AdS Biology and Quantum Information Science

1. 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)

2. 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

3. 19 Nov 2022 Quantum Information 2 Quantum Information Science 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)

4. 19 Nov 2022 Quantum Information 3  Quantum Information Science  Quantum Chemistry  Quantum Space Science  Quantum Finance  Quantum Biology Agenda

5. 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

6. 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

7. 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.

8. 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

9. 19 Nov 2022 Quantum Information Quantum Computing Microsoft IBM Rigetti

10. 19 Nov 2022 Quantum Information Using a Quantum Computer 9 Source: D-Wave Systems, Inc. https://cloud.dwavesys.com/leap/resources/demos

11. 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)

12. 19 Nov 2022 Quantum Information 11 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.

13. 19 Nov 2022 Quantum Information 12 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).

14. 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

15. 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

16. 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.

17. 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

18. 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. 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

20. 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

21. 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 +

22. 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)

23. 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

24. 19 Nov 2022 Quantum Information 23 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

25. 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

26. 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

28. 19 Nov 2022 Quantum Information 27 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)

29. 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)

30. 19 Nov 2022 Quantum Information 29  Quantum Information Science  Quantum Chemistry  Nitrogen sequestration and batteries  Quantum Space Science  Quantum Finance  Quantum Biology  Neural Signaling  Neuroscience Physics  Genomics  Practical Application  Neurodegenerative Disease  Protein Pathologies Agenda

31. 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.

32. 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)

33. 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

34. 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

35. 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

36. 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

37. 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

38. 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

39. 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

40. 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

41. 19 Nov 2022 Quantum Information 40 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)

42. 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

43. 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.

44. 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

46. 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

47. 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

48. 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

49. 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

50. 19 Nov 2022 Quantum Information 49  Quantum Information Science  Quantum Chemistry  Quantum Space Science  Quantum Finance  Quantum Biology  AdS/Biology  Quantum Neuroscience  AdS/Neuroscience  Practical Applications  Genome Physics  Alzheimer’s Disease Agenda

51. 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.

52. 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

53. 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

54. 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

55. 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

56. 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

58. 19 Nov 2022 Quantum Information Quantum Neuroscience 57 Network Science Machine Learning Materials Science Neuroscience Theoretical Physics Quantum Information Science

59. 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

60. 19 Nov 2022 Quantum Information 59 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

61. 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

62. 19 Nov 2022 Quantum Information 61 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

63. 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

64. 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)

65. 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.

66. 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

67. 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)

68. 19 Nov 2022 Quantum Information Quantum Neuroscience 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

69. 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

71. 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

72. 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

73. 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)

74. 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

75. 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

76. 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

77. 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)

78. 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

79. 19 Nov 2022 Quantum Information 78 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

80. 19 Nov 2022 Quantum Information Phytoplankton: Diffusion (Heggerud) 79 ∂tu1 = D1∂xu1 – α1∂xu1 + [g1 (γ1 (x,t)) – d1(x)]u1 ∂tu2 = D2∂xu2 – α2∂xu2 + [g2 (γ2 (x,t)) – d2(x)]u2 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)

81. 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

82. 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

84. 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

85. 19 Nov 2022 Quantum Information DIYbio Citizen Polygenic Risk Analysis 84 Source: Nebula Genomics  Alzheimer’s Disease  36 SNP analysis  92nd percentile in 5,000 Nebula user base Danielle Posthuma Lab, the Netherlands

86. 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

87. 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.

88. 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.

89. 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

90. 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

91. 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)

92. 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.

94. 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.

95. 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

96. 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

97. 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

98. 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

99. 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

100. 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)

101. 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

102. 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)

103. 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

104. 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).

105. 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.

106. 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).

107. 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

108. 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

110. 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

111. 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

112. 19 Nov 2022 Quantum Information 111 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)

113. 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

114. 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.

115. 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 Thank you! Questions? AdS: AdS/CFT correspondence (anti de-Sitter space)

116. 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

117. 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?

118. 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

119. 19 Nov 2022 Quantum Information 118 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

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