclear coordinates (Hellman-Feynman theorem)  Vibrational normal modes and frequencies in the harmonic approximation  Compute Hessians and vibrational modes with expressions for higher-order energy derivatives 49 Sources: Arrazola, J.M., Jahangiri, S., Delgado, A. et al. (2021). Differentiable quantum computational chemistry with PennyLane. arXiv:2111.09967v2; McArdle, S., Endo, S., Aspuru-Guzik, A. et al. (2020). Quantum computational chemistry. Reviews of Modern Physics. 92(1):015003. Fermion to qubit mapping for Lithium Hydride (LiH)
  • 51. 4 Sep 2022 Quantum Information 50  What are Quantum Technologies?  Foundational Tools  Quantum Cryptography  Quantum Machine Learning  Quantum Chemistry  Advanced Applications  Quantum Space Science  Quantum Finance  Quantum Biology Agenda
  • 52. 4 Sep 2022 Quantum Information 35 International Spaceports (Aug 2022) 51 Source: https://www.go-astronomy.com/space-ports.php Newest Spaceport: ESRANGE (Sweden)  14 U.S., 21 international
  • 53. 4 Sep 2022 Quantum Information 14 FAA-Permitted U.S. Spaceports (May 2022) 52 Source: https://www.faa.gov/space/spaceports_by_state  Military, commercial, private space entrepreneurship SpaceX: 155 successful rocket launches (Jun 2022)
  • 54. 4 Sep 2022 Quantum Information Space-based Arctic Control  Melting polar ice opens up shipping lanes and geopolitical control 53 Northwest Passage (Canada) Northeast Passage (Russia) Northern Sea Route
  • 55. 4 Sep 2022 Quantum Information Space-based Arctic Communications  Sustainable development of the Arctic  Isolated fragile environment  Provide communications infrastructure from space via satellite-based services  Connectivity, environmental protection, weather and climate monitoring, illegal activity detection  Pentagon (Air Force) expands satellite-based command and control capability in the Arctic (May 2022)  OneWeb, Starlink  LEO voice and data services  Ease of switching space internet providers 54 Source: https://www.airforcemag.com/a-space-internet-experiment-for-the-arctic-is-among-vanhercks-priorities Secure Communication Space Internet Service Icebreaker
  • 56. 4 Sep 2022 Quantum Information Quantum Space Warfare  Precision weaponization in space  LEO/GEO communications, sensing, lidar/radar 55 Sources: Krelina, M. (2021). Quantum Warfare: Definitions, Overview and Challenges. arXiv:2103.12548v1. Farnborough International Airshow announcement Jul 2022 https://www.bbc.com/news/technology-62177614 UK: 164 mile drone superhighway planned for security, monitoring, automated mail and prescription delivery
  • 57. 4 Sep 2022 Quantum Information Why Quantum and Space?  Automated decision-making required  Autonomous rovers, unmanned spacecraft, remote space habitats require intelligent decision-making with little or no human guidance 56 Sources: Smelyanskiy, V.N., Rieffel, E.G., Knysh, S.I. et al. (2012). Near-Term Quantum Computing Approach for Hard Computational Problems in Space Exploration. arXiv:1204.2821v2; NASA Space Communications Plan. (2007). http://tinyurl.com/spacecomm NASA Space Communications Networks  Combinatorial problems  NP-hard, would like to solve autonomously in space  Secure asynchronous communications Deep Space Network (DSN) Near Earth Network (NEN) Space Network (SN) Earth-Mars roundtrip : 10-40 minutes
  • 58. 4 Sep 2022 Quantum Information Deep Space Quantum Computing  NASA managing deep space communications with quantum computing (Azure Quantum) (Jan 2022)  Jet Propulsion Lab (JPL) coordinates space missions through the Deep Space Network (DSN)  Global network of large radio antennae (California, Spain, Australia) in constant communication with spacecraft as the earth rotates  Missions make several hundred requests per week when spacecraft is visible to the antenna  Especially high-fidelity data operations: Perseverance Rover (2020) and James Webb Space Telescope (2021)  Quantum-inspired optimization algorithms  Reduced runtime to produce a mission schedule from two hours to 2-16 minutes 57 Sources: https://quantumzeitgeist.com/nasa-now-manages-its-space-missions-through-quantum-computing https://cloudblogs.microsoft.com/quantum/2022/01/27/nasas-jpl-uses-microsofts-azure-quantum-to-manage-communication-with- space-missions/
  • 59. 4 Sep 2022 Quantum Information Space Automation Technology Remote Quantum Monitoring  Remote monitoring system developed for inaccessible quantum devices  Autonomous quantum devices operating in secure remote environments: space, volcanoes, hospitals, energy plants  Due to the high sensitivity of quantum apparatus, a stable environment is essential  Use remote monitoring technology to access  Temperature  Pressure  Laser beams  Magnetic fields  Test setup  Quantum monitoring network  Across cold atom laboratories with a shared laser system 58 Source: Barrett, T.J., Evans, W., Gadge, A. et al. (2022). An environmental monitoring network for quantum gas experiments and devices. Quantum Sci. Technol. 7:025001. Quantum sensors assess the safety of electric vehicle batteries
  • 60. 4 Sep 2022 Quantum Information Practical Application Time on Mars 59 Sources: https://www.giss.nasa.gov/tools/mars24, https://marsclock.com  15-minute communications delay (10-40 minute), hence  Rover-helicopter coordination  Mars24 Sunclock  Earth-day and Martian-sol  Asynchronous time-tech
  • 61. 4 Sep 2022 Quantum Information Planetary Surfaces  Remarkable similarity  Automated data registration 60 Surface of Mars (NASA) Surface of Venus (Russian Academy of Sciences) Source: Smelyanskiy, V.N., Rieffel, E.G., Knysh, S.I. et al. (2012). Near-Term Quantum Computing Approach for Hard Computational Problems in Space Exploration. arXiv:1204.2821v2.
  • 62. 4 Sep 2022 Quantum Information ISS and Quantum 61 Source: https://www.issnationallab.org/ispa-quantum-technologies Astronaut Christina Koch unloads new hardware for the Cold Atom Lab - International Space Station (week of 9 Dec 2019)  Cold atom lab (2019)  Study Bose-Einstein condensates  Test states of matter not available on Earth  Viscosity, conductivity, mechanical motion properties  Describe unique quantum mechanical behavior  Benefit of space- based research  Vacuum of space  Low-interference  Microgravity
  • 63. 4 Sep 2022 Quantum Information 62 QC and ISS: SEAQUE mission (est. launch 2022)  ISS to host quantum communications test  SEAQUE space entanglement and annealing quantum experiment Source: https://www.jpl.nasa.gov/news/space-station-to-host-self-healing-quantum-communications-tech-demo 1. Produce and detect pairs of entangled photons  Entanglement source based on integrated optics  Automated alignment in space without operator intervention 2. Self-heal from radiation damage  Accumulated defects manifest as “dark counts” in detector output, overwhelming signal  Periodically repair radiation- induced damage with a bright laser to maintain detector array Milk carton-sized quantum experiment to sit outside the ISS (Nanoracks Bishop airlock)
  • 64. 4 Sep 2022 Quantum Information QC and CERN  IBM quantum 27-qubit Falcon processor  Use QSVM (quantum support vector machine) with quantum kernel estimator algorithms to identify Higgs boson-producing collisions 63 Source: Nellist, C. on behalf of the ATLAS Collaboration (2021). tt + Z / W / tt at ATLAS. SNSN-323-63. arXiv:1902.00118v1. CERN is one IBM Quantum Network hub (2021)  Simulation frameworks:  Google TensorFlow Quantum, IBM Quantum, Amazon Braket  20-qubit analysis of 50,000 events  Hardware platform: ibmq- paris (superconducting)  15-qubit analysis of 100 events
  • 65. 4 Sep 2022 Quantum Information QC and CERN: Dark Matter/Dark Energy  LHC top quark + Higgs boson production  Top quark: attractive (“bare quark”) is not bound  Dark matter/dark energy experiments  Direct observation of Higgs boson production associated to top-quark pairs  Use machine learning for improved classification of events (signal against background noise)  Quantum computing: exploit exponentially large qubit Hilbert space  Identify quantum correlations in particle collision datasets more efficiently than classically  Use quantum classifier to distinguish events associated with Higgs particle production 64 Sources: Carminati, F. (2018). Quantum thinking required. Cern Courier. 58(9):5. https://research.ibm.com/blog/cern-lhc-qml#fn-1.
  • 66. 4 Sep 2022 Quantum Information Quantum Astronomy 65 GHZ: Greenberger-Horne-Zeilinger Source: Khabiboulline, E.T., Borregaard, J., De Greve, D. & Lukin, M.D. (2019). Optical Interferometry with Quantum Networks. Physical Review Letters. 123(7):070504.  Optical interferometry network  Collect and store distant source light  Qubit codes in quantum memory  Retrieve quantum state nonlocally via entanglement-assisted parity checks  Extract phase difference without loss  Quantum teleport quantum states  GHZ states (3+ qubits) to preserve coherence across the quantum network  Quantum teleport memory (qubit states)  Apply quantum Fourier transform  Obtain intensity distribution as the probabilities of measurement outcome Collect and Store Light in Quantum Memory Quantum Teleportation European Southern Observatory’s Very Large Telescope (Chile): four 8.2-meter telescopes
  • 67. 4 Sep 2022 Quantum Information 66  What are Quantum Technologies?  Foundational Tools  Quantum Cryptography  Quantum Machine Learning  Quantum Chemistry  Advanced Applications  Quantum Space Science  Quantum Finance  Quantum Biology Agenda
  • 68. 4 Sep 2022 Quantum Information Quantum Finance  Optimize complexity  Portfolio allocation  Trading and arbitrage opportunities  Capital allocation  Credit scoring (feature selection)  Risk assessment  Risk-return optimization – combinatorial explosion  Four years of analysis of an eight-asset portfolio with monthly transactions already a number of configurations greater than the number of atoms in the known universe 67 Source: D-Wave Systems: Quantum in Financial Services. https://www.dwavesys.com/solutions-and-products/financial-services Case Study: BBVA (European bank) Aim: find management strategies with the highest Sharpe ratio (a metric reflecting the rate of return at a given level of risk) Result: evaluated 10382 possible portfolios in 171 seconds to identify a portfolio with a Sharpe ratio of 12.16
  • 69. 4 Sep 2022 Quantum Information Quantum blockchains application Quantum finance and econophysics 68 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 1Quantum amplitude estimation: technique used to estimate the properties of random distributions € $ ¥ € 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 estimation1 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
  • 70. 4 Sep 2022 Quantum Information Quantum finance (references) 69 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).
  • 71. 4 Sep 2022 Quantum Information 70  What are Quantum Technologies?  Foundational Tools  Quantum Cryptography  Quantum Machine Learning  Quantum Chemistry  Advanced Applications  Quantum Space Science  Quantum Finance  Quantum Biology Agenda
  • 72. 4 Sep 2022 Quantum Information Quantum Biology  Quantum Biology: application of quantum methods to investigate the complexities of biology and the role of quantum effects in biology (e.g. magneto-navigation) 71 Sources: Swan, M., dos Santos, R.P. & Witte, F. (2022). Quantum Neurobiology. Quantum Reports. 4(1):107-127. Ball, P. (2011). The dawn of quantum biology. Nature. 474:272-74. https://qubbe.uchicago.edu/research/imaging.html Imaging and Sensors In-cell Targeting Neural Sequencing (BIOS.health) Clinical Translation Connectome Parcellation Schrödinger What is Life?
  • 73. 4 Sep 2022 Quantum Information The Human Brain 72  86 billion neurons, 242 trillion synapses  ~10,000 incoming signals to each neuron  Not “big numbers” in the big data era  But all-to-all connectivity possibilities complex to model, but formerly intractable projects coming into reach  Quantum BCI and whole-brain modeling 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 Source: Swan, M., dos Santos, R.P., Lebedev, M.A. & Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific. Neural Entities and Quantum Computation
  • 74. 4 Sep 2022 Quantum Information 73 Connectome Project Status 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
  • 75. 4 Sep 2022 Quantum Information Levels of Organization in the Brain 74  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.
  • 76. 4 Sep 2022 Quantum Information Multiscalar Neuroscience 75 Source: Cook, S.J. et al. (2019). Whole-animal connectomes of both Caenorhabditis elegans sexes. Nature. (571):63-89.  C. elegans motor neuron mapping (completed 2019)  302 neurons and 7500 synapses (25:1)  Human: 86 bn neurons 242 tn synapses (2800:1)  Functional map of neuronal connections
  • 77. 4 Sep 2022 Quantum Information 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 76 Implicated in neuropathologies of Alzheimer’s, Parkinson’s, stroke, cancer Synaptic Integration Math: PDE (Partial Differential Equation: multiple unknowns)
  • 78. 4 Sep 2022 Quantum Information Dendritic Spike Integration  Two kinds of neuronal spiking  Somatic (axon) spikes  Dendritic spikes  (a) Dendritic spine receives EPSP  (b) Local spiking activity along dendrite  (c ) Aggregate dendritic spikes at axon 77 EPSP: excitatory postsynaptic potential (contrast with IPSP: inhibitory postsynaptic potential) Source: Williams, S.R. & Atkinson, S.E. (2008). Dendritic Synaptic Integration in Central Neurons. Curr. Biol. 18(22). R1045-R1047. (a) (b) (c)
  • 79. 4 Sep 2022 Quantum Information Alzheimer’s Disease Proteome  Cluster analysis of protein changes  1,532 proteins changed more than 20% in Alzheimer’s disease  Upregulation: immune response and cellular signaling pathways  Downregulation: synaptic function pathways including long term potentiation, glutamate signaling, and calcium signaling 78 “Omics” 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 Hotspot Clustering Analysis Sources: Hesse 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). Minehart et al. (2021). Developmental Connectomics of Targeted Microcircuits. Front Synaptic Neuroscience. 12(615059).
  • 80. 4 Sep 2022 Quantum Information Glutamate (excitatory) and GABA (inhibitory)  Post-synaptic density (PSD) proteins 79 Sources: Sheng, M. & Kim, E. (2011). The Postsynaptic Organization of Synapses. Cold Spring Harb Perspect Biol. 3(a005678):1- 20. Image: presynaptic terminal – post-synaptic density: Shine, J.M., Muller, E.J., Munn, B. et al. (2021). Computational models link cellular mechanisms of neuromodulation to large-scale neural dynamics. Nat Neuro. 24(6):765-776. Glutamate (Excitatory) Receptor GABA (Inhibitory) Receptor Major proteins at Glutaminergic and GABAergic synapses
  • 81. 4 Sep 2022 Quantum Information Waves and Neural Field Theory 80 Source: Complete References: Swan et al. (2022). Quantum Computing for the Brain, Swan et al. (2022) Quantum Neurobiology, https://www.slideshare.net/lablogga/quantum-neuroscience-crispr-for-alzheimers-connectomes-quantum-bcis Area What is the Math? Reference Quantum image reconstruction (via quantum algorithms) Kiani et al., 2020 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) EEG QML Variational quantum classifier (VQE) Aishwarya et al., 2020 EEG QML Quantum wavelet neural networks (RNNs) Taha & Taha, 2018 EEG QML: Parkinson’s Feature extraction (794 features/21 EEG channels) DBS Koch et al., 2019 EEG/fMRI integration Epilepsy: bifurcation; Resting State: bistability Shine et al., 2021 Single neuron Hodgkin-Huxley, integrate-and-fire, theta neurons Swan et al., 2022 Local ensemble FitzHugh-Nagumo, Hindmarsh-Rose, Morris-Lecor Swan et al., 2022 Neural field theory Jansen-Rit, Wilson-Cowan, Floquet, Kuramoto oscillator, FPE Breakspear, 2017 Swan et al., 2022 Synchrony as a bulk property of the brain Columnar microscale current (local field potentials) integrated by magnitude, distribution of simultaneously-arriving signals Nunez et al., 2015  Imaging waveform reconstruction  Field theory for collective behavior of neurons
  • 82. 4 Sep 2022 Quantum Information  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) 81 Sources: Maldacena, J. (1999). The large N limit of superconformal field theories and supergravity. Intl. J. Theor. Phys. 38(4):1113-33. 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
  • 83. 4 Sep 2022 Quantum Information AdS/CFT Studies 82 Category 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/Mathematics AdS/Thermal Systems; AdS/Geometry Shenker & Stanford, 2014; Hazboun 2018 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 AdS/Brain/Cloud Interface Swan, 2023 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., 2018; Cottrell et al., 2019  Describe a complex bulk volume with a boundary theory in one less dimension Sources: Maldacena, J.M. (1999). The large N limit of superconformal field theories and supergravity. Intl. J. Theor. Phys. 38(4):1113–33; Swan et al. (2022). Quantum Computing for the Brain. London: World Scientific.
  • 84. 4 Sep 2022 Quantum Information AdS/Neuroscience  AdS/CFT Correspondence  Mathematics to compute physical system with a bulk volume and a boundary surface  AdS/Brain (Neural Signaling)  Multiscalar phase transitions  Floquet periodicity-based dynamics  bMERA tensor networks and matrix quantum mechanics for renormalization  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. & 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. 83 Tier Scale Signal 1 Network 10-2 Local field potential 2 Neuron 10-4 Action potential 3 Synapse 10-6 Dendritic spike 4 Molecule 10-10 Ion charge
  • 85. 4 Sep 2022 Quantum Information Neuroscience Physics 84 Neuroscience Physics Neurobiological Description Reference 1 AdS/Neuroscience AdS/Brain AdS/Memory Bulk-boundary relationship describes complicated volume from surface in one fewer dimensions: multiscalar neural signaling (network-neuron-synapse-ion); excited state memory capture Swan et al., 2022 Dvali, 2017 2 Chern-Simons Neuroscience Topological invariance: geometrical curve min-max indicates exception (genetic mutation, protein folding, molecular docking) Bajardi et al., 2021 3 Neural Dynamics (chaos-based) (multiscalar space-time regimes) Bifurcation explains epileptic seizure Bistability explains healthy resting state Wang et al., 2022 Breakspear, 2017 4 Network Neuroscience Graph-theoretic multiscalar structure-function link in brains Bassett et al., 2018 5 Neuronal Gauge Theories Gauge fields reset universal symmetry (free energy) in signaling Sengupta-Friston, 2016 6 Molecular Knotting DNA compaction, histone spooling, DNA chirality inversion Leigh et al., 2021 7 Topological Materials (novel matter phases) Quantum spin liquids (QSL) and fractional quantum Hall state (FQHE) per disordered spins: signaling as emergence Winter & Valenti, 2021 Frenkel & Hartnoll, 2021 8 Potential quantum effects in the brain Higher-order cognition, memory, attention, consciousness Craddock et al., 2019 Source: Swan, M. et al. (2022). Quantum Computing for the Brain. London: World Scientific.  Neuroscience physics: neuroscience interpretation of foundational physics findings
  • 86. 4 Sep 2022 Quantum Information Chern-Simons Biology Genome Physics  Model DNA and RNA as knot polynomial  Chiral molecule twisted left-to-right in supersymmetry breaking as knot polynomial  t-RNA anti-codon also in knot structure 85 Right-hand nucleic acid modeled as Hopf fibration with S3 group action to projective space of genetic code  Gauge group  Gauge group of gene geometric translation is group action of transcription process  Genetic code as brane Wilson loop EV  Genetic code is average expectation value of Wilson loop operator of coupling between hidden state and twist D-brane and anti-D-brane over superspace of cell membrane Source: Capozziello, S., Pincak, R., Kanjamapornkul, K. & Saridakis, E.N. (2018). The Chern-Simons current in systems of DNA- RNA transcriptions. Annalen der Physik. 530(4): 1700271.
  • 87. 4 Sep 2022 Quantum Information Genome Physics  Dynamics of chromatin looping  Genomes folded into loops and topologically associating domains (TADs) by CTCF (CCCTC- binding factor) and cohesin (loop lifecycle (10-30 min)  DNA Matter Phases  Spatial organization of chromosomes leads to heterogeneous chromatin motion and drives the liquid- or gel-like dynamical behavior of chromatin 86 Sources: Gabriele et al. (2022). Dynamics of CTCF- and cohesin-mediated chromatin looping revealed by live-cell imaging. Science. 376(6592):496-501. Salari et al. (2021). Spatial organization of chromosomes leads to heterogeneous chromatin motion and drives the liquid- or gel-like dynamical behavior of chromatin. bioRxiv preprint doi: https://doi.org/10.1101/2021.05.10.443375. Topologically-associating domains (TADs)
  • 88. 4 Sep 2022 Quantum Information Genome Physics  DNA Sol-Gel phase transition  Role of gelation (CTCF site anchoring) in orchestrating genetic locus rearrangement without loops or crosslinks  DNA condensation and damage repair  Chromatin manipulation and DNA damage detection 87 Sources: Takata et al. (2013). Chromatin Compaction Protects Genomic DNA from Radiation Damage. PLoS ONE. 8(10):75622. Khanna et al. (2019). Chromosome dynamics near the sol-gel phase transition dictate the timing of remote genomic interactions. Nature Communications. 10:2771.
  • 89. 4 Sep 2022 Quantum Information Genome Physics Molecular Knotting 88 Sources: Lim, N.C.H. & Jackson, S.E. (2015). Molecular knots in biology and chemistry. Journal of Physics: Condensed Matter. 27:354101. Leigh, D.A. et al. (2021). A molecular endless (74) knot. Nature Chemistry. 13:117–122. Lewandowska et al., 2017.  Alexander polynomial knot classification  Number = crossing (complexity measure)  Index subscript = order within that crossing  Ex: trefoil knot with three crossings (31)  DNA (long biopolymer) forms chiral, achiral, torus, twist knots  Simple trefoil (31) knots to 9+ crossings  Viral genomic DNA: chiral and torus knots  Molecular nanoweaving  Zinc and iron ions used to weave ligand strands to form a molecular endless 74 knot  Organic molecule (collagen peptide) nanoweaving in 90-degree kagome lattices of weft-warp threads Molecular trefoil knot
  • 90. 4 Sep 2022 Quantum Information DNA Chirality Inversion 89 DNA Chirality Inversion Liquid Crystal  Add chiral dopant (LuIII) to solution  Liquid-crystal DNA unfolds and refolds into opposite chirality  Remove dopant  Initial chirality returns  Result: low-cost alternative to covalent bond breaking  Liquid crystal: matter state between liquid and crystal  Attractive to manipulate: flows like a liquid with molecules arranged in a lattice (crystal) Source: Leigh Laboratory: Katsonis, N. et al. (2020). Knotting a molecular strand can invert macroscopic effects of chirality. Nature Chemistry. 12:939-944. Dopant: Lanthanide ions LuIII
  • 91. 4 Sep 2022 Quantum Information Ice Phytoplankton Whales Krill swarm Krill distribution Whale distribution Phytoplankton distribution Multiscalar System: Food-Web Ecosystem Southern Ocean: Phytoplankton – Krill Swarm – Whale Primary factors: light, nutrients Secondary factors: temperature Primary factors: daylight (solar elevation, radiation), proximity to Antarctic continental slope Secondary factors: current velocities and gradients Primary factors: foraging availability, distance to neighbors Secondary factors: predation, light, physiological stimuli, reproduction HSO = f (P1, K1, W1, s, ) ∂s ∂P1 ∂s ∂K1 ∂s ∂W1 , , f (P, K, W, s) + g (P, K, W, s) + h (P, K, W, s) = i (P, K, W, s) ∂s ∂W ∂s ∂K ∂s ∂P Krill swarm mathematical modeling (03/28/22) Mathematical Model by Ecosystem Tier  Phytoplankton: Reaction-diffusion-advection per light spectrum differentiation, coupled plankton-oxygen dynamics, fluid dynamics and Brownian motion (Heggerud, 2021)  Krill swarm: Lagrangian (Brownian motion, spatial distribution) (Hofmann, 2004); hydrodynamic signal per drafting within front neighbor propulsion jet (Murphy, 2019); Kuramoto oscillator for time and space synchrony (O’Keeffe, 2022)  Krill-whale relation: hotspot clustering, statistical field theory (Miller, 2019) Light Spectrum Differentiation
  • 92. 4 Sep 2022 Quantum Information Order, Disorder, Chaos  Order (arrangement), disorder (confusion), chaos (self-organization: confusion gives way to order)  Flocking: 3D orientation vis-à-vis 5-10 neighbors  Swarmalators: self-synchronization in time and space  Krill self-position in propulsion jet of nearest front neighbor (draft) as a hydrodynamic communication channel that structures the school (via metachronal stimulation of individual krill pleopods (~fins)) 91 Source: Murphy et al. (2019). The Three-Dimensional Spatial Structure of Antarctic Krill Schools in the Laboratory. Scientific Reports. 9(381):1-12. Krill swarm: 30,000 individuals per square meter (largest known aminal aggregations) Flocking: 3D orientation vis-a-vis 5-10 nearest neighbors Black holes, quasi- particles, quantum spin liquids, schooling, flocking, swarming
  • 93. 4 Sep 2022 Quantum Information Practical Application Quantum Life Sciences  Computer-aided drug design for small-molecule drugs  Accelerate discovery of selectively-binding chemical compounds with minimal off- target effects  Protein structure prediction, engineering, and design  Predict protein structure from amino acid sequence  Generate complex biomolecules  Precision medicine, pathology, and imaging analysis 92 Case Study: GlaxoSmithKline and Menton AI Aim: identify antiviral peptides that block infection. Create a fixed chemical backbone as a peptide scaffold, and explore the combinatorial space of possible amino acid compositions specific to the scaffold Result: identify several promising peptide designs of natural and synthetic amino acids Source: D-Wave Systems: Quantum in Life Sciences. https://www.dwavesys.com/solutions-and-products/life-sciences  90% of new drug development efforts ineffective
  • 94. 4 Sep 2022 Quantum Information Galleri Blood Test Cancer Blood Test for over 50 Cancer Types 93 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  Concierge availability online ($995)
  • 95. 4 Sep 2022 Quantum Information 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) 94 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
  • 96. 4 Sep 2022 Quantum Information 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) 95 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 CRISPR/Cas9 therapeutic strategies are being evaluated on pre-clinical Alzheimer’s disease models (Hanafy, 2020)
  • 97. 4 Sep 2022 Quantum Information 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 96 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
  • 98. 4 Sep 2022 Quantum Information 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 97 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).
  • 99. 4 Sep 2022 Quantum Information Glia and Calcium Signaling 98  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.
  • 100. 4 Sep 2022 Quantum Information 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 99 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.
  • 101. 4 Sep 2022 Quantum Information Alzheimer’s Disease 100 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.  Patient case:  Left: Subject with protective Christchurch APOE3R136S mutation (rs121918393) A not C: heavy Aβ plaque burden (top), but limited tau tangles (bottom), and no early onset Alzheimer’s disease  Right: Control case with Paisa mutation Presenilin 1 (rs63750231): low Aβ plaque burden (top), substantial tau tangles (bottom), and early-onset Alzheimer’s  Implication: CRISPR-based genetic cut-paste study Plaques (top red): No Early-onset Alzheimer’s Tangles (bottom red): Early-onset Alzheimer’s  Contra indicating plaques and tangles
  • 102. 4 Sep 2022 Quantum Information Personalized Genomics for Brain Disease  Personalized genomic screening for brain disease  Synaptome analysis + genomic data  133 brain diseases caused by mutations  Neurological (AD, PD), motor, affective, metabolic disease  1,461 proteins human neocortex postsynaptic density  PSD, CaMKIIa, App, Syngap, GluA, Plp1, Vcan, Hapln1, CRMP, Ras, Sh3gl, PKA, Shank3 101 Sources: Grant, S.G.N. (2019). Synapse diversity and synaptome architecture in human genetic disorders. Hum Mol Gen. 28(R2):R219-25. A. Heo, S., Diering, G.H., Na, C.H. et al. (2018). Identification of long-lived synaptic proteins by proteomic analysis of synaptosome protein turnover. PNAS. 115(16):E3827-36. B. Bayes, A., van de Lagemaat, L.N., Collins, M.O. et al. (2011). Characterization of the proteome, diseases and evolution of the human postsynaptic density. Nat. Neurosci. 14:19-21. B. 133 Brain Diseases per ICD-10 Classification caused by genetic mutation and faulty proteins A. 1,461 Synapse Proteins influencing molecular and cellular function
  • 103. 4 Sep 2022 Quantum Information Aging Brain: Synaptic Decline  Brainwide atlas of synapses across mouse lifespan  Whole-brain data of 12 regions and 109 anatomical subregions  Isocortex, olfaction, hippocampus, cortical subplate, striatum, pons, pallidum, thalamus, hypothalamus, midbrain, medulla, cerebellum  Lifespan changes in three phases  Phase 1 (0-2 mos): number of puncta increase rapidly  Phase 2 (2-12 mos): rate of increase in puncta density slows and characterized by relative stability (adulthood is reached at 6 mos)  Phase 3 (12-18 mos): puncta density decline, synapse size increase 102 Source: Cizeron, M., Qiu, Z., Koniaris, B. et al. (2020). A brainwide atlas of synapses across the mouse life span. Science. 369:270- 75. Two scaffolding proteins (PSD95: green; SAP102: magenta) across 18-month mouse lifespan: in older age, the protein density declines for both, and the size of the SAP proteome inflates
  • 104. 4 Sep 2022 Quantum Information 103  What are Quantum Technologies?  Foundational Tools  Quantum Cryptography  Quantum Machine Learning  Quantum Chemistry  Advanced Applications  Quantum Space Science  Quantum Finance  Quantum Biology Agenda
  • 105. 4 Sep 2022 Quantum Information 104 The fast pace of quantum information study is enabling a new tier of scientific problem-solving Early-adopter fields: space science, biology, chemistry, finance, cryptography, physics Thesis
  • 106. 4 Sep 2022 Quantum Information 105 Next-generation Materials  New forms of Consumer Electronics  Continue trend of miniaturization and functionality improvement  Metamaterial plasmonics  Replace lasers with near field optics  More efficient field generator Source: Oka & Kitamura. (2019). Floquet engineering of quantum materials. Ann. Rev. Cond. Matt. Phys. 0:387–408 Ma et al. (2021). Topology and geometry under the nonlinear electromagnetic spotlight. Nature Materials. 20:1601–1614. Novel Quantum Materials (Ma, 2021)  Nonlinear quantum phase materials  Use topology and quantum geometry methods to detect new electromagnetic responses in quantum materials Novel Materials
  • 107. 4 Sep 2022 Quantum Information 106 Quantum Math Quantum Science Classical Mindset Quantum Mindset Quantum Mindset Classical Mind Quantum Mind The self-knowing time series Classical Math Classical Science Mindset progression  All physics and mathematics ever developed until recently was with the Classical Mindset 5 properties: symmetry, topology, superposition, entanglement, interference Hyperbolic band theory (Bloch theorem), quantum statistics Quantum machine learning (Born machine, neural operators)
  • 108. 4 Sep 2022 Quantum Information Quantum Mind as Self-knowing Time Series  Thinking in the mode of physics concepts  Time series as the foundational clue  Ideal-real tiers, integration of diverse scale domains  Time dilation in thought  Radical uncertainty, all events are probabilistic  Knowability trade-offs (time-location, speed-energy, etc.)  Superpositioned thinking  Holding multiple positions in mind simultaneously before collapsing to a measurement 107 Quantum microscopy Schrödinger cat states Hyperbolic space Source: https://www.slideshare.net/lablogga/critical-theory-of-silence
  • 109. 4 Sep 2022 Quantum Information Quantum Science Fields 108 Source: Swan, M., dos Santos, R.P. & Witte, F. (2020). Quantum Computing: Physics, Blockchains, and Deep Learning Smart Networks. London: World Scientific. Quantum Biology Quantum Neuroscience Quantum Machine Learning € $ ¥ € Early-adopter fields: space science, biology, chemistry, finance, cryptography, physics Quantum Cryptography Quantum Space Science Quantum Finance Foundational Tools Advanced Applications Quantum Chemistry
  • 110. 4 Sep 2022 Quantum Information Quantum Mathematics by Field 109 Source: Swan, M., dos Santos, R.P. & Witte, F. (2022). Quantum Information Science. IEEE Internet Computing. Special Journal Issue: Quantum and Post-Moore’s Law Computing. January/February 2022. Quantum Discipline What is the Math? 1 Quantum Cryptography Lattice problems (group theory) difficulty of learning with errors, shortest vector, the other thing Difficulty of lattice problems (finding shortest vector to an arbitrary point); learning-with-errors and Fiat- Shamir with Aborts over module lattices, short integer solutions over NTRU lattices and has functions over lattices 2 Quantum Machine Learning Variational algorithms, Neural ODE, Neural PDE (neural operators), QGANs QNN, TN, QSVM/Q RKHS Q Kernel Learning 3 Quantum Chemistry Waves: atomic wavefunction (approximation) Ground-state excited-state energy functions, total system energy Qubit Hamiltonians, VQE 4 Quantum Space Science Quantum optimization algorithms (Azure); optics; QAOA; AdS/CFT, BH, chaos, TN, MERA, RG 5 Quantum Finance Quantum estimation algorithm Quantum amplitude estimation: technique used to estimate the properties of random distributions Chern-Simons (topological invariance) 6 Quantum Biology Waves: Fourier transform, Fourier slice theorem & Radon transform; QML (VQE) Single-neuron: Hodgkin-Huxley, integrate-and-fire, theta neuron Local ensemble: FitzHugh-Nagumo, Hindmarsh-Rose, Morris-Lecor Neural field theory: Jansen-Rit, Wilson-Cowan, Floquet, Kuramoto oscillators, Fokker-Planck equations Neuroscience Physics: AdS/CFT, Chern-Simons, gauge theory, bifurcation & bistability Swarmalator: phytoplankton (diffusion); krill (Brownian motion, Kuramoto oscillator); whale (clustering)  Mainly heterogeneous (recurrence: Chern-Simons)
  • 111. 4 Sep 2022 Quantum Information Risks and Limitations 110  Quantum domain is hard to understand  Complex, non-intuitive  Human-Technology Relation  Personal data monopoly domination  Google, Apple, Facebook, Microsoft  Digital divide widens (cost, accessibility)  Overwhelm (right to non-adoption in increasingly technologized world)  Lack of empowering relation with technology  Humans willingly enframed as standing reserve instead of technology as background enabler  Alienation (one-way panopticon video surveillance via biometrics, drones) Heidegger, The Question Concerning Technology + -
  • 112. Santa Ana CA, 4 Sep 2022 Slides: http://slideshare.net/LaBlogga Melanie Swan, PhD Quantum Technologies University College London Quantum Information Space, Biology, and Computation Thank you! Questions? “Outside there was silence, as there is and has been and always should be. The perfect silence of the spheres.” - Elizabeth Bear, Ancestral Night, 2019, p. 384
  • 113. 4 Sep 2022 Quantum Information 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 The Fountain, Monto, 2018 Elastic: Flexible Thinking in a Time of Change, Mlodinow, 2018 The new skillset: elastic thinking includes neophilia (affinity for novelty), schizotypy (perceiving the unusual), imagination, and integrative thinking Exercise means that 60 really is the new 30, releasing anti- inflammatory IL-6 which enhances cognitive performance through telomere lengthening and mitochondrial genesis 112 Livewired: The Inside Story of the Ever- Changing Brain, Eagleman, 2020 More than simple neural plasticity, the brain is “livewired” to constantly absorb changes by interacting with its environment Neocortex learns a model of the world and constantly updates it; no centralized control mechanism; cortical columns make predictions; aggregate neuron strength wins A Thousand Brains, Hawkins, 2021 Question what we think we know. Conversations are for being open-minded not for convincing. Be humble, curious, and open Think Again, Grant, 2021 Human intelligence is based on abductive inference which is not fully understood; it cannot be reduced to induction or deduction, or encoded and programed, hence at present, computers cannot be trained to think as humans The Myth of Artificial Intelligence, Larson, 2021
  • 114. 4 Sep 2022 Quantum Information Space Quiz (as of 1 Sep 2022) 113 1. Number of humans who have been to space? (Jun 2022)  (LEO, GEO, ISS, 90-seconds of 0-g space flight) 2. Number of confirmed exoplanet discoveries? 3. Number of international spaceports? 4. Number of FAA-permitted U.S. spaceports? 5. Number of countries in Africa? (calibration question)
  • 115. 4 Sep 2022 Quantum Information Jokes 114  Why was the amoeba moving in the microscope?  To get to the other slide  Which side of the brain has the most neurons?  The inside  What did the EEG say to the neuroscientist?  Nothing, it just waved  What do glial cells see at the ballet?  Schwann Lake  What is a cat's favorite type of neuron?  Purr-kinje cells (Purkinje cell) Quantum Mechanics and Space  Police officer: “Sir, did you know there’s a dead cat in your trunk?”  Schrödinger: “Well, now I do~!”  A neutron walks into a bar  For you, no charge  A quantum particle walks into two bars  How many astronomers does it take to change a light bulb?  3 plus or minus 75  How was the restaurant on the moon?  Good food but not much atmosphere  The new gravity book  I just can’t put it down  Astronomy  One star is easy to find, but you have to wait until daytime Biology and Neuroscience Coffee and doughnuts are the same to a topologist
  • 116. 4 Sep 2022 Quantum Information 115 Appendix Quantum Chemistry Quantum Computing Quantum Finance Quantum Medicine Laser Microscopy: six pairs of atoms
  • 117. 4 Sep 2022 Quantum Information Mathematical Approaches to Neuroscience 116 Behavioral tier Classical approach Quantum approach 1 Network-neuron Behavior: neuronal firing Task: integrate empirical data (EEG, MEG, fMRI, tractography etc.) • Orbit and bifurcation: Turing instability to Hopf instability and Bogdanov-Takens bifurcation (codimensionality >1), piecewise functions, Floquet periodicity • Criticality-triggered phase transition: various models • QAOA: MaxCut partition functions, MaxSET max independent set, graph coloring, Hamiltonians • AdS/Brain and bMERA • Quantum kernel learning • Quantum control theory 2 Neuron-synapse Behavior: action potential to neurotransmitter to action potential Task: Signal transduction: E-to-C and C-to-E (E: electrical, C: chemical) • Synaptic integration: ODE but need PDE (radial-longitudinal reaction-diffusion of calcium) • Near-far fast-slow space-time based signal attenuation • Charge-voltage differentials • Lateral-dorsal (in pyramidal) • MPS spin-state criticality scattering model • Anharmonic oscillators • Amplitude estimation • Continuous-time quantum walks and UV-IR correlations • Quasicrystal non-Fermi liquid phase transitions 3 Synapse-ion Behavior: ion reception Task: molecular dynamics model of ion docking • Topology, elliptical geometry • Bayesian, ANOVA analysis • Microscopy data acquisition (behaving brain, etc.) • VQE (molecular energies) • QBism (quantum Bayesian) • GBS (femtochemistry) • QML (GAN feeds QNN) Source: Swan, M., dos Santos, R.P., Lebedev, M.A. & Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific.
  • 118. 4 Sep 2022 Quantum Information Mathematic Problem Reformulation 117 Neuroscience problem Classical requirements Quantum reframe 1 Network-neuron Empirical datastream integration (EEG, MEG, fMRI, tractography, connectome, synaptome) • Multiscalar integration of diverse space-time and dynamics regimes • Unknown statistical distributions (apply partial Fokker-Planck equations and mean-field, Jansen-Rit, oscillatory neural dynamics) • Scale renormalization as a feature (MERA tensor networks and quantum kernel learning RKHS) • Advanced probabilistic methods (Born machine) find statistical distributions and generate new data 2 Neuron-synapse Synaptic integration • Radial-longitudinal reaction- diffusion PDEs • Superpositioned quantum information state modeling 3 Synapse-ion a. Electrical-chemical signal conversion b. Astrocyte calcium signaling c. Ion transfer d. Excitatory-inhibitory (GLUT-GABA) at dendritic arbors • Synaptogamin vesicles • EPSP (head)/IPSP (spine) • Dendritic head ellipses • Piecewise functions • Floquet periodicity • Orbit-instability • Bifurcation • Chaotic neural dynamics • Holographic partitions • Scrambling Hamiltonian: information spread • SYK model: bosonic- fermionic operators of strongly correlated system • Superconducting condensate Source: Swan, M., dos Santos, R.P., Lebedev, M.A. & Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific.
  • 119. 4 Sep 2022 Quantum Information Quantum Information Science techniques Tackle New Problem Classes 118 High- dimensionality quantum platforms Quantum mathematics Practical advance: quantum computation Theoretical advance: foundational physics • Ion trap • Rydberg arrays • Cold atom arrays • Neutral atoms • GBS (Gaussian boson sampling) • Optical platforms • Random tensors (1/N expansion, melonic diagrams, large D branching polymers) • QAOA alternating cost-mixing Hamiltonians • Partition functions • Variational quantum eigensolver (VQE) • Graph coloring • Max independent set and MaxSAT • Superpositioned quantum information state modeling • Ladder operators Continuous-time quantum walks • GHZ-states • GBS/graph theory • Quantum kernel learning (RKHS) • Global timekeeping: quantum clock network • Materials: superconductivity • Materials: new topological matter phases not reaching thermal equilibrium • Operators: winding- unwinding distribution growth • SYK operators • Quantum Bayesian updating (QBism) Quantum Theory (Quantum Information Science canon) Source: Swan, M., dos Santos, R.P., Lebedev, M.A. & Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific.