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- 1. Quantum Computing Lecture 2: Advanced Concepts Mountain View CA, July 28, 2020 Slides: http://slideshare.net/LaBlogga Melanie Swan
- 2. 28 July 2020 Quantum Computing Theoretical Model of Quantum Reality Quantum reality is information-theoretic and computable Lecture 1: Quantum Computing basics (hardware) Lecture 2: Advanced concepts (control software between macroscale reality and quantum microstates) Lecture 3: Application (B/CI neuronanorobot network) 1
- 3. 28 July 2020 Quantum Computing Agenda Reality is Information-theoretic The AdS/CFT Correspondence Black Holes and Information Theory Zero-knowledge Proof Technology Two-tier Information Systems Planck Scale Implications Conclusion 2 Quantum Computing 2. Advanced Concepts
- 4. 28 July 2020 Quantum Computing 3 The AdS/CFT Correspondence is a conceptual model on par with probability, and perhaps superseding probability, for considering scale-encompassing problems in a range of fields including information theory and quantum materials The AdS/CFT Correspondence might serve as a macroscale control lever for the manipulation of quantum reality AdS/CFT Correspondence: Claim that any physical system with a bulk volume can be described by a boundary theory in one fewer dimensions Thesis AdS/CFT Correspondence (Anti-de Sitter Space/Conformal (basic) Field Theory)
- 5. 28 July 2020 Quantum Computing 4 Newton General Relativity Human scale Very large and very heavy Quantum Mechanics Very small and very light Physical Domains of Reality LIGO 2018 LHC Higgs Boson 2015
- 6. 28 July 2020 Quantum Computing 5 Newton General Relativity Human scale Very large and very heavy Quantum Mechanics Quantum Gravity Very small and very light Very small and very heavy Physical Domains of Reality Puzzles about black holes, the big bang, and dark energy LIGO 2015 LHC Higgs Boson 2015
- 7. 28 July 2020 Quantum Computing Agenda Reality is Information-theoretic The AdS/CFT Correspondence Black Holes and Information Theory Zero-knowledge Proof Technology Two-tier Information Systems Planck Scale Implications Conclusion 6 Quantum Computing 2. Advanced Concepts
- 8. 28 July 2020 Quantum Computing Black hole entropy scales by area not volume Entanglement Area Law: Bekenstein-Hawking, 1973-75 Classical (von Neumann) entropy scales by volume Example: room filled with computer hard drives, amount of information storage based on volume; in black hole, area Implication Since anything can be thrown into a black hole, and entropy increases, black hole entropy must be a general feature of quantum systems, not just a property of black holes Insight: Reality is Information-theoretic 7 Sources: Preskill, J. (2000). Quantum information and physics: Some future directions. J. Modern Opt. 47(2/3):127–37. Kaplan, J. Lectures on AdS/CFT from the Bottom Up. In quantum systems (like a black hole) entropy scales by area not volume
- 9. 28 July 2020 Quantum Computing Since quantum entropy scales by area not volume, the immediate implication is the computability of quantum systems Area easier to calculate than volume Many-body physics problems become solvable Tensor networks: computational tool for instantiating quantum systems MERA (multi-scale entanglement renormalization ansatz) incorporates entanglement (Vidal, 2008) AdS/CFT correspondence modeled as entangled quantum system (Swingle, 2012) Entropy: MERA Tensor Networks 8 Sources: Vidal, G. (2008). A class of quantum many-body states that can be efficiently simulated. Phys. Rev. Lett. 101. 110501; Swingle, B. (2012). Entanglement renormalization and holography. Phys. Rev. D 86. 065007. Theme: computability of quantum systems Represent many-body wave function with N spins (a) as tensor network (b) (a) (b)
- 10. 28 July 2020 Quantum Computing Timeline: Quantum Information Theory 9 Event Description Reference 1 Bekenstein-Hawking entropy formula Black hole entropy scales by area not volume Bekenstein (1973), Hawking (1975) 2 Holographic principle Complementary views of the same physical phenomena Susskind ('t Hooft), 1995 3 AdS/CFT correspondence Bulk/boundary correspondence (gauge/gravity duality) Maldacena, 1998 4 AdS/CFT entanglement entropy formula Boundary entanglement entropy related to bulk minimal surface Ryu & Takayanagi, 2006 5 MERA tensor networks for quantum mechanics Tensor network formulation for quantum mechanical entanglement Vidal, 2008 6 Apply MERA to AdS/CFT Model the AdS/CFT correspondence as an entangled quantum system Swingle, 2012 Theme: physical reality made more explicit and as a result, computable Black hole entropy formula Area
- 11. 28 July 2020 Quantum Computing AdS/CFT Correspondence & Info Theory 10 Event Description Reference 1 AMPS thought experiment: black hole firewall paradox posed Claim: information is knowable about outwardly-radiating bits from a black hole Almheiri et al., 2013 2 The AdS/CFT correspondence is an information theory problem Claim: true, but not enough time to compute useful information, even with a quantum computer Harlow & Hayden, 2013 3 Interpretation of AdS/CFT as a quantum error-correcting code Quantum error correction as a model for the AdS/CFT correspondence Almheiri et al., 2015 4 Exact solution of AdS/CFT as quantum error-correcting code Formalizing a specific holographic quantum error correction code Pastawski et al., 2015 5 Machine learning implementation of the AdS/CFT correspondence Repeated novel basic physics discovery through AdS/QCD machine learning results Hashimoto et al., 2018, 2020 (Github) Theme: routine application of the correspondence in quantum computing and machine learning Source: Hashimoto et al. (2018; 2020) Neural ODE and Holographic QCD; Deep Learning and Holographic QCD; GitHub: https://github.com/AkinoriTanaka-phys/DL_holographicQCD
- 12. 28 July 2020 Quantum Computing Agenda Reality is Information-theoretic The AdS/CFT Correspondence Black Holes and Information Theory Zero-knowledge Proof Technology Two-tier Information Systems Planck Scale Implications Conclusion 11 Quantum Computing 2. Advanced Concepts
- 13. 28 July 2020 Quantum Computing Holographic Principle A 3D volume reconstructed on a 2D surface (bug on windshield) Two different descriptions of the same physics Holographic Correspondence (gauge-gravity duality) Gravity theories & gauge theories are field-based (Maldacena 1997) Gauge theories treat next scale level down from atoms Quantum chromodynamics (subatomic particles) Proton: three quarks bound together by gluons (lines of flux/field strength, like electromagnetic field lines, gravitational fields) The Holographic Principle 12 Sources: Susskind, L.; Maldacena, J. Gluons hold Quarks together to form a Proton Fields/Lines of Flux Matter particles: fermions (quarks) Force particles: bosons (gluons)
- 14. 28 July 2020 Quantum Computing Apply information theory to physics (Harlow & Hayden, 2013) Formalization of the holographic principle/gauge-gravity duality Claim: Any physical system with a bulk volume can be described by a boundary theory in one fewer dimensions Bug on windshield : particles are smeared out on the black hole event horizon in one fewer dimensions than in the bulk interior AdS/CFT Correspondence (Anti-de Sitter Space/Conformal Field Theory) 13 Sources: Harlow, D. & Hayden, P. (2013). Quantum computation vs. firewalls. J. High Energ. Phys. 2013:85; Pastawski, S., et al. Is spacetime a quantum error-correcting code? arXiv:1503.06237, 2015; Escher, Circle Limits. AdS/CFT “soup can” Escher Circle Limits Quantum error correcting code Implications for Geometry emerges from entanglement = QECC Time/space emergence Black hole information paradox
- 15. 28 July 2020 Quantum Computing How it is possible for entangled bits of quantum information to radiate out of a black hole? (Hawking, 1975) Hawking radiation is real, but BH interior contra laws of physics Holographic principle: complementary views of the same phenomenon to different observers Far-off observer only sees information smearing out or being compressed in 2D on the event horizon of the black hole (the boundary) and never actually entering the black hole (the bulk) Near-by observer that is jumping into the black hole sees the information going into the bulk interior in 3D Different views of the same physics means no paradox Far-off observer seeing 2D and near-by observer seeing 3D Information smears on event horizon like a bug on a windshield Black Hole Information Paradox 14 Sources: Susskind, L.; Maldacena, J.; Gravity: particle wave functions: gauge theory: field geometry
- 16. 28 July 2020 Quantum Computing Agenda Reality is Information-theoretic The AdS/CFT Correspondence Black Holes and Information Theory Zero-knowledge Proof Technology Two-tier Information Systems Planck Scale Implications Conclusion 15 Quantum Computing 2. Advanced Concepts
- 17. 28 July 2020 Quantum Computing Black Holes and Information Theory 16 Use a quantum computer to model entangled pairs Model all pairs of entangled particles in a black hole Determine for a given particle whether its entangled partner has radiated out or is still in the black hole interior Conclusion: the problem is computable, but not within a useful time frame (i.e. the life time of the universe) Source: Harlow & Hayden, 2013. Hawking radiation Quantum information bits radiating out of a black hole are entangled Cannot measure a qubit (per the no- measurement principle), but can measure the other particle in the entangled pair to obtain information about the particle
- 18. 28 July 2020 Quantum Computing Relating the Bulk and the Boundary 17 Somewhat counterintuitive Flat boundary surface (classical domain) and bulk interior (quantum domain) Boundary entropy scales by volume (classical domain) and bulk entropy scales by area (quantum domain) Entropy is a measure of entanglement Ryu-Takayanagi formula (2006) relates bulk-boundary entanglement Engage bulk-boundary entanglement relationship through Causal wedge reconstruction (a) Entanglement wedge reconstruction (b) Source: Images: Raamsdonk (2016) Lectures on Gravity and Entanglement; Beni Yoshida blog (2017) (a) (b)
- 19. 28 July 2020 Quantum Computing The Correspondence is a QECC 18 Holographic quantum codes Source: Preskill, 2015 Quantum error correcting code (fully-tiled) Quantum error correcting code (start) Tree graph (simple code) Bulk entanglement The central qubit is encoded in a block of five surrounding qubits, and can be recovered from any three (or erased by any three) Bulk regions are entangled with each other and the boundary. This relationship is expressed in the entanglement wedge reconstruction Implement quantum error correcting code with pentagon tiling. Any pentagon can be contracted with any two downstream pentagons The error correcting code is tiled to the boundary by contracting each pentagon with downstream pentagons (tensor network index contraction) QECC: Quantum error correcting code
- 20. 28 July 2020 Quantum Computing Protects qubits from loss or damage (spin reversal) Qubits are more sensitive to environmental damage and state decay than classical information bits Cannot correct qubits with redundant backup copy (classical method) per no-cloning rule of quantum information Quantum Entanglement and Error Correction 19 Rely on entanglement property of qubits Quantum bits are entangled with one another Embed qubits into a larger state with an excess of qubits (ancilla: ancillary or extra qubits) If qubit is lost or damaged, the message can be reconstituted from the entangled qubits Measure qubits indirectly via entanglement relationships (parity measurement)
- 21. 28 July 2020 Quantum Computing Quantum Error Correction 20 Shor’s code: 9-qubit ancilla Stabilizer code checks for spin flips along X-Y-Z axis Code instantiates a single logical qubit of data as three physical qubits for each scenario of the three axes Parity check: pair-wise evaluation to see whether the first and second qubit have the same value, and the second and third qubit have the same value, without revealing the value If one of the qubits disagrees with the other two, it can be reset to their value Ancilla length 9-qubit (Shor), 7-qubit (Steane), 5-qubit
- 22. 28 July 2020 Quantum Computing Implement error correction with AdS/CFT correspondence Encode a single logical spin (in the bulk) into a larger block of entangled physical spins (on the boundary), to protect the bulk spin against erasure Pentagon code Explicit tensor network model that can be solved and implemented (vs. Shor/Steane’s theoretical codes) Each tensor has one open leg which creates a structure for computational flow from bulk to boundary Tensor indices differentially contracted to execute the code Logical operators (qubits) in the bulk mapped to physical operators (qubits) in the boundary (the protective ancilla) Holographic Error Correction 21 Source: Pastawski, F., Yoshida, B., Harlow, D., Preskill, J. (2015). Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence. J. High Energ. Phys. 6(149):1-53. Holographic error- correction code
- 23. 28 July 2020 Quantum Computing Quantum Error Correction Codes (QECC) 22 Various encoding schemes proposed Syntax: [ancilla size, logical bit size, distance], bit format Qutrit code: [3,1,2]3 means 3 physical qutrits, to protect 1 logical qutrit, over a distance metric of 2 (deletions up to 1 can be protected (2–1 = 1)), and the bit format is 3 (a qutrit, not a qubit) Pentagon code: [5,1,3]2 means 5 physical qubits, 1 logical qubit, with distance 3, and bit format 2 (qubit as opposed to qutrit) 1 logical degree-of-freedom in the bulk (pentagon center) to 5 physical degrees-of-freedom on the boundary (5 sides of pentagon) Holographic Code Code Structure [ancilla size, logical bit size, distance] Quantum Information Bits Physical Logical Distance and # Deletions Protected Quantum Information Digit Format Qutrit code [3,1,2]3 3 1 2;1 Qutrit Pentagon code [5,1,3]2 5 1 3;2 Qubit
- 24. 28 July 2020 Quantum Computing Agenda Reality is Information-theoretic The AdS/CFT Correspondence Black Holes and Information Theory Zero-knowledge Proof Technology Two-tier Information Systems Planck Scale Implications Conclusion 23 Quantum Computing 2. Advanced Concepts
- 25. 28 July 2020 Quantum Computing Nature’s Quantum Security Features 24 Nature has built-in security features at the quantum scale that are useful for quantum computing Principle Security Feature 1 No-cloning theorem Cannot copy quantum information 2 No-measurement principle Cannot measure quantum information without damaging it (eavesdropping is immediately detectable) 3 Quantum statistics Provable randomness: distributions could only have been quantum-generated (implications for quantum cryptography) 4 Quantum error correction Error correction via ancilla (larger state of entangled qubits) 5 BQP (QSZK) computational complexity Quantum information domains compute quickly enough to perform their own computational verification (zero- knowledge proofs)
- 26. 28 July 2020 Quantum Computing Can calculate information about entangled particles radiating out of a black hole, but not in a useful amount of time BQP: the computational complexity class of problems that can be solved with a quantum computer BQP (bounded-probability quantum polynomial) Between P and P-SPACE Contained within QSZK (quantum statistical zero knowledge) The information-theoretic approach can identify which kinds of problems can be solved quickly Recognizing a problem as a form of BQP suggests that although quantum computers may be able to calculate it, it may not be solvable within a reasonable amount of time Black Holes and Computational Complexity 25 QSZK: the set of computational problems with yes-no answers for which the prover can always convince the verifier of yes instances, but will fail with high probability for no instances (Watrous, 2002)
- 27. 28 July 2020 Quantum Computing Computational Complexity and Quantum Computing 26 Computational complexity: amount (time and space) of computing resources required to solve a problem QC: one-tier improvement in computational complexity Canonical Traveling Salesperson Problem: check twice as many cities in half the time using a quantum computer Solve the next tier of designated problem difficulty with the current tier’s computational resource (in time and space) NP becomes solvable in P, EXP becomes solvable in NP Example: factoring large numbers becomes time-reasonable P: polynomial time (e.g. solvable in human-reasonable amount of time); NP: non-polynomial (not solvable in human-reasonable amount of time); EXP: exponential (requires exponential time/space to solve) Computational Complexity BQP
- 28. 28 July 2020 Quantum Computing Black Hole Zero-knowledge Proofs BQP performs its own truth verification BQP (the class of problems solvable with a quantum computer) computes quickly and soundly enough to provide computational verification of its activity Black hole (any quantum information domain) provides computational verification as a built-in operating feature Zero-knowledge property of quantum information No traditional prover-verifier relationship because quantum computer does the verification so fast, verifier is not necessary For QSZK/BQP problems, the verification can be conducted directly using the computer itself without a prover (Watrous, 2002) Implication: quantum computing has verification (zero- knowledge proof technology) built into it as a feature 27 Source: Watrous, J. (2002). Quantum statistical zero-knowledge. arXiv:quantph/0202111;
- 29. 28 July 2020 Quantum Computing Computational Verification Computational verification Verification is conducted directly by the computer System provides verification of its result as part of the proof of its activities The computational system serves as a third party, performing truth verification as a feature of the general operation of the system, relying upon mathematical soundness The system-performed computational verification is presented to an external party as part of the proof Implication: computational verification becomes a standard feature of computing systems Applies to both classical and quantum computing 28
- 30. 28 July 2020 Quantum Computing Implication: A self-contained qudit system can perform its own computation, error correction, and proof, as a complete unit of computational complexity Qudits: quantum digits, units of quantum information described by a superposition of d states Qubit: 2-state quantum information unit (0/1) Most closely related to classical information bits (0/1) Qutrit: 3-state quantum information bits Efficient error correction: correct any state with 2 of 3 qutrits Encode 3D XYZ-axis spins in qutrit ancilla Ququat: 4-state quantum information bits) Qusept: 7-qudit system (maximum tested) 29 Theoretical Computing Advance Source: Fonseca et al. (2018). Survey on the Bell nonlocality of a pair of entangled qudits. Phys. Rev. A 98:042105.
- 31. 28 July 2020 Quantum Computing Black Holes and Computational Verification 30 Black Holes perform their own Zero-knowledge Proofs As any BQP (quantum computing) computational complexity class, black holes compute so quickly as to perform their own computational verification Claims about quantum computing Quantum computers are not fast enough to calculate useful information about an evaporating black hole Quantum computers are fast enough to provide their own computational verification
- 32. 28 July 2020 Quantum Computing Agenda Reality is Information-theoretic The AdS/CFT Correspondence Black Holes and Information Theory Zero-knowledge Proof Technology Two-tier Information Systems Planck Scale Implications Conclusion 31 Quantum Computing 2. Advanced Concepts
- 33. 28 July 2020 Quantum Computing Zero-knowledge Proof Technology Zero knowledge A mathematical soundness attribute that it is not necessary to have any knowledge of an underlying process (i.e. zero knowledge), only the result Zero-knowledge proof Proof that reveals no information except the correctness of the proposition in question. Proof output is a one bit answer: T/F Standardized zero-knowledge proof technology Efficient computational proofs Information security Having no knowledge (zero knowledge) of the underlying information keeps it private, all that is necessary is the one-bit answer indicating the truth value of the proof 32 Source: Goldwasser, S., Micali, S. & Rackoff, C. (1989). The knowledge complexity of interactive proof systems. SIAM J. Comput. 18(1):186-208.
- 34. 28 July 2020 Quantum Computing Zero-knowledge Proof Systems Proof systems with verification built into the process Example: a worker punches a time clock every hour and submits the time-stamped records at the end of the day for verification. The supervisor does not need to check the worker’s activity every hour, only confirm the oracular (third- party) output of the time punches at the end of the day Blockchain non-interactive proof systems Operated and verified by computational third-party (oracle) IPFS (Interplanetary File System) proof of space and time Proof of having provided the space of computer storage resources over time, cumulatively-verified computationally STARKs (Scalable Transparent Arguments of Knowledge) Holographic proof (proof in which every statement contains information about the entire proof so is easily verifiable) 33 Sources: Fisch, B. (2018). PoReps: Proofs of space on useful data. ia.cr/2018/678; Ben-Sasson et. al. (2018). Scalable, transparent, and post-quantum secure computational integrity. ia.cr/2018/046. Quantum secure
- 35. 28 July 2020 Quantum Computing Blockchain Zero-knowledge Proof Systems 34 SNARKs (Succinct Non-interactive ARguments of Knowledge) Bulletproofs (very small very fast (like a bullet), no trusted setup) STARKs (Succinct Trusted ARguments of Knowledge; large proofs, quick verification, no trusted setup, based on error-correction codes) Use case trade-off: proof time (time to execute the proof) vs verification time (time to verify the proof) Comparison of Zero-knowledge Proof Systems Sources: Ben-Sasson et al. (2014). Zerocash: Decentralized Anonymous Payments from Bitcoin. IEEE Symposium on Security & Privacy; Bunz et al. (2018). Bulletproofs: Short Proofs for Confidential Transactions and More. 39th IEEE Symposium on Security and Privacy; Ben-Sasson et. al. (2018). Scalable, transparent, and post-quantum secure computational integrity. ia.cr/2018/046. ZKP System Proof Size Trusted setup required? Proof Time Verification Time Post-Quantum Secure? SNARKs (2014) 1.3 KB (Sapling) Yes Fast Fast No Bulletproofs (2018) 1-2 KB No Fast Not very fast Yes STARKs (2018) 20-30 KB (was 200 KB) No Not very fast Very fast Yes
- 36. 28 July 2020 Quantum Computing Zero-knowledge Proof Systems STARKs 35 STARKs (Scalable Transparent Arguments of Knowledge) STARKs are a blockchain-based computational oracular proof method (create consistency apparatus) 1. Error-correcting code (Reed-Solomon code) used to smooth and encode proof data into an artificial apparatus created for the purpose of the proof 2. The proof body is an elaborate structure of internal consistencies that fall into place if random queries to it are true, and otherwise evaluates as false (e.g. if an imposter is attempting to submit a fake proof) 3. At the end, the prover sends a summary of the proof body and random verification queries to the verifier, who easily checks its validity computationally Source: Ben-Sasson et. al. (2018). Scalable, transparent, and post-quantum secure computational integrity. ia.cr/2018/046.
- 37. 28 July 2020 Quantum Computing Agenda Reality is Information-theoretic The AdS/CFT Correspondence Black Holes and Information Theory Zero-knowledge Proof Technology Two-tier Information Systems Planck Scale Implications Conclusion 36 Quantum Computing 2. Advanced Concepts
- 38. 28 July 2020 Quantum Computing AdS/CFT Correspondence is ZK ProofTech 37 Zero-knowledge proofs are in the shape of a hologram Two different perspectives of the same information Both evaluate as true Like black hole observers, far-off in 2D, near-by in 3D Proofs are in the form of a two-level information system 1. The underlying information 2. The proof as an assessment of the underlying information Both evaluate as true from different views of the information Local observer (prover) sees the dimensional detail of the private information and knows the information is true Remote observer (verifier) sees the one-fewer dimensional evaluation of the information as a one-bit value that is true
- 39. 28 July 2020 Quantum Computing Two-tier Information Systems 38 Extending the information-theoretic interpretation of the AdS/CFT correspondence Many messy bulk processes must provably run in real- time, resulting in an informationally-compressed answer Messy Bulk Process Boundary Output 1 Air particles moving in a room Temperature 2 Consumer buying and selling GDP 3 Quantum mechanical reality: particles jiggling Macroscale reality: table 4 Information entering black hole interior in 3D Information smeared out in 2D on black hole event horizon 5 Ancilla of larger entangled state Error-corrected qubit 6 Hash function Hash 7 Zero-knowledge proof T/F value 8 Proof-of-work mining Confirmed transaction block 9 Holographic annealing Lowest energy state of system 10 Protein folding Conformal protein TemperatureAir Particles
- 40. 28 July 2020 Quantum Computing The correspondence as a control mechanism Two-tier holographic information systems Instantiate controllable holographic processes (with the correspondence formalism) Run holographic processes Run a process in the bulk and obtain the answer in the boundary in one fewer dimensions Well-formedness features naturally- imported from quantum mechanical reality Mathematical soundness Computational verification (zero-knowledge proof systems) Emergent bulk structure for free (geometry, space and time) 39
- 41. 28 July 2020 Quantum Computing Stakes: Control Particle-many Fleets Deploy the correspondence as a control mechanism Use surface theories to direct bulk processes Within quantum computing and beyond Standard tool for dimension-spanning Bring swarms of “particle”-type units under control Identify “particle-many domains” that can be controlled at the macroscale (or one dimension up) Fleet-many units : taxis, inventory items, nanorobots, synthetic synapses in a B/CI, asteroid mining vehicles 40
- 42. 28 July 2020 Quantum Computing Quantum information system design Physical reality: long-distance and short-distance description of the same phenomenon (ex: temperature) Macroscale reality is boundary theory to quantum mechanical bulk Lens: holographic POV and computational complexity 41 AdS/smart network correspondence Correspondence and QIS Design Long-distance and Short-distance Descriptions in Field Theory Systems Microstate environment Bulk EFT (describing microstates) Macrostate metric Boundary CFT (describing macrostates) 1 Bulk Effective field theory Boundary (d-1) Conformal field theory 2 Air particles Quantum mechanics, wave function Temperature, Pressure Statistical mechanics 3 Water molecules Particle physics, QCD Waves Hydrodynamics 4 Atoms in a crystal Spin glass Superconducting materials Condensed matter physics 5 Quantum information structure (geometry, time, space) SNQFT (smart network quantum field theory) Deep learning particle output, holographic consensus SNFT (smart network field theory)
- 43. 28 July 2020 Quantum Computing 42 Complex Systems are systems characterized by properties of nonlinearity, emergence, spontaneous order, adaptation, and feedback loops Reality is comprised of Complex Systems
- 44. 28 July 2020 Quantum Computing Complex Systems are difficult to Predict 43 1789 2010 ??? French Revolution Tiananmen Square Next political event Arab Spring Turkish coup 1989 2016 Source: Handbook of Cliometrics. (2016). Editors: Diebolt, Claude, Haupert, Michael Musculo-skeletonFinancial RiskEcological Food Web Social Network How do macroscale events arise from the collective behavior of atomic parts?
- 45. 28 July 2020 Quantum Computing 44 “Waiting for Carnot” problem Source: Kelly, K. (1994). Out of Control. Waiting for Carnot’s explanation of complex heat cycle Formal explanations, causal models, and unifying theories are not available in complex domains Biology, Markets, Quantum Physics Definitive thermodynamic model of the heat cycle
- 46. 28 July 2020 Quantum Computing 45 Effective (Field) Theory Prediction Coarse- graining How to Explain Complex Phenomena? Source: Dedeao, S. SFI, Lecture 1: Coarse-Graining, Renormalization & Universality Fine-grained Theory Calibration Small-scale Measurement Simulation Agent-based modeling Lattice QCD Protein Folding Renormalization group: rolling up scale levels (Wilson)
- 47. 28 July 2020 Quantum Computing Complex Systems: AdS Control Lever 46 Deploy the AdS/CFT Correspondence to span macrostates and microstates in complex systems Macroscale reality is a surface theory from which to activate the complex quantum mechanical bulk Macrostate Surface Messy Bulk Complexity Source: Schweitzer, F., et al. 2009. Economic Networks: The New Challenges. Science. 325:422-5. Simon, H.A. 1996. The Sciences of the Artificial. Third edition. MIT Press, Cambridge, MA. Temperature Septillions of particles Macroscale reality Underlying quantum mechanical reality Consumer buying/selling GDP AdS Control Lever
- 48. 28 July 2020 Quantum Computing Agenda Reality is Information-theoretic The AdS/CFT Correspondence Black Holes and Information Theory Zero-knowledge Proof Technology Two-tier Information Systems Planck Scale Implications Conclusion 47 Quantum Computing 2. Advanced Concepts
- 49. 28 July 2020 Quantum Computing 48 Newton General Relativity Human scale Very large and very heavy Quantum Mechanics Quantum Gravity Very small and very light Very small and very heavy Physical Domains of Reality
- 50. 28 July 2020 Quantum Computing Emergence of bulk geometry, space, time Spatial transformations Symmetry (Bogoliubov transformations) Radial directionality (inward-outward orientation to bulk center) Entropy (Ryu-Takayanagi bulk-boundary entanglement entropy) Temporal transformations Boundary defined as Cauchy surface (plane with time dimension) MERA tensor networks and random tensors to iterate time and connect regions with geometry and regions with particle interaction Example: construct one-dimensional conformal field theories from tensors that only depend on the time variable (Witten, 2016) Geometric spacetimes (Qi, 2017, Holographic coherent states) Superposition of geometries: boundary state described as a superposition of different spatial geometries in the bulk 49 Sources: Witten, E. (2016). An SYK-Like Model Without Disorder. arXiv:1610.09758 [hep-th]; Qi, X.-L., Yang, Z. & You, Y.-Z. (2017). Holographic coherent states from random tensor networks. JHEP 08(060):1-34. Correspondence-identified Emergence
- 51. 28 July 2020 Quantum Computing Time and Space at the Planck scale 50 Source: Loop and Spin Foam Quantum Gravity: A Brief Guide for Beginners. In Approaches to Fundamental Physics: An Assessment of Current Theoretical Ideas, 2007, pp. 151-84. DOI: 10.1007/978-3-540-71117-9_9. Spin Networks Snapshot of Time and Space at the Planck scale Spin Foam Evolution of Spin Networks over Time Artistic Rendering One proposal: group field theory (spin networks)
- 52. 28 July 2020 Quantum Computing Diverse Temporal Regimes General Relativity: relativistic time (experienced time) Time dilation: age faster mountain top than sea level Twin problem, grandfather paradox, one party traveling Quantum Mechanics: atomic time (clock time) Measured regular movement of atomic particles Klein-Gordon, Dirac, QFT (many particles) Diverse Spatial Regimes General Relativity: geometric space, phase space Quantum Mechanics: Hilbert space (vector space), momentum space, configuration space, various polarizations of space Diverse Regimes of Time and Space 51 Time dilation Atomic clock
- 53. 28 July 2020 Quantum Computing Positions 1. Time and space are emergent Time and space exist, not fundamentally, but as derived from other entities or structures (i.e. quantum matter and its relations, entanglement) What precedes: geometry or dynamics? Geometry (domains in which there is behavior) Dynamics (the parameters of behavior) 2. Time and space are fundamental Time and space exist as concrete and basic “furniture” of reality that cannot be derived from other entities or structures 52 Source: http://www.hss.caltech.edu/content/dennis-lehmkuhl Time and Space: Emergent or Fundamental?
- 54. 28 July 2020 Quantum Computing Planck Scale Computation? 53 Newton (1687) Difference Engine (1786) Transistor (1947) Quantum Mechanics (1905) Quantum Gravity (2016) ?? (2075e) Planck scale (1×10−35) Atomic scale (1×10−9) Classical scale (1×101) Scale Scientific Discovery Computing Paradigm Concept Source: Feynman, R.P. (1960) There's Plenty of Room at the Bottom. Engineering and Science. 23(5):22-36. Quark scale (1×10−15) Quantum Computing (2019) The emergence of time and space (bulk structure) is relevant for computational complexity (computational difficulty, time/space necessary to compute)
- 55. 28 July 2020 Quantum Computing Agenda Reality is Information-theoretic The AdS/CFT Correspondence Black Holes and Information Theory Zero-knowledge Proof Technology Two-tier Information Systems Planck Scale Implications Conclusion 54 Quantum Computing 2. Advanced Concepts
- 56. 28 July 2020 Quantum Computing Risks and Limitations Overreaching application of AdS/CFT Correspondence But, proliferation and results in many fields (materials, plasma) Original paper widely cited (over 10,000 references) Complaint tenor about “exact” application Wide conceptual application (e.g. information compression) What is the core math to apply, so many permutations SYK model, JT gravity, random tensors, information geometry Centrality of wave functions and probability Beyond-probability physics could examine other aspects such as the spectra of operators, entanglement, entropy (irreversibility), and field fluctuations; all of which do not rely on probability Even the word “quantum” already directs the approach 55 Original paper Source: Maldacena, J. (1998). The large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 2:231–52.
- 57. 28 July 2020 Quantum Computing AdS/CFT Studies 56 AdS/CFT Correspondence Variation Application Functionality Reference AdS/CFT AdS/Conformal Field Theory Cosmology, particle physics Susskind, 1995 AdS/CMT AdS/Conformal Materials Theory Strongly coupled systems: plasma, condensed matter, superconductors Sergio & Pires, 2014; Hartnoll et al., 2018 AdS/ML AdS/Machine Learning Rewrite Ryu-Takayanagi bulk- boundary entropy relation with maxflow–mincut theorem Hashimoto et al., 2018 AdS/DLT AdS/Distributed Ledger Technology Holographic consensus, quantum smart routing, certified randomness Kalinin & Berloff, 2018 AdS/BCI AdS/Brain Cloud Interface Holographic B/CI control, ad-hoc fields, neurocurrencies, IPLD for brain Swan, 2020 AdS/CMT (condensed matter theory) Understand more about exotic superconducting materials: cuprates, pnictides, heavy fermions, organics Emergence of superconductivity at low temperatures AdS/ML (machine learning) Emergence of optimal algorithms
- 58. 28 July 2020 Quantum Computing Conclusion 57 Quantum mechanical reality is computable AdS/CFT Correspondence The claim that any physical system with a bulk volume can be described by a boundary theory in one fewer dimensions Model black holes or any quantum system Acts as a quantum error correction code In quantum systems (like a black hole) entropy scales by area not volume AdS/CFT image: Daniel Harlow
- 59. 28 July 2020 Quantum Computing Conclusion 58 Black holes perform their own Zero- knowledge Proofs Any quantum computational complexity class (like a black hole) computes so quickly as to perform its own computational verification Nature’s built-in quantum security features No cloning, no measurement, quantum statistics, quantum error correction, zero- knowledge proofs (computational verification) The correspondence is a control lever from macroscale reality to quantum reality Macroscale reality Underlying quantum mechanical reality AdS Control Lever
- 60. 28 July 2020 Quantum Computing 59 Heptapod to linguist Louise Banks: We don’t use a Latin script for written language, we use semagrams Alien intelligence to humans: We don’t use probability at scale tiers down to the Planck length: we use entanglement energy Speculative Stakes: Alternative Worldviews Arrival remark adapted from: Source: Chiang, Ted. (2002). Story of Your Life. In Arrival. New York: Vintage Books.
- 61. 28 July 2020 Quantum Computing Practical Stakes: Understanding the Brain Challenge: tackle large-scale next-generation projects Particle accelerators: LHC upgrade (HL-LHC: High- Luminosity Large Hadron Collider 2026e) 50-100x greater computing capacity required Chemistry/Biology: Avogadro’s # domains (a trillion trillion) Brain (final frontier): Whole brain emulation, Brain/Cloudmind Interface (BCI collaborations) 60 Source: Cook, Steven J. et al. Whole-animal connectomes of both Caenorhabditis elegans sexes. Nature. (571):63-89, 2019. Avogadro’s number: (6 × 1023) or (0.6 of a trillion × a trillion)
- 62. 28 July 2020 Quantum Computing 61 The AdS/CFT Correspondence is a conceptual model on par with probability, and perhaps superseding probability, for considering scale-encompassing problems in a range of fields including information theory and quantum materials The AdS/CFT Correspondence might serve as a macroscale control lever for the manipulation of quantum reality AdS/CFT Correspondence: Claim that any physical system with a bulk volume can be described by a boundary theory in one fewer dimensions Thesis AdS/CFT Correspondence (Anti-de Sitter Space/Conformal (basic) Field Theory)
- 63. Quantum Computing Lecture 2: Advanced Concepts Mountain View CA, July 28, 2020 Slides: http://slideshare.net/LaBlogga Thank you! Questions? Melanie Swan