AdS Biology and Quantum Information Science

Pleasanton CA, 19 Nov 2022
Slides: http://slideshare.net/LaBlogga
Melanie Swan, PhD
Research Associate
University College London
AdS/Biology and
Quantum Information Science
“Outside was the perfect silence of the spheres.”
- Elizabeth Bear, Ancestral Night, 2019, p. 384
AdS: AdS/CFT correspondence (anti de-Sitter space)

19 Nov 2022
Quantum Information 1
Quantum Technologies Research Program
2015 2019 2020
Blockchain Blockchain
Economics
Quantum
Computing
Quantum
Computing
for the Brain
2022
Image: Thomasian, 2021, Nat
Rev Endocrinol. 18:81-95, p. 12

19 Nov 2022
is a fast-growing discipline advancing many areas of
science and inaugurating a level of problem-solving
Thesis
“Quantum makes a wide range of problems in many fields accessible.
Fundamentally new formulations of problems may be required”
– Monroe et al., U.S. Community Study on the Future of Particle
Physics, 2022, arXiv:2204.03381v1 (paraphrase)

19 Nov 2022
 Quantum Information Science
 Quantum Chemistry
 Quantum Space Science
 Quantum Finance
 Quantum Biology
Agenda

19 Nov 2022
Quantum Information
Quantum Information
4
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
Quantum Information: the
information (physical properties)
of the state of a quantum system
Nobel Prize
2022
Nobel Prize 1998
Nobel Prize 2016
2022
“groundbreaking experiments
using entangled quantum
states, where two particles
behave like a single unit even
when they are separated.
Their results have cleared the
way for new technology based
upon quantum information”
Cat

19 Nov 2022
Quantum Information
Quantum Scale
5
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

19 Nov 2022
Quantum Information
Status
Quantum Computing
 Various quantum computing platforms available
 Critique of quantum computing: so far only useful in specific
cases such as optimization problems (linear algebra)
6
Open Quantum Testbeds
(Sandia, LBL)
Industry (Cloud-based)
Source: Landahl, A. (2022). Sandia National Laboratories.

19 Nov 2022
Quantum Information
Status
Quantum Computing available via Cloud Services
7
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

19 Nov 2022
Quantum Information
Quantum Computing
Microsoft
IBM
Rigetti

19 Nov 2022
Quantum Information
Using a Quantum Computer
9
Source: D-Wave Systems, Inc. https://cloud.dwavesys.com/leap/resources/demos

19 Nov 2022
Quantum Information
“Y2K of crypto” threat
NIST Post-Quantum Cryptography
 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
10
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)

19 Nov 2022
NIST Algorithm Selection
 NIST: 26 of 69 algorithms advanced 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
 Implication: quantum networks
 Entanglement generation
 Key exchange (Bell pairs)
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.

19 Nov 2022
Basic Concept
What is Quantum Computing?
 Computing: change of state between 0/1
 Move information around & and perform a computation
 Quantum: use atoms, ions, photons to compute
 Classical computing: serial not parallel
 Quantum computing: treat more than one status at the
same time, compute all transactions simultaneously
 Fundamentally, a different way of computing
 Degreed physicists sought as product managers (Gartner)
 Shift big data analysis to quantum to find hidden correlations
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).

19 Nov 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
13
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

19 Nov 2022
Quantum Information
 A qubit (quantum bit) is the basic unit of
quantum information, the quantum version
of the classical binary bit
14
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 of 0 or 1
Implication: test permutations simultaneously
Classical Bit Quantum Bit (Qubit)
Sources: https://www.newsweek.com/quantum-computing-research-computer-flagship-eu-452167: Dawid Carrasquilla, Carleo,
Wang et al. (2022). Modern applications of machine learning in quantum sciences. arXiv: 2204.04198.
Practical example: 1-qubit
quantum machine learning
classification task

19 Nov 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
15
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.

19 Nov 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
16
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

19 Nov 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
17
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

19 Nov 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)
18
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

19 Nov 2022
Quantum Information
Moore’s Law
19
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. Chips already
must address
quantum effects

19 Nov 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
20
2500 BC
Abacus
20th Century
Classical
21st Century
Quantum
Abacus -> Logarithm as Classical -> Quantum
+

19 Nov 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 et al.
(2015) Deep Learning. Nature. 521(7553):436-44. P. 439. Wang et al. (2019) Benchmarking TPU, GPU, and CPU Platforms for Deep
Learning. arXiv:1907.10701. Pikulin et al. (2021). Protocol to identify a topological superconducting phase. arXiv:2103.12217v1.
GPU TPU QPU
Peak teraFLOPs in 2019 benchmarking analysis
2 125 420
21
Topological superconductor QPU: superconducting-buffer-
semiconductor chip layers; superconducting properties
extend to semiconductor to produce topological phase (red)

19 Nov 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
 “I think we’ll make about four copies a week” – State Street Bank, adopting a xerograph
22
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
UNIVAC computer (1950s):
465 multiplications per
second (faster than Hidden
Figures human computers)
Billions of
times faster

19 Nov 2022
Next-generation Materials
Plasmonic Quantum Materials
Sources: 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. Huang, Averitt (2022).
Complementary Vanadium Dioxide Metamaterial with Enhanced Modulation Amplitude at THz Frequencies. arXiv:2206.11930v1.
On-demand Quantum Materials at
THz Frequencies (Averitt 2022)
Novel Quantum Materials (Ma, 2021)
 New forms of Consumer Electronics
 Replace lasers with near field optics
 More efficient field generator
 Metamaterials
 Plasmonics, spintronics, magnonics,
holonics, excitonics, viscous electronics
 Nonlinear quantum phase materials
 Use light to manipulate materials
properties (resonant and non-resonant)
 Create novel matter phases
 Nonlinear and tunable InAs (Indium Arsenide)
plasmonic disks and mushrooms
 Metamaterial-quantum material coupling in
insulator-to-metal transition superconductors

19 Nov 2022
Quantum Information
Quantum Science Fields
24
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: cryptography, chemistry, biology, finance, space science
Quantum
Cryptography
Quantum Space
Science Quantum Finance
Foundational
Tools
Advanced
Applications
Quantum
Chemistry

19 Nov 2022
Quantum Information
Quantum Studies in the Academy
25
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
 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

19 Nov 2022
 Quantum Finance
 Quantum Biology
Agenda

19 Nov 2022
Quantum Chemistry: find ground state energy
Nitrogen Fixation
 Ammonia produced by cleaving Nitrogen triple bond
 Haber-Bosch process: 2% earth’s energy consumption
 Plants: energy efficient charge-cleaving
 MoFe protein (Molybdenum Iron)
 Small metal cluster cut by quantum knife
 Quantum computing implication
 Find molecule ground state, charge distribution, copy cleave
Sources: Landahl, A. (2022). Sandia National Laboratories. Morrison, C.N., Hoy, J.A., Zhang, L. et al. (2015). Substrate Pathways in
the Nitrogenase MoFe Protein by Experimental Identification of Small Molecule Binding Sites. Biochemistry. 54:2052−2060.
Nature: energy-efficient Fertilizer Production
5 potential access pathways from
protein surface to FeMo-cofactor
(active site) (Morrison, 2015)

19 Nov 2022
Quantum Information
 Atomic precision applications
28
Sources: Delgado (2022). How to simulate key properties of lithium-ion batteries with a fault-tolerant quantum computer. arXiv:
2204.11890. Vasylenko (2021). Element selection for crystalline inorganic solid discovery. Nat Comm. 12:5561. Hogg (2022).
Acoustic Power Management by Swarms of Microscopic Robots. arXiv:2106.03923v2.
Collective acoustic-harvesting
power management by medical
nanorobot swarms (Hogg 2022)
Simulate properties of lithium-ion batteries
to find Li3SnS3Cl (Vasylenko 2021)
Quantum Chemistry: find ground state energy
Energy and Battery Technology
Autonomous robotic
nanofabrication (Leinen 2020)
Quantum battery simulation (Delgado 2022)

19 Nov 2022
 Nitrogen sequestration and batteries
 Quantum Finance
 Quantum Biology
 Neural Signaling
 Neuroscience Physics
 Genomics
 Practical Application
 Neurodegenerative Disease
 Protein Pathologies
Agenda

19 Nov 2022
Quantum Information
35 Terrestrial Spaceports (Nov 2022)
30
Source: https://www.go-astronomy.com/space-ports.php
Newest Spaceport:
ESRANGE (Sweden)
 14 U.S.

19 Nov 2022
Quantum Information
14 FAA-Permitted U.S. Spaceports (Nov 2022)
31
Source: https://www.faa.gov/space/spaceports_by_state
 Military, commercial, private space entrepreneurship
SpaceX: 155
successful
rocket launches
(Jun 2022)

19 Nov 2022
Quantum Information
Space-based Arctic Control
 Melting polar ice
 New shipping
lanes
 Scramble for
geopolitical control
32
Northwest
Passage
(Canada)
Northeast
Passage
(Russia)
Northern Sea Route

19 Nov 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
33
Source: https://www.airforcemag.com/a-space-internet-experiment-for-the-arctic-is-among-vanhercks-priorities
Secure Communication
Space-based Internet Service
Icebreaker

19 Nov 2022
Quantum Information
Quantum Space Warfare
 Precision weaponization in space
 LEO/GEO communications, sensing, lidar/radar
34
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

19 Nov 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
35
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, need 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

19 Nov 2022
Quantum Information
Multiplanetary Society
Time on Mars
36
Sources: https://www.giss.nasa.gov/tools/mars24, https://marsclock.com
 Practical challenge
 15-minute communications
delay (10-40 minute), hence
 Rover-helicopter coordination
 Mars24 Sunclock
 Earth-day and Martian-sol
 Asynchronous
time-tech

19 Nov 2022
Quantum Information
Deep Space Quantum Computing
 JPL using Azure Quantum (Microsoft) (Jan 2022)
 Manage several hundred weekly mission requests
 Requirement: synchronize global communications network of
large radio antennae (California, Spain, Australia) in constant
communication with spacecraft as earth rotates
 New requirement: high-fidelity data operations for Perseverance
Rover (2020) and James Webb Space Telescope (2021)
 NASA deep space network using quantum-inspired
optimization algorithms
 Result: produce schedule in
2-16 minutes vs 2 hours
37
JPL: Jet Propulsion Lab (Pasadena CA) 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/
NASA Deep Space Network

19 Nov 2022
Quantum Information
Planetary Surfaces
 Remarkable similarity
 Automated data registration
38
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.
Machine Learning Image Analysis

19 Nov 2022
Quantum Information
ISS and Quantum
39
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

19 Nov 2022
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)

19 Nov 2022
Quantum Information
Quantum Computing and CERN
 IBM quantum 27-qubit Falcon processor
 Identify Higgs boson-producing collisions
 Use QSVM (quantum support vector machine)
with quantum kernel estimator algorithms
41
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

19 Nov 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
42
Sources: Carminati, F. (2018). Quantum thinking required. Cern Courier. 58(9):5. https://research.ibm.com/blog/cern-lhc-qml#fn-1.

19 Nov 2022
Quantum Information
Quantum Astronomy
43
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

19 Nov 2022
 Quantum Finance
 Quantum Biology
Agenda

19 Nov 2022
Quantum Information
Quantum Finance
 Optimize complexity
1. Option pricing
2. Trade identification
3. Portfolio optimization
4. Risk management
 Quantum amplitude estimation
 Estimate properties of a
random distribution
 Result: quadratic speedup in
convergence rate vs classical
Monte Carlo methods
45
Source: D-Wave Systems: Quantum in Financial Services. https://www.dwavesys.com/solutions-and-products/financial-services
Case Study: BBVA (European bank)
Optimize Risk vs Return
Aim: find management strategies with the
highest Sharpe ratio (a metric reflecting
the rate of return at a given level of risk)
Challenge: combinatorial explosion of 4-yr
monthly transactions for 8 asset portfolio
Result: evaluated 10382 possible portfolios
in 171 seconds to identify a portfolio with
a Sharpe ratio of 12.16
Evaluating payoff function

19 Nov 2022
Quantum Information
Quantum Amplitude Estimation
 Aim: estimate probability of measuring “1” in the last qubit
 System setup
 Define a unitary operator to act on qubit register
 Create an estimation operator to act on the system and
approximate the eigenvalues of the estimation operator
 System deployment and measurement
 Apply Hadamard gates to put qubits in equal superposition
 Evolve system and apply inverse quantum Fourier transform
 Measure end
qubit state
46
Source: Stamatopoulos, N., Egger, D.J., Sun, Y. et al. (2020). Option pricing using quantum computers. Quantum. 4(291).
arXiv:1905.02666v5.
Probability Amplitude: inner
product of two quantum state
vectors (complex number)
Quantum amplitude
estimation circuit
for option pricing
Evaluate payoff function

19 Nov 2022
Quantum Information
Quantum Finance: Econophysics
47
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 option pricing, trade
identification, portfolio optimization, and risk management
 Model markets with physics: wavefunctions, gas, Brownian motion
Chern-Simons
topological
invariants

19 Nov 2022
Quantum Information
Quantum Finance (references)
48
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.
Evaluate payoff function
Quantum amplitude estimation circuit for option pricing
Source: Stamatopoulos (2020).
Load random distribution

19 Nov 2022
 Quantum Finance
 Quantum Biology
 AdS/Biology
 Quantum Neuroscience
 AdS/Neuroscience
 Practical Applications
 Genome Physics
 Alzheimer’s Disease
Agenda

19 Nov 2022
Quantum Information
Physics-Biology Relation
 Long-time interest in biology as a physical system
 Bohr, Light and Life, Copenhagen, 1932
 Delbruck, Genetics as an information science, 1937
 “The same matter with orderly properties in physics arranges itself in
the most astounding fashion in the living organism” (paraphrase)
 Schrödinger, What is Life?, 1944
 Genes seem to be an aperiodic crystal, an arrangement of atoms
that is specific not random, but not regularly repeating as a crystal
 Pauling, 1948, Nature of Forces between Large Molecules of
Biological Interest
 Currently new biophysics via mathematical approaches
 Topology: Chern-Simons, knotting, compaction
 Chern-Simons: solvable Quantum Field Theory (QFT)
 Read curvature min-max as system event (signal, mutation, fold)
 Topology, being 3d (3d+), is already quantum-circuit ready
50
Source: Swan, M. dos Santos, R.P., Lebedev, M.A. & Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific.

19 Nov 2022
Quantum Information
 Describe a bulk volume with a boundary
theory in one fewer dimensions
 Any physical system: universe, brain, cell, room
 A gravity theory (bulk volume) is equal to a gauge
theory or a quantum field theory (boundary
surface) in one fewer dimensions
 AdS5/CFT4 (5d bulk gravity) = (4d Yang-Mills
supersymmetry QFT)
 AdS/CFT Mathematics: AdS/DIY
 Metric (ds=)
 Operators (O=)
 Action (S=)
 Hamiltonian (H=)
Holographic Duality
AdS/CFT Correspondence (Anti-de Sitter Space/Conformal Field Theory)
51
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. arXiv:1802.01040.
IMAGE: van Raamsdonk, M. (2015). Gravity and Entanglement. http://pirsa.org/15020086.
Anti-de Sitter Space: hyperbolic
(negative curvature) space
Escher Circle Limits Error correction
Models of Space
Anti-de Sitter Space
de Sitter Space

19 Nov 2022
Quantum Information
AdS/CFT Studies
52
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/Thermal Systems Shenker & Stanford, 2014
6 AdS/Mathematics AdS/Information Geometry Hazboun 2018
Biology & Neuroscience
7 AdS/Biology Multiscalar duality mapping in biology Swan et al., 2022
8 AdS/Brain
AdS/Neural Signaling
AdS/Information Theory (Memory)
Holographic Neuroscience Willshaw et al., 1969
Swan et al., 2022
Dvali, 2018
9 AdS/BCI AdS/Brain/Cloud Interface Swan, 2023e
Information Science
10 AdS/TN (AdS/MERA) AdS/Tensor Networks Swingle, 2012; Vidal, 2007
11 AdS/QIT AdS/Quantum Information Theory Hayden et al., 2016
12 AdS/DLT AdS/Blockchain Technology Kalinin & Berloff, 2018
13 AdS/ML & AdS/QML AdS/(Quantum) Machine Learning Hashimoto et al., 2018; Cottrell et al., 2019
Sources: Maldacena, J.M. (1999). The large N limit of superconformal field theories and supergravity. Intl. J. Theor. Phys.
38(4):1113–33; Swan, M. dos Santos, R.P., Lebedev, M.A. & Witte, F. (2022). Quantum Computing for the Brain. London: World
Scientific.
Holographic duality (AdS/CFT): the
same physical system expressed in
one greater or one fewer dimensions
e.g. AdS5/CFT4, AdS2/CFT1

19 Nov 2022
Quantum Information
AdS/CFT Studies
53
Domain Direction Description Bulk Boundary
1 AdS/CFT Boundary-to-Bulk Use AdS/CFT to explore bulk
emergence and develop a theory
of quantum gravity
Quantum gravity
(unknown theory)
Standard quantum field
theory (known)
2 AdS/CMT Bulk-to-Boundary Identify quantum field theory of
novel materials for use in
superconducting, condensed
matter physics; AdS/SYK
Classical gravity
theory (known)
Similar bulk parameters
(temperature, entropy)
in black holes, plasmas
Quantum field theory of
unconventional
materials (unknown)
3 AdS/QCD Boundary-to-Bulk Use available strong force
empirical data: identify bulk
thermal phase transition with
lattice chiral condensate data
Identify bulk thermal
phase transition
Lattice QCD values of a
chiral condensate
at finite-temperature
4 AdS/QCD Bulk-to-Boundary Describe QCD (the quantum field
theory of the strong force) in terms
of a gravitational theory
Quark-gluon plasmas
behave like a fluid with
low viscosity, similar to
that of black holes
Cannot separate
quarks-gluons
experimentally in
particle accelerators
5 AdS/ML Boundary-to-Bulk Interpret machine learning
framework with AdS/CFT
mathematics
Emergent neural
network architecture
per learning data
patterns
Available input data
6 AdS/Mathematics Boundary-to-Bulk Mathematical solving tool Identify bulk geometry Known example data
Sources: Maldacena, J.M. (1999). The large N limit of superconformal field theories and supergravity. Intl. J. Theor. Phys.
38(4):1113–33; Swan, M. dos Santos, R.P., Lebedev, M.A. & Witte, F. (2022). Quantum Computing for the Brain. London: World
Scientific.
 Bidirectional solving

19 Nov 2022
Quantum Information
 AdS/SYK (Sachdev-Yi-Kitaev) model
 Solvable model of strongly interacting fermions
 AdS/SYK: black holes and unconventional materials have
similar properties related to mass, temperature, and charge
 SYK Hamiltonian (HSYK) finds wavefunctions for 2 or 4 fermions
 Or up to 42 in a black-hole-on-a-superconducting-chip formulation
Black Hole on a Chip
Solve AdS/CFT Duality in either Direction
54
Sources: Sachdev, S. (2010). Strange metals and the AdS/CFT correspondence. J Stat Mech. 1011(P11022).. Pikulin, D.I. &
Franz, M. (2017). Black hole on a chip: Proposal for a physical realization of the Sachdev-Ye-Kitaev model in a solid-state
system. Physical Review X. 7(031006):1-16.
Direction Domain Known Unknown
1 Boundary-to-bulk Theoretical physics Standard quantum field
theory (boundary)
Quantum gravity (bulk)
2 Bulk-to-boundary
(AdS/SYK)
Condensed matter,
superconducting
Classical gravity (bulk) Unconventional materials
quantum field theory (boundary)
Ψ : Wavefunction
HSYK : SYK Hamiltonian
(Operator describing evolution
and energy of system)
Bethe-Salpeter equation

19 Nov 2022
Quantum Information
AdS/Biology
55
 Multiscalar systems with different space-time regimes
 2-tier systems needing integration (from bulk or boundary)
 Tumor, fMRI + EEG imaging, how molecules drive behavior
 Entanglement (correlation) renormalization across scales
 MERA, random tensor networks, melonic diagrams
 Entanglement entropy (interrelated correlations across system tiers)
 Entropy (number of possible system states)
 Non-ergodicity: (efficiency) biology does not cycle through all
configurations per temperature (thermotaxis), chemotaxis, energy
 Maxwell’s demon in biology (Davies, 2019), information engines
 Conservation across system scales
 Biophysical gauge symmetry (system-wide conserved quantity)
 Presence of codes (DNA, codons, neural codes)
Source: Swan, M. dos Santos, R.P., Lebedev, M.A. & Witte, F. (2022). Quantum Computing for the Brain. London: World Scientific.
AdS/Biology: Interpretation of
the AdS/CFT correspondence
in biological systems

19 Nov 2022
 Quantum Finance
 Quantum Biology
 AdS/Biology
 Genome Physics
Agenda

19 Nov 2022
Quantum Information
57
Network
Science
Machine
Learning
Materials
Science
Neuroscience
Theoretical
Physics
Quantum
Information
Science

19 Nov 2022
Quantum Information
 Quantum (neuro)biology: application of quantum methods
to investigate problems in (neuro)biology and the possible
role of quantum effects
 Brute physical processes & higher-order cognition, memory, attention
 Quantum consciousness hypothesis (microtubules)
 Research topics
 Traditional (~2010)
 Avian magneto-navigation,
photosynthesis, energy transfer
 Contemporary
 Imaging (EEG, fMRI, etc.)
 Protein folding
 Genomics
 Collective behavior: neural signaling, swarmalator
58
Quantum Biology
Swarmalator: animal aggregations that self-coordinate in time and space
Human data: imaging (brain wave activity); Model organism data: behaving (task-driven spatiotemporal signaling data)
Source: Swan, M., dos Santos, R.P. & Witte, F. (2022). Quantum Neurobiology. Quantum Reports. 4(1):107-127.
Imaging In-cell Targeting
Connectome Parcellation

19 Nov 2022
Quantum Neuroscience Methods
Swarmalator: animal aggregations that self-coordinate in time and space (e.g. crickets, fish, birds)
Source: Swan, M. dos Santos, R.P., Lebedev, M.A. and Witte, F. (2022). Quantum Computing for the Brain. London: World
Scientific.
Research Topic Mathematical Physics Approaches
1 Imaging (EEG, fMRI,
MEG, etc.)
Wavefunctions: Fourier transform, Fourier slice theorem & Radon transform; QML (VQE); quantum
tomography image reconstruction (electrical and chemical (Calcium) wave forms)
2 Protein folding Lowest-energy configuration (Hamiltonian), spin glass, quantum spin liquid, Chern-Simons
Ground-state excited-state energy functions, total system energy
Qubit Hamiltonians, VQE
3 Genomics Lowest-energy knotting compaction, Chern-Simons (topological invariance)
Quantum optimization algorithms (Azure); optics; QAOA; AdS/CFT, BH, chaos, TN, MERA, RG
Quantum amplitude estimation: technique used to estimate the properties of random distributions
Collective Behavior
4 Neural Signaling Single-neuron: Hodgkin-Huxley (1963), 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
5 Swarmalator Swarmalator: phytoplankton (diffusion); krill (Brownian motion, Kuramoto oscillator); whale (clustering)
 Recurrent theme: topology (e.g. Chern-Simons)
 Solvable QFT curvature min-max = event (signal, mutation, fold)
 Quantum topological materials approach entails
 Topology: Chern-Simons, knotting, compaction

19 Nov 2022
Quantum Information
Levels of Organization in the Brain
60
 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.
 Human brain
 86 billion neurons, 242 trillion synapses
 ~10,000 incoming signals to each neuron
 Not large numbers in the big data era, but unclear how connected

19 Nov 2022
Structure: 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 is not function

19 Nov 2022
Quantum Information
Function: Motor Neuron Mapping Project Status
Multiscalar Neuroscience
62
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

19 Nov 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
63
Implicated in neuropathologies of Alzheimer’s, Parkinson’s, stroke, cancer
Synaptic Integration
Math: PDE (Partial Differential
Equation: multiple unknowns)

19 Nov 2022
Quantum Information
Neural Signaling Modeling
 Example problem: integrate EEG and fMRI data
 Different time, space, and dynamics regimes
 Epileptic seizure: chaotic dynamics (straightforward)
 Resting state: instability-bifurcation dynamics (system
organizing parameter interrupted by countersignal)
 Challenging problem: collective behavior
 Neural field theories, neural gauge theories
64
Scale Models
1 Single neuron Hodgkin-Huxley, integrate-and-fire, theta neurons
2 Local ensemble FitzHugh-Nagumo, Hindmarsh-Rose, Morris-Lecor
Linear Fokker-Planck equation (FPE) (uncorrelated behavior)
Nonlinear FPE, Fractional FPE (correlated behavior)
3 Population group
(neural mass)
Neural mass models (Jansen-Rit), mean-field (Wilson-Cowan), tractography,
oscillation, network models
4 Whole brain
(neural field theories)
(neural gauge theories)
Neural field models, Kuramoto oscillators, multistability-bifurcation, directed
percolation random graph phase transition, graph-based oscillation, Floquet
theory, Hopf bifurcation, beyond-Turing instability
Sources: Breakspear (2017). Papadopoulos, L., Lynn, C.W., Battaglia, D. & Bassett, D.S. (2020). Relations between large-scale
brain connectivity and effects of regional stimulation depend on collective dynamical state. PLoS Comput Biol. 16(9). Coombes, S.
(2005). Waves, bumps, and patterns in neural field theories. Biol Cybern. 93(2):91-108.

19 Nov 2022
Quantum Information
Neural Dynamics: Complex Statistics
65
FPE: Fokker-Planck equation: partial differential equation describing the time evolution of the probability density function of particle
velocity under the influence of drag forces; equivalent to the convection-diffusion equation in Brownian motion
Source: Breakspear, M. (2017). Dynamic models of large-scale brain activity. Nat Neurosci. 20:340-52.
Approach Description Statistical Distribution Neural Dynamics
1 Neural ensemble
models
Small groups of neurons,
uncorrelated states
Normal (Gaussian) Linear Fokker-Planck
equation (FPE)
2 Small groups of neurons,
correlated states
Non-Gaussian but known
(e.g. power law)
Nonlinear FPE, Fractional
FPE
3 Neural mass models Large-scale populations of
interacting neurons
Unrecognized Wilson-Cowan, Jansen-Rit,
Floquet model, Glass
networks, ODE
4 Neural field models
(whole brain)
Entire cortex as a continuous
sheet
Unrecognized Wavefunction, PDE,
Oscillation analysis
 Need physics-inspired field theories to model collective
behavior of neurons (unknown statistical distributions)
 Neural ensemble: normal distribution (FPE) and
power law distribution (nonlinear FPE, fractional FPE)
 Neural mass: Wilson-Cowan, Jansen-Rit, Floquet, ODE
 Neural field theory: wavefunction, oscillation, bifurcation, PDE

19 Nov 2022
Quantum Information
Biological System of the Neuron
 Neuronal waveform spike integration
 Electrical
 Axonal spikes
 Dendritic NMDA spikes
 Chemical
 Dendritic sodium spikes
 Dendritic calcium spikes
66
EPSP: excitatory postsynaptic potential (contrast with IPSP: inhibitory postsynaptic potential)
Sources: Williams, S.R. & Atkinson, S.E. (2008). Dendritic Synaptic Integration in Central Neurons. Curr. Biol. 18(22). R1045-R1047.
Poirazi et al. (2022). The impact of Hodgkin–Huxley models on dendritic research. J Physiol. 0.0:1–12.
(a)
(b)
(c)
(a) Dendritic spine receives EPSP
(b) Local spiking activity along dendrite
(c) Aggregate dendritic spikes at axon
Dendritic sodium, NMDA,
calcium spikes (Poirazi)

19 Nov 2022
Quantum Information
Wavefunctions: Neural Field Theory
67
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

19 Nov 2022
Quantum Information
Glutamate (excitatory) & GABA (inhibitory)
 Post-synaptic density (PSD) proteins
 Receiving neuron grows-shrinks
temporarily in response to signal
 Suggests geometry-topology modeling
68
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

19 Nov 2022
 Quantum Finance
 Quantum Biology
 AdS/Biology
 Genome Physics
Agenda

19 Nov 2022
Quantum Information
AdS/Neuroscience Research Programs
 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. 70
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

19 Nov 2022
Quantum Information
AdS/Brain (Neural Signaling)
71
NMDA: N-methyl-D-aspartate Sources: Gandolfi, D., Boiani, G.M., Bigiani, A. & Mapelli, J. (2021). Modeling Neurotransmission:
Computational Tools to Investigate Neurological Disorders. Int. J. Mol. Sci. 22:4565. Williams, S.R. & Atkinson, S.E. (2008).
Dendritic Synaptic Integration in Central Neurons. Current Biology. 18(22). R1045-47.
Bulk: ionic transfer
Boundary: signal impulse
 Tensor network model of dendritic integration
 Influence of dendritic conductance on synaptic
integration, membrane potential changes, signal
propagation and synaptic plasticity (Gandolfi, 2022)
 Model of +/= amplification by distance (Williams, 2008)
 Conduct quantum modeling (e.g. tensor network)
 TN modeling of classical pops out entanglement
relationships in data (hidden correlations)
 Signal: NMDA (electric), sodium/calcium (chemical)
Signal as minimal cut
through fewest tensor legs
Boundary:
Signal
Bulk:
Neurons

19 Nov 2022
Quantum Information
AdS/Brain: Molecular to Mesoscale Model
72
MERA: Multiscale Entanglement Renormalization Ansatz (guess)
Source: Vidal, G. (2007). Entanglement renormalization. Phys Rev Lett. 99(220405).
Boundary
Bulk
Boundary
Vidal, 2007
UV (near high-energy)
and IR (far low-energy)
correlations in a system
Neuron
Network
AdS/Brain
Synapse
Molecule
Network
Neuron Synapse
Neuron
Molecule
Synapse
Multiple Nested Bulk-Boundary Tiers
Mathematical Models
Network: Melonic, small-world, synchrony (Gurau, Lynn-Bassett, Nunez)
Neuron: Threshold subunit pooling, NMDA/sodium channels (Mel, Poirazi)
Synapse: Reaction-diffusion elliptical spine head geometry (Cugno-Sejnowski)
Molecule: Ca2+ signaling, dendritic ion channels (Sudhof, Kim & Sheng)
UV
IR
UV
Spherical coordinates for 3D
spike head geometry (Cugno)
Lifted AdS/MERA (McMahon)

19 Nov 2022
Quantum Information
 Analogy to food-web ecosystem multiscalar model
 AdS Math: define units, operators, mapping, action (S=)
AdS/Brain: Multiscalar Correspondence
73
Neuron
Network
AdS/Brain
Synapse
Molecule
Tier Scale Neural Signaling
Event
Swarmalator
Model
Food-web
Ecosystem Event
Math Approach
1 Network 10-2 Local field potential Whale Predation Distribution
2 Neuron 10-4 Action potential Krill Swarm Lagrangian
3 Synapse 10-6 Dendritic spike Phytoplankton Availability Diffusion
4 Molecule 10-10 Ion docking Light gradient Incidence angle Advection
Source: Swan, M. dos Santos, R.P., Lebedev, M.A. and Witte, F. (2022). Quantum Computing for the Brain. London: World
Scientific.
Krill
Whale
AdS/Krill
Phytoplankton
Light gradient

19 Nov 2022
Quantum Information
AdS/Krill: 4-tier Food-web Ecosystem
 Largest known animal aggregation
 30,000 individuals per square meter
 Global impact
 Aggregate biomass: 500 million tons worldwide
 Food source for whales, seals, penguins, squid, fish, birds
 Distribution: dispersed patches to dense swarms (Southern Ocean)
 Remove 39 mn tons carbon from the surface ocean each year (Belcher 2020)
 Krill morphology and activity
 Zooplankton invertebrates weighing 2 grams (0.07 oz), ~5 cm long
 Eat phytoplankton (microscopic suspended plants) and under-ice algae
 Spend the day at depth, rise to ocean surface at night (traveling hundreds of meters)
 10-year lifespan if avoiding predation
 Can survive up to 200 days without food (body shrinks but not eyes)
 Reproduction: lay 10,000 eggs at a time, several times per Jan-Mar spawning season
 Eggs laid near surface, sink over a 10-day period before hatching
74
Source: BAS British Antarctic Survey: Tarling et al. (2018). Varying depth and swarm dimensions of open-ocean Antarctic krill
Euphausia superba Dana, 1850 (Euphausiacea) over diel cycles. Journal of Crustacean Biology. 38(6):716–727. Belcher-Tarling
(2020). Why krill swarms are important to the global climate. Frontiers for Young Minds. 8(518995):1–8.
Krill swarm

19 Nov 2022
Quantum Information
Multiscalar Ecosystem Mathematics
 Krill ecosystem math
 Reaction-diffusion + Lagrangian oscillation – statistical predation
 Phytoplankton: diffusion problem modeled as Brownian motion with
light gradient (Heggerud, 2021)
 Krill swarm: Lagrangian (Brownian motion) (Hofmann, 2004) with
Kuramoto oscillator for time and space synchrony (O’Keeffe, 2022)
 Krill-whale: hotspot clustering, statistical field theory (Miller, 2019)
 Brain ecosystem math
 Topology + nonlinear oscillator – reaction-diffusion degradation
 3D elliptical geometrical molecular dendritic gradient (Cugno, 2018)
 Kuramoto oscillators in nonlinear networks (Budzinski, 2022)
 Protein buildup and clearance kinetics (Bressloff, Goriely, 2021)
75

19 Nov 2022
Quantum Information
Quantum Ecosystem Model
Krill Ecosystem
Statistical distribution (Miller)
2d Lagrangian (Hofmann)
Diffusion (Heggerud)
4-tier Multiscalar system: light-phytoplankton-krill-whale
similar to neural signaling ion-synapse-neuron-network
Ice
VQE: variational quantum eigensolver; VAE: variational autoencoder; QAOA: quantum approximate optimization algorithm;
RKHS (reproducing kernel Hilbert space) (quantum kernel learning), QNN: quantum neural network
Krill swarm density (%) = forces acting on krill whale predation (death rate)
phytoplankton density –
+
light gradient +
∂tu1 = D1∂xu1 – α1∂xu1 + [g1 (γ1 (x,t)) – d1(x)]u1
2
γ1 (x,t) = a1(λ) k1(λ) I(λ, x)dλ
ʃ
____
dXi =
dt
phytoplankton density
light gradient
forces acting on krill whale predation
MVBS120kHz - MVBS38kHz
dB re 1 m−1
+
–
Brain Ecosystem
Real and imaginary complex-valued
Kuramoto model
–
Path integral reaction-diffusion PDE;
Graph Laplacian n-concentration
Smoluchowski model (Bressloff, Goriely)
+
Spine head curvature
produces pseudo-
harmonic functions
(Cugno-Sejnowski)
Laplacian diffusion equation and
nonlinear flux through spine neck
Transition to synchrony
(Budzinski-Sejnowski)

19 Nov 2022
Quantum Information
Quantum Krill: 4-Tier Ecosystem Model
B. Enhanced
A. Basic
Optical analysis of light
spectrum gradient (Heggerud)
Swarmalator
hydrodynamic: O’Keeffe
(Kuramoto oscillator),
Ghosh (ring), Murphy (jet)
Lotka-Volterra predator-
prey model spiking
neuronal network
excitatory-inhibitory
model (Lagzi)
Statistical distribution (Miller)
2d Lagrangian (Hofmann)
Mathematics Diffusion (Heggerud)
Statistical analysis: 11 krill
swarm characteristics
analyzed in relation to
whale presence-absence
using Boosted regression
trees (BRTs) via a logit
(quantile function) (to
achieve local regularization
and prevent overfitting by
optimizing the number of
trees, learning rate, and
tree complexity
Quantum circuits
Random tensor network
QML: RKHS, QNN,
Quantum walk
VQE, VAE, QAOA, Quantum
amplitude estimation
Two species non-local
reaction-diffusion-advection
model to consider niche
differentiation via absorption
spectra separation. (rate of
change of) density of
phytoplankton species as
diffusion minus buoyancy
plus absorbed photons
minus death rate
Spatial light attenuation
through vertical water column
Ice
2d spatial Lagrangian
model based on four
random forces acting on
krill individuals:
displacement, response
to food gradients,
nearest neighbor
interaction (attraction or
repulsion), and
predation
VQE: variational quantum eigensolver; VAE: variational autoencoder; QAOA: quantum approximate optimization algorithm;
RKHS (reproducing kernel Hilbert space) (quantum kernel learning), QNN: quantum neural network
Krill swarm density (%) = forces acting on krill whale predation (death rate)
phytoplankton density –
+
light gradient +
4-tier Multiscalar system: light-phytoplankton-krill-whale
similar to neural signaling ion-synapse-neuron-network

19 Nov 2022
Ice
Phytoplankton
Whales
Krill swarm
Krill distribution
Whale distribution
Phytoplankton distribution
Multiscalar System: 4-tier 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 & 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
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

19 Nov 2022
Quantum Information
Phytoplankton: Diffusion (Heggerud)
79
D1, D2 > 0 Turbulence diffusion coefficients
Sinking/buoyancy coefficients (constants)
α1, α2 ϵ ℝ
γ1 (x,t) Number of absorbed photons
Death rate of the species at depth x and maximum L
d1(x) ϵ C [0,L]
γ1 (x,t) = a1(λ) k1(λ) I(λ, x)dλ
ʃ
u1 (x, t)
x Vertical depth in the water column
Density of phytoplankton species1,2 (depth x, time t)
(rate of change of) Density of Phytoplankton species =
Diffusion – Buoyancy + (Absorbed Photons – Death Rate)
D1u1 = D2u2
Source: Heggerud, C.M., Lam, K.-Y. & Wang, H. (2021). Niche differentiation in the light spectrum promotes coexistence of
phytoplankton species: a spatial modelling approach. arXiv:2109.02634v1.
Absorption spectra
k1(λ)
Action spectrum (proportion of absorbed photons used for photosynthesis)
a1(λ)
I(λ, x)dλ Incident light spectrum (wavelength intensity) of sunlight entering water column (Lambert-Beer’s Law)
Growth rate of species as a function of absorbed photons
g1 (γ1 (x,t))
Ice
2
2
No outcompeting species in the basic model
Enhanced model: attenuation of light through
the vertical water column, spatially explicit
diffusivity of phytoplankton and potential for
system buoyancy regulation (advection)

19 Nov 2022
Quantum Information
Krill: 2d Lagrangian (Forces) (Hofmann)
80
*Enhanced model: additional variable (equation not included)
Source: Hofmann, E.E., Haskell, A.G.E., Klinck, J.M. & Lascara, C.M. (2004). Lagrangian modelling studies of Antarctic krill
(Euphausia superba) swarm formation. ICES Journal of Marine Science. 61:617e631.
____
β
D
dXi =
dt
X, Y Two horizontal spatial dimensions
dYi
dt
=
____ Krill swarm formation factors:
D: Random displacement
F: Response to food gradients
N: Nearest neighbor interaction
attraction-repulsion
P: Predation
Vf (food,t) Foraging speed
Direction coefficient
local
P = P0(1-e-γρ )
ρ swarm density*
ρlocal < ρtarget
ρlocal < ρrepulsive
ρtarget < ρlocal < ρrepulsive
Diffusion motion
F Foraging motion
N Neighbor-induced motion
α Foraging angle
mFA Minimum turning angle
λFR Increased turning due to food
γ Predation rate constant
P Predation rate
λ Random turning modifier*
Lagrangian model to simulate Antarctic krill swarm formation
κ Neighbor response coefficient
ζ
δ Turning potential*
Sensing distance*
Turning threshold*
Ψ

19 Nov 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))
81
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 iper square meter
Flocking: 3D orientation vis-a-vis 5-10 nearest neighbors
Black holes, quasi-
particles, quantum
spin liquids,
schooling, flocking,
swarming
Hydrodynamic jet orientation
vis-à-vis nearest neighbor

19 Nov 2022
 Quantum Finance
 Quantum Biology
 AdS/Biology
 Genome Physics
Agenda

19 Nov 2022
Quantum Information
DIYbio Citizen
Direct-to-Consumer Whole Genome
83
Source: Nebula Genomics
 300+ personalized reports for health condition risk (Nov 2022)
 Quick incorporation of new research findings

19 Nov 2022
Quantum Information
DIYbio Citizen
Polygenic Risk Analysis
84
Source: Nebula Genomics
 36 SNP analysis
 92nd percentile in 5,000
Nebula user base
Danielle Posthuma Lab,
the Netherlands

19 Nov 2022
Quantum Information
DIYbio Citizen
Big Data Approach to Genomics
85
Source: Nebula Genomics and Posthuma Lab: https://pubmed.ncbi.nlm.nih.gov/?term=Posthuma D&sort=date&page=3
 Multicenter (16) polygenic approach (400+)
 Discovery n = 8074; replication n = 5042 individuals
 Alzheimer's disease
 Cerebrospinal fluid biomarkers
 Amyloid-beta 42 (Aβ42) and phosphorylated
tau (pTau) levels in cerebrospinal fluid
 Protective genetic effects
 Early-onset
 Novel loci
 Common variants
 Height, antisocial behavior, depression,
mental health, insomnia, intelligence, stroke,
aneurysm, migraine, schizophrenia

19 Nov 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
86
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.

19 Nov 2022
Quantum Information
Chern-Simons Biology
Genome Physics
 Model DNA and RNA as knot polynomial
 Chiral molecule twisted left-to-right in supersymmetry breaking
 t-RNA anti-codon also in knot structure
87
Right-hand nucleic acid modeled as
Hopf fibration with S3 group action
on projective space of genetic code
 Gauge group
 Gauge group of gene geometric translation
is group action of transcription process
 Genetic code as Wilson loop
 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
 Phospholipid membrane chirality induces
Chern-Simons couplings at low temperature
Sources: 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. Smolin, L. (2020). Natural and bionic neuronal membranes: possible sites
for quantum biology. arXiv:2001.08522v1.

19 Nov 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
Molecular
kagome weave

19 Nov 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

19 Nov 2022
Quantum Information
DNA Transcription per Chromatin Looping
 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
90
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)

19 Nov 2022
Quantum Information
DNA Matter Phases
 DNA Solid-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
91
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.

19 Nov 2022
 Quantum Finance
 Quantum Biology
 AdS/Biology
 Genome Physics
Agenda

19 Nov 2022
Quantum Information
Quantum Neurodegeneration Mathematics
 Toxic protein build-up without clearance
 Alzheimer’s (Aβ-tau), Parkinson’s (alpha-synuclein), ALS (TDP-43)
 Intervention strategy: prevent build-up or improve clearance
93
Big Data Genomics: multicenter
(thousands of patients), polygenic
statistical aggregation +/- risk
contribution (thousands of SNPs)
(Posthuma, 2022)
Protein kinetics: (buildup & clearance):
Reaction-diffusion (Fisher–Kolmogorov,
heterodimer, Smoluchowski); vascular & AB-tau
degeneration on separate tracks (Goriely, 2022)
AD/ML: identify fast-paced
protein build-up (homotopy
vs. Newton’s method for
PDEs), non-convex
optimization (Hao, 2022)
Protein folding: Topological complexity:
Vassiliev measure describes continuous
knotting nature of protein folding in 95%
of proteins studied (Wang 2022)
Simplicial
3-complex
Source (not discussed in subsequent slides): Wang, J. & Panagiotou, E. (2022). The protein folding rate and the geometry and
topology of the native state. Scientific Reports. 12:6384.

19 Nov 2022
Quantum Information
Alzheimer’s Disease
94
Sources: Telegraph: https://www.telegraph.co.uk/news/2022/09/21/shmoose-mutant-protein-raises-alzheimers-risk-50pc/
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: Control Subject with protective Christchurch
APOE3R136S mutation (rs121918393) A not C
 Heavy Aβ plaque burden (top), limited tau tangles (bottom)
 No early onset Alzheimer’s disease
 Right: Subject with Paisa mutation Presenilin 1 (rs63750231)
 Low Aβ plaque burden (top), substantial tau tangles (bottom)
 Early-onset Alzheimer’s disease
Plaques (top red): No
Early-onset Alzheimer’s
Tangles (bottom red):
Early-onset Alzheimer’s
 30% over 85 estimated to
be at risk (Telegraph, 2022)
 Imaging contributes to tau
tangles not Aβ plaques as
suggestive of pathology

19 Nov 2022
Quantum Information
Machine Learning
Alzheimer’s Disease Mathematics
95
Source: Huang, Y., Hao, W. & Lin, G. (2022). HomPINNs: Homotopy physics-informed neural networks for learning multiple
solutions of nonlinear differential equations. Computers and Mathematics with Applications. 121:62-73;
https://medium.com/swlh/non-convex-optimization-in-deep-learning-26fa30a2b2b3
 Convex optimization advance to non-convex optimization
 Multiple feasible regions, curvature, saddle points, local minima
 Time-exponential number of variables and constraints
 Partial differential equations (PDEs) (multiple unknowns)
 (Isaac) Newton’s method
 Root-finding algorithm
 Produces successively better root approximations
 Homotopy (same topology) [alternative to gradient descent]
 Finds a map of inputs to outputs as a continuous deformation
 Resource-costly but accommodates a wider range of situations
Non-convex
optimization
Basic convex
optimization

19 Nov 2022
Quantum Information
Machine Learning
ML/AD: Identify Fast-paced Protein Build-up
96
Source: Hao, W., Lenhart, S., Petrella, J.R. (2022). Optimal anti-amyloid-beta therapy for Alzheimer’s disease via a personalized
mathematical model. PLoS Comput Biol. 18(9):e1010481.
 ML/PDE predictive model of AD biomarker trajectories
 Result: faster protein build-up suggests intervention candidate
 Personalized treatment plans
 Per cerebrospinal fluid (CSF), MRI, cognitive biomarkers
 In-silico clinical trials of 2 anti-amyloid-beta treatments
 Personalized optimal treatment regimens
 Optimal control allows for time-varying controls
 Achieve goal to minimize cognitive impairment and the level of
amyloid in the brain while minimizing side effects
Amyloid beta Aβ accumulation initiates tau
protein phosphorylation (phosphorylated tau, τp)
A0 is the initial condition of amyloid beta at age T0, Kab
is the carrying capacity, λAβ is the Aβ growth rate

19 Nov 2022
Quantum Information
Prion-like Idea of Alzheimer’s Disease
97
Source: Fornari, S., Schafer, A., Jucker, M., Goriely, A. & Kuhl, E. (2019). Prion-like spreading of Alzheimer’s disease within the
brain’s connectome. J. R. Soc. Interface. 16:20190356.
 30 years of research, no causal understanding
 All older individuals with plaques, only some with dementia
 Protein spread along connectome networks
 Parkinson’s Disease: alpha-synuclein
 Alzheimer’s Disease: amyloid-beta (Aβ), tau
 Hyperphosphorylated sites open pathogen docking
 Prion hypothesis
 Misfolded proteins: infectious agents aggregate healthy proteins
 Pathological proteins adopt prion-like mechanisms to spread
 Multiscalar model of AD comorbidity
 Simultaneous brain vascularization problems (own kinetics)
 Model prion kinetics: Fisher–Kolmogorov, Smoluchowski model
 Aim: reduce production, improve clearance
Tau protein
misfolding in
Alzheimer’s
disease

19 Nov 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
98
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

19 Nov 2022
Quantum Information
Galleri Blood Test
Cancer Blood Test for over 50 Cancer Types
99
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
 DIY availability online ($995)

19 Nov 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)
100
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

19 Nov 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)
101
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)

19 Nov 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
102
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

19 Nov 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
103
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).

19 Nov 2022
Quantum Information
Glia and Calcium Signaling
104
 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.

19 Nov 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
105
“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).

19 Nov 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
106
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

19 Nov 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
107
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

19 Nov 2022
 Quantum Finance
 Quantum Biology
Agenda

19 Nov 2022
Quantum Information
Conclusion
 Quantum information science
 Subfields: quantum materials and quantum computing
 Solve certain kinds of problems, needs error correction
 Above all: three+ dimensional (lattice models, topology)
 Quantum chemistry
 Find ground state energy (phase estimation algorithm)
 Quantum space science
 Build communications networks (entanglement generation)
 Quantum finance
 Optimize portfolio, pricing, risk (amplitude estimation algorithm)
 Quantum biology
 Understand protein buildup-clearance (diffusion equations)
109

19 Nov 2022
Quantum Information
Quantum Mathematics by Field
110
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)
 Recurring theme: Chern-Simons topology

19 Nov 2022
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 a Classical Mindset
5 properties: symmetry,
topology, superposition,
entanglement, interference
New Quantum Sace-time Thinking:
Hyperbolic band theory (Bloch
theorem), quantum statistics
Quantum machine learning (Born
machine, neural operators)

19 Nov 2022
Quantum Information
Quantum Mindset: Hyperbolic 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, alt.time domains
 Radical uncertainty, all events are probabilistic
 Knowability trade-offs (time-location, speed-energy, etc.)
 Superpositioned thinking
 Hold multiple positions in mind
simultaneously before collapsing
to a measurement
112
Quantum microscopy
Schrödinger cat states Hyperbolic space
Source: https://www.slideshare.net/lablogga/critical-theory-of-silence
Philosophy-aided Physics: Kant, Hegel, and hyperbolic time

19 Nov 2022
Quantum Information
Risks and Limitations
113
 Quantum domain is hard to understand
 Complex, non-intuitive, alienating
 Quantum computing
 Only for specific problems, early stage and
non-starter without technical advance in error
correction (Preskill 2021)
 Substantial worldwide investment in
quantum initiatives
 Needed for next-generation quantum internet
networks, quantum cryptography
 Ability to coordinate next-tier of even larger
and more complex humanity-serving projects
Heidegger, The Question
Concerning Technology
+
-
Source: Preskill, J. (2021). Quantum computing 40 years later. arXiv:2106.10522.

Pleasanton CA, 19 Nov 2022
Slides: http://slideshare.net/LaBlogga
Melanie Swan, PhD
Research Associate
University College London
AdS/Biology and
“Outside was the perfect silence of the spheres.”
- Elizabeth Bear, Ancestral Night, 2019, p. 384
Thank you!
Questions?
AdS: AdS/CFT correspondence (anti de-Sitter space)

19 Nov 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
115
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

19 Nov 2022
Quantum Information
Quiz Questions (as of 1 Nov 2022)
116
1. Number of humans who have been to space? (Jun 2022)
 (e.g. LEO, GEO, ISS, 90-seconds of 0-g space flight)
2. Number of confirmed exoplanet discoveries? (Nov 2022)
3. Number of terrestrial spaceports?
 Number of U.S. FAA-permitted spaceports?
4. Percent of earth’s energy spent on the Haber-Bosch
process of nitrogen fixation to make ammonia?

19 Nov 2022
Quantum Information
Jokes
117
 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~!”
 Police officer: “Sir, do you know how
fast you were going?”
 Heisenberg: “No, but I know where I am”
 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
Biology and Neuroscience
Topologically, coffee cups and
doughnuts are the same

19 Nov 2022
Appendix
 Neuroscience Mathematics
 Quantum Machine Learning
 Quantum Algorithms
 Quantum Chemistry Primer
 Conceptualization of Space & Time
Quantum
Chemistry
Quantum
Computing
Quantum
Finance
Quantum
Medicine
Laser Microscopy:
six pairs of atoms

19 Nov 2022
Quantum Information
Mathematical Approaches to Neuroscience
119
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.

19 Nov 2022
Quantum Information
Mathematic Problem Reformulation
120
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

19 Nov 2022
Quantum Information
Quantum Information Science techniques
Tackle New Problem Classes
121
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)

19 Nov 2022
Appendix
Quantum
Chemistry
Quantum
Computing
Quantum
Finance
Quantum
Medicine
Laser Microscopy:
six pairs of atoms

19 Nov 2022
 Quantum machine learning
 Implement machine learning algorithms on quantum platforms
 Study quantum problems with machine learning techniques
Quantum Machine Learning
Shine et al., 2021

19 Nov 2022
Quantum Information
 Routine for wavefunctions/Hamiltonians
124
Source: Dawid Carrasquilla, Carleo, Wang et al. (2022). Modern applications of machine learning in quantum sciences. arXiv:
2204.04198.
Integer factorization: Shor’s algorithm Variational optimization of quantum circuits
Neural quantum states: NN-
derived variational states for
wavefunction approximation
Example: nanoflake wafer
placement, ETH Zurich, p. 184
Hamiltonian learning (one-spin system):
reconstruct the map from measurements
to underlying Hamiltonian parameters
Classification task
on one qubit

19 Nov 2022
Quantum Information
Review: Supervised Learning (2011)
 YouTube: user-classified data
perfect for Supervised Learning
 2 mn cat videos of 800 mn total
YouTube videos (Aug 2022)
125
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/

19 Nov 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
126
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.

19 Nov 2022
Quantum Information
 Quantum Machine Learning (QML)
versions of all three ML architectures
127
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

19 Nov 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
128
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

19 Nov 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)
129
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).

19 Nov 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
130
Source: Iqbal, A., Khan, R. & Karayannis, T. (2019). Developing a brain atlas through deep learning. Nat. Mach. Intell. 1:277-87.

19 Nov 2022
Quantum Information
Status of AI
AI Writes a Paper about Itself
131
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).

19 Nov 2022
Appendix
Quantum
Chemistry
Quantum
Computing
Quantum
Finance
Quantum
Medicine
Laser Microscopy:
six pairs of atoms

19 Nov 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
133
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

19 Nov 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)
134
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)

19 Nov 2022
Quantum Information
Quantum Walks
 Quadratically faster per ballistic
propagation through lattice walk
environment vs classical diffusive spread
135
Sources: Kendon. V. (2020). How to Compute Using Quantum Walks. EPTCS. 315:1-17. Dadras et al. (2019). Experimental
realization of a momentum-space quantum walk. Phys. Rev. A. 99:043617. Codling, E.A., Plank, M.J. & Benhamou, S.
(2008). Random walk models in biology. J. R. Soc. Interface. 5:813–834.
 Walk travels through all paths in superposition
 -> 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)
3d random walks in
biology (via FPE)

19 Nov 2022
Quantum Information
Quantum Error Correction Codes (QECC)
136
 Syntax: [ancilla size, logical bit size, distance], bit format
 Qutrit code: [3,1,2]3
 3 physical qutrits, protect 1 logical qutrit, over a distance metric of 2,
the bit format is 3 (qutrit)
 Pentagon code: [5,1,3]2
 5 physical qubits, 1 logical qubit, with distance 3, bit format 2 (qubit)
 1 logical degree-of-freedom in the bulk (pentagon center) to 5 physical
degrees-of-freedom on the boundary (5 sides of pentagon)
Holographic
Code
Code Syntax:
[ancilla, logical bits,
distance], format
Quantum
Information Bits
Physical Logical
Distance Metric Quantum
Information Bit
Format
Qutrit code [3,1,2]3 3 1 2 Qutrit
Pentagon code [5,1,3]2 5 1 3 Qubit
Source: Swan, M., dos Santos, R.P. & Witte, F. (2020). Blockchain Physics: Quantum Computing, Distributed Ledgers, Machine
Learning, and other Smart Network Technologies. London: World Scientific.

19 Nov 2022
Quantum Information
Pentagon Code: Quantum Error Correction
137
 Pentagon code: [5,1,3]2
 5 physical qubits, 1 logical qubit, with distance 3, bit format 2 (qubit)
 1 logical degree-of-freedom in the bulk (pentagon center) to 5 physical
degrees-of-freedom on the boundary (5 sides of pentagon)
 Code operation
 Start from set of 3 uncontracted physical sites on the boundary
 Reconstruct the logical states on the near-boundary
pentagons from the 3 boundary physical sites
 Use these physical states as inputs on
the next layer of pentagons to
reconstruct their logical states
 Repeat to bulk center
Holographic
Code
[Ancilla, logical bits,
distance], bit format
Quantum Information Bits
Physical Logical
Distance Metric Bit Format
Pentagon code [5,1,3]2 5 1 3 Qubit
Source: Pastawski, F., Yoshida, B., Harlow, D., Preskill, J. (2015). Holographic quantum error-correcting codes: Toy models for the
bulk/boundary correspondence. J. High Energ. Phys. 6(149):1-53. Cao & Lackey. (2020). arXiv:2010.05960. Gesteau (2020).
Alternate setup:
squares & hexagons
encoded in Bacon-
Shor code (Cao)
HaPPY code (author names) [5,1,3]2

19 Nov 2022
Appendix
Quantum
Chemistry
Quantum
Computing
Quantum
Finance
Quantum
Medicine
Laser Microscopy:
six pairs of atoms

19 Nov 2022
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.

19 Nov 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
140
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

19 Nov 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
141
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

19 Nov 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
142
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)

19 Nov 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
143
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)

19 Nov 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)
144
Source: Arrazola, J.M., Jahangiri, S., Delgado, A. et al. (2021). Differentiable quantum computational chemistry with PennyLane.
arXiv:2111.09967v2

19 Nov 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
145
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

19 Nov 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
146
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)

19 Nov 2022
Appendix
Quantum
Chemistry
Quantum
Computing
Quantum
Finance
Quantum
Medicine
Laser Microscopy:
six pairs of atoms

19 Nov 2022
Quantum Information
New ideas of Space
We are Here~!
148
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)

19 Nov 2022
Quantum Information
New ideas of Time
Seeing farther back into the Big Bang
149
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

19 Nov 2022
Quantum Information
New ideas of other potential Life
5,246+ Exoplanets Discovered (Nov 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)
150
Source: https://www.jwst.nasa.gov/content/about/comparisonWebbVsHubble.html
Radial Velocity
(Yellow: Kepler, Pink: Terrestrial)
Transit
(Blue: space-based telescopes)
Detection
Method:
5,000+

19 Nov 2022
Quantum Information
New ideas of where we fit
The Large and Small Scale Universe
151
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)

AdS Biology and Quantum Information Science

More Related Content

What's hot

Similar to AdS Biology and Quantum Information Science

More from Melanie Swan

Recently uploaded

AdS Biology and Quantum Information Science