Quantum Computing Lecture 2: Advanced Concepts

Quantum Computing
Lecture 2: Advanced Concepts
Mountain View CA, July 28, 2020
Slides: http://slideshare.net/LaBlogga
Melanie Swan

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

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

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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)

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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

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Quantum Computing 5
Quantum Mechanics Quantum Gravity
Very small and very light Very small and very heavy
Puzzles
about black
holes, the
big bang,
and dark
energy
LIGO
2015
LHC
Higgs
Boson
2015

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Quantum Computing
 Agenda
 Conclusion
6
Quantum Computing

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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

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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)

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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

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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

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Quantum Computing
 Agenda
 Conclusion
11
Quantum Computing

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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)

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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

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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

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Quantum Computing
 Agenda
 Conclusion
15
Quantum Computing

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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

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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)

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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

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)

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

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

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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

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Quantum Computing
 Agenda
 Conclusion
23
Quantum Computing

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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)

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)

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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

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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;

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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

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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.

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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

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Quantum Computing
 Agenda
 Conclusion
31
Quantum Computing

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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.

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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

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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

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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.

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Quantum Computing
 Agenda
 Conclusion
36
Quantum Computing

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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

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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

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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

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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

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)

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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

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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?

28 July 2020
“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

28 July 2020
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)

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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

28 July 2020
Quantum Computing
 Agenda
 Conclusion
47
Quantum Computing

28 July 2020
Quantum Mechanics Quantum Gravity
Very small and very light Very small and very heavy

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

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)

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

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?

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)

28 July 2020
Quantum Computing
 Agenda
 Conclusion
54
Quantum Computing

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.

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

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

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

28 July 2020
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.

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)

28 July 2020
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)

Quantum Computing
Lecture 2: Advanced Concepts
Mountain View CA, July 28, 2020
Slides: http://slideshare.net/LaBlogga
Thank you!
Questions?
Melanie Swan

Quantum Computing Lecture 2: Advanced Concepts

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