Table of Contents
Quantum Computing Topics
Question: “Is training an AI-system more energy efficient with quantum computing?”
Answer: Yes, very much more energy efficient because quantum computing uses no electricity at all since it does not exist yet in physical reality! See Quantum computers don’t exist yet (See Practical Quantum computer and Mikhail Dyakonov). They are still just a quantum theory!“
Research: Quantum computing
“A quantum spin liquid is a superposition of spin states, fluctuating but entangled. It's fair to say that this process, should it create a quantum spin liquid with quantum superposition, will have made a qubit, the basic building block of a quantum computer.” — Daniel Haskel, physicist and group leader, XSD”
The entire theory of quantum computing is based on the old theory of superposition
- , which is based on the many-worlds interpretation of Hugh Everett and is linked to the famous Schrodinger Cat Problem. Its prime assumption is that quantum states are superimposed physically.
More Research
Course Notes
What you'll learn
“This is an introduction to quantum computing meant for those in IT, cybersecurity, and related fields who might not have substantial math or physics background. The concepts will be explored with minimal mathematics. This would include basic concepts, the use of the Bloch sphere, quantum superposition, and quantum gates. Particular attention will be paid to practical applications of quantum computing such as the quantum computing impact of quantum cryptography and quantum security, Quantum resistant cryptography and the NISTIR 8240.”
Quantum computing is “real fast” and “real soon now” (“any day now”) “approaching a practical reality.” “QC impacts the future of computing as well as security issues.”
According to Quantum FUD, “QC will render current asymmetric cryptographic methods insecure. That requires QC resistant algorithms. IT personnel and cybersecurity professionals must have at least a basic conceptual understanding of quantum computing” in order to see through the QC FUD and not have Quantum panic
What you’ll learn and how you can apply it
Understand conceptually quantum computing Have a fundamental understanding of quantum gates Know the impact of QC on cybersecurity and cryptography Understand the basics of quantum resistant cryptography
This live event is for you because…
IT personnel (programmers, network admins, etc.) can gain an understanding of quantum computing without having an extensive physics and math background.
The impact of QC on IT and cybersecurity is so significant that all professionals in these fields need to have at least a working knowledge.
It is a prerequisite for more advanced training.
Segment 1: Introductory concepts (45 mins)
- What is quantum physics
How does it relate to computing
Segment 2: Just a little math (45 mins)
Some very basic discussion of vectors Bra-ket notation Probabilities
Segment 3: Quantum Computing and Security (45 mins)
Current cryptography
What QC means to current cryptography
NIST competition
A look at some specific algorithms.
Segment 4: The near future (30 mins)
Current state of QC and coming steps
QC Challenges
QC and AI
Fair Use Source for Commentary: https://learning.oreilly.com/live-events/basic-introduction-to-quantum-computing/0636920360872/0636920063843
Research Slides
Quantum Computing
Basic Quantum Physics Concepts
Defining quantum computing
Exploring the impact
Discussing current developments
CLASSICAL PHY
1687 – N SI
e C
wto S
n’s Philosophiae
Mathematica
1788 – Lagrange’s Mecanique
Analytique
1834 – Hamiltonian mechanics
Classical Physics
1864 – Maxwell’s equations
1900 – Boltzmann’s
entropy equation
1900 – Planck’s constant
1913 – Bohr’s model of the atom
Quantum Physics
1925 – Pauli exclusion principle
1926 – Schrodinger equation
1948 – Feynman's path
integral formulation
1954 – Everett’s many-world theory
PARTICLES AND
particle Duality
Particles
Waves
Bounce off or shatter
Interfere
Are distinct
Can be superimposed
Early 20th century discovered
1. Light waves exhibited particle like properties –
phenomena cal ed photo-electric effect in which light impinging on certain metals cause emission of electrons in a billiard ball like impact.
2. Electrons (particles) exhibit wave like properties – they can pass through each other ! Phenomenon of electron interference
Quantum Physics - Basics
THE BEG
Lo I
uiN
s dN
e I
B N
roglG
ie S
( OF
1892– QU
1987) h A
y N
po TU
thesize M
d PHY
that parti SI
cle C
s, i S
ncluding
electrons, could also have wavelike behaviors.
Heisenberg showed it is impossible to take any measurement of an object without disturbing it.
The Heisenberg uncertainty principle states that it is fundamentally impossible to know precisely both the velocity and position of a particle at the same time.
QUANTUM-WA
QVE
u DU
antu A
m LITY
Physics - Basics
Niels Bohr and Werner Heisenberg were the architects of this quantum world view, along with Planck, Einstein, de Broglie, Schrodinger, Pauli and Dirac.
Particle nature of light was proposed by Einstein in 1905 to explain the photo-electric effect. Particles of light are called light quanta or photons.
The quantum world is probabilistic, not deterministic
UNCERTAINT
Q Y
u
antum Physics - Uncertainty
WAVE FUNCT
Quan IO
tu N
m Physics – Wave Function Collapse
HAMILTONIAN
Q OPE
uantuRA
m TOR
Physics - Hamiltonian
HAMILTONIAN
Q OPE
uantu RA
m TOR
Physics - Hamiltonian
Quantum Physics – Wave Function
SCHRÖDINGER’S EQUATION
Quantum Physics - Schrödinger equation
Time dependent version
ENTANGLEME
Qu NT
antum Physics - Entanglement
Entanglement begins with two particles being generated in such a way that the quantum state of each quantum particle is inextricably linked to the other.
Essentially the two particles have a quantum state such that each particle cannot be truly described independently. Thus, properties such as momentum, polarization, spin, etc. are correlated.
The hidden variables hypothesis contends that the particles actually have some hidden variables that, right at the moment the particles are separated, determining the outcome of properties such as spin. This would mean that there really is no non-locality, simply variables we don't know about. Einstein was a proponent of this idea. However, no experiments have given any evidence to support this.
BELL’S INEQ
Q U
u A
anLIT
tu Y
m
Physics – Bell’s Inequality
In 1964, John Bell proposed a method to test for the existence of the proposed hidden variables. To gain an intuitive understanding of Bell's inequality, let us consider two photons that are entangled. Bell realized that the only way to account for the perfect correlation in quantumly entangled particles, without invoking nonlocality, was that there must be pre-existing values.
A basic intuitive understanding of Bel 's inequalities is actually rather simple. : Assuming hidden variables, this leads to strict limits on the possible values of the correlation of subsequent measurements that can be obtained from the pairs of entangled particles. And However, experiments simply don't show that.
BELL’S INEQ
Q U
u A
anLIT
tu Y
m
Physics – Bell’s Inequality
QUANTUM ME
Qu CH
antu A
m NI
Ph CS
ysics – Orbitals
The only quantity that can be known is the probability for an electron to occupy a certain region around the nucleus.
Orbitals are different from orbits in that they represent probability maps that show a statistical distribution of where the electron is likely to be found —-
QUANTUM ME
Qu CH
antu A
m NI
Ph C
ys A
ic L
s MO
– OrD
b EL
itals
In the quantum-mechanical model, a number and a letter specify an orbital.
The lowest-energy orbital is called the 1s orbital.
It is specified by the number 1 and the letter s.
The number is cal ed the Principal quantum number ( n) and it indicates the relative size and energy of atomic orbitals.
n specifies the atom’s major energy levels, called the principal energy levels.
Each energy sublevel relates to orbitals of different shape.
n =1 only 1 sublevel s
n =2 2 subleves s,p
n =3 3 sublevels s, p, d
n =4 4 sublevesl s, p, d, f
What is a
quantum
computer?
A quantum computer is a
machine that performs
calculations based on the laws of
quantum mechanics, which is the
behavior of particles at the sub-
atomic level.
WILL WE G
Q E
uaT THE
nt
RE
um Computing – Will it Happen?
The March 2019 issue of IEEE Spectrum has an article by Mikhail Dyakonov. Dr. Dyakonov is a professor of physics at Laboratoire Charles Coulomb (L2C), Université Montpellier - CNRS in France.
Most experts believe quantum computing will be a practical reality within the near future. When it does, all current, classical, asymmetric cryptography algorithms will be obsolete. This includes all the current algorithms used in e-commerce, online banking, and secure network communications. Therefore, new cryptographic solutions must be found.
IBM CEO is “opining” that we are only 5 years from practical quantum computer.
—- 22
Quantum Computing
In 1982 Richard Feynman conceived of a “quantum mechanical computer“
—- 23
Quantum Computing
“I think I can safely say that nobody understands quantum mechanics” - Feynman
- 1982 - Richard Feynman proposed the idea of creating machines based on the laws of quantum mechanics instead of the laws of classical physics.
- 1985 - David Deutsch developed the quantum Turing machine, showing that quantum circuits are universal.
Quantum Computing
“Although any calculation that can be performed on a classical digital computer could also be performed on a quantum computer, doing so would be foolish for most problems. It is much harder to manipulate and measure qubits than it is bits. But hard computational problems exist for which no efficient classical algorithms are known.”
Weiss, D. S., & Saffman, M. (2017). Quantum computing with neutral atoms. Physics Today, 70(7), 44.
—- 25
Quantum Computing – Shor’s Algorithm
Peter Shor developed Shor's algorithm. On a quantum computer it can factor an integer N in polynomial time (actual time is log N). This is substantially faster than the most efficient
known classical factoring algorithm (the
general number field sieve) which works in
sub-exponential time.
Peter Shor was awarded the Gödel Prize of
the ACM and a MacArthur Foundation
Fellowship in 1999
—- 26
LEV GRO
Q VE
ua R
ntum Computing – Grover’s Algorithm
Grover's algorithm is essentially a search algorithm. It was developed by Lev Grover in 1996.
The efficacy of Grover’s algorithm has been proven mathematically in multiple ways. It is one of the algorithms that confirm that power we will realize from quantum computers one decoherence is solved.
Lev Grover Indian-American computer scientist, BS from Indian Institute of Technology, Ph.D. from Stanford.
Quantum Computing – Probabilistic
Quantum physics is largely probabilistic.
—- 28
Quantum Computing – Quantum Supremacy
John Preskil coined the term quantum supremacy referring to a quantum computer solving a particular problem that is either unsolvable or extremely impractical to solve with a classical computer.
October 2019 Google and NASA performed calculations using the Sycamore quantum computer approximately 3 mil ion times faster than can be done on the fastest classical computer.
TWO BRANCHES
QKD
Quantum
Computing
QUANTUM KE
Q Y
ua DI
nt STRI
um C B
o UTION
mputing (
– QKD)
QKD
Quantum entanglement
BB84 protocol: Charles H. Bennett and Gil es Brassard (1984) uses photon polarization states to transmit information.
The Six-state protocol, often simply called SSP was published by Bechmann-Pasquinucc and Gisn in 2019 in a paper entitled “Incoherent and Coherent Eavesdropping in the 6-state protocol of Quantum Cryptography”.
E91 protocol: Artur Ekert (1991) uses photons that are entangled.
QUANTUM KE
Q Y
ua DI
nt STRI
um C B
o UTION
mputing (
– QKD)
QKD
Four companies currently offering QKD products
ID Quantique (Geneva)
MagiQ Technologies, Inc. (New York)
QuintessenceLabs (Australia)
SeQureNet (Paris).
QUANTUM K
Q EY
ua E
nt XCH
um C A
o NGE
mputing – QKD
The goal is to enable Alice and Bob to agree on a private key, even in the face of an eavesdropper, Eve.
Like Diffie-Hel man, the protocol is stil susceptible to a “man-in-the-middle”
attack.
But unlike Diffie-Hel man, the protocol does not depend on the difficulty of computing discrete logarithms or any other computational problem.
Quantum Computing – BB84 Protocol
1.
Alice sends Bob a stream of photons randomly polarized in one of 4 polarizations: bit encoding: 0 1 0 1
2.
Bob measures the photons in random orientations
e.g.: x + + x x x + x (orientations used)
\ ]] | Chinese researchers have developed the Jiuzhang 2 66 qubit programmable photon-based quantum computer and used it to solve a task 1024 times as fast as classical computers. The problem solved was rather obscure, it involves Gaussian boson sampling (GBS), a classical simulation algorithm . Zuchongzi and Jiuzhang 2.0 are currently China's two leading quantum computers. ---- 41 BUT WHA Qua T nt DO um C WE o N mputE i ED ng – How Many Do We Need IBM announces the Hummingbird processor with 65 qubits
November 2021 IBM announces new processor named Eagle, which features 127 qubits. This processor also reduces interference, thus reducing errors.
In 2022 IBM plans to introduced IBM Osprey a processor with 400+ qubits.
November 2021, Finland now announces its first 5-qubit quantum computer is operational. This demonstrates that more nations and companies are getting involved in quantum computing.
– Developments
2021 Harvard-MIT Center for Utracold Atoms develops a programmable quantum
simulator with 256 qubits https://news.harvard.edu/gazette/story/2021/07/harvard-
led-physicists-create-256-qubit-programmable-quantum-simulator/
CURRENT
Q E
uaXCI
nt TING
um Co TRE
mputiND
ng S
– Developments
Researchers using Google’s Sycamore quantum computer, verified their theoretical vision of a ‘time crystal’. Crystals are made up of repeating units of atoms. A time crystal is a change that repeats through a system. Put more formally: a time crystal is a quantum system of particles whose lowest energy state is actually one in which the particles are in repetitive motion. Because this is the systems quantum ground state, it cannot lose energy and come to rest. These were first posited as theoretical constructs in 2012 by Nobel Laurate Dr. Frank Wilczek of MIT
https://www.sciencealert.com/physicists-used-a-quantum-computer-to-show-their-
time-crystal-design-is-the-real-deal
A LOT OF
Q W
ua ORK
nt
DON
um Co
E RE
mputi C
ng –EN
D-TLY
Wave
D-Wave systems produces quantum like computing systems that utilized quantum annealing
In May of 2016 IBM made a quantum processor available to the general public via a cloud solution Note: D-Wave is now also getting into the quantum gate business https://www.zdnet.com/article/there-are-two-types-of-quantum-computing-now-dwave-says-it-will-offer-both/
There are even programming languages developed for quantum computing —-
Quantum Computing – Adiabatic
Quantum Computing
This is rather complex. It is based on the adiabatic theorem that was first posited by Max Born and Vladimir Fock. The theorem states A physical system remains in its instantaneous eigenstate if a given perturbation is acting on it slowly enough and if there is a gap between the eigenvalue and the rest of the Hamiltonian's spectrum. What this means is that a quantum mechanical system when subjected to gradually changing conditions wil adapt is form. This does not work in rapidly changing conditions because there is insufficient time. This theorem is used to allow a system to evolve towards a solution. This is much like annealing.
Quantum Computing – Quantum Annealing
Quantum annealing (QA). Quantum annealing is used mainly for problems where the search space is discrete (combinatorial optimization problems).
Quantum annealing starts from a quantum-mechanical superposition of all possible states (candidate states) with equal weights. Then the system evolves with a time dependent equation (the Schrodinger equation).
Note: In metallurgy, annealing is a heat treatment that alters the microstructure of a material causing changes in properties such as strength and hardness. Commonly done by heating the material until it glows then letting it slowly cool to room temperature.
—- 50
Quantum Computing – What it does well
Solving integer factorization (Shor’s algorithm)
Solving the Discrete Logarithm Problem
Grover's algorithm searches a database using quadratically fewer queries to the database than that are required by classical algorithms.
The Quantum algorithm for linear systems of equations or “HHL Algorithm”, named after its discoverers Harrow, Hassidim, and Lloyd, is expected to provide speedup over classical counterparts
THE MAJOR PL
Quant AYERS
um Computing – Major Players
IBM
DWAVE
RIGETTI
Cambridge Quantum Computing
Honeywell
ionQ
AT&T (working with California Institute of Technology)
Honeywell
HP
Northrop Grumman
Raytheon
QUANT
QuaUM P
nt
RO
um CoGRAMMI
mputing NG
– Programming Languages
QASM and OpenQASM
Quil
Q# (Extension of C#)
Q Language (extension of C++)
QMASM (D-Wave)
Qiskit (developed by IBM, uses Python)
Blackbird (used by Xanadu Quantum Technologies)
ProjectQ (uses Python)
Forest (Rigetti, uses Python)
QUANT
Q UM P
uant
RO
um CoGRAMMI
mputing NG
– Circuit based
Quantum Processors
China Jiuzhang uses photonics 76 qubit
Google Sycamore uses nonlinear superconducting resonate 53 qubit
Google Bristlecone uses superconducting 72 qubit
Xanadu Quantum Technologies x24 uses photonics 24 qubit
IBM IBM Q 53 uses superconducting 53 qubit
IBM IBM Eagle uses superconducting 127 qubit
IBM IBM Manhattan uses superconducting 65 qubit
Intel Tangle Lake uses superconducting 49 qubit —-
QUA
QNT
ua UM P
nt
R
um C O
o GRA
mputi MMI
ng – NG
Annealing based
Quantum Processors
D-Wave 2x 1152 qubit
D-Wave D-Wave 2000Q 2048 qubit
D-Wave D-Wave Advantage 5760 qubit
Quantum Computing – Obstacles
The most prominent obstacle is controlling or removing quantum decoherence. This usually means isolating the system from its environment as interactions with the external world cause the system to decohere.
However, internal factors in the quantum computer itself can cause decoherence.
—- 56
Quantum Computing – Decoherence
Theoretically, a quantum system could maintain coherence indefinitely if it were completely isolated from the external environment; however, no system is perfectly isolated from its environment. It has even been demonstrated that cosmic rays and background environmental radiation can contribute to decoherence in quantum computers. Even entanglements can occur between the quantum computing system and its environment.
In addition to the external environment, the system itself can be an issue. For example, the physical equipment needed for things like implementing quantum gates, is constructed of atoms and particles that have quantum properties. In general, many systems are only able to maintain coherence for a matter of microseconds to a few seconds.
.
57
Quantum Computing – Decoherence
One method used to help combat decoherence is super cooling to just a fraction of one Kelvin. In fact, some systems cool to a few nanokelvins.
If you are not familiar, or don't recall the Kelvin scale, 0 Kelvin is the equivalent to -273.15 Celsius or -459.67 Fahrenheit. This is not arbitrary.
The point 0 Kelvin is absolute zero, which implies no thermal energy at all. Thus, nanokelvins are literally a fraction of a degree above absolute zero. To provide some context, temperatures in space are often around 2.7 Kelvin. Obviously, proximity to heat sources such as stars can alter that. The surface of Pluto plummets to about 40 Kelvin. So, quantum computing relies on temperatures that are much colder than Pluto, and even colder than deep space.
SUPERC
Q OOL
uant ING
um C M
o ETHODS
mputing – Supercooling
Helium-3 has a boiling point of 3.19 K
Helium-4 has a boiling point of 4.214 K
Liquid Helium is commonly used
Intel uses cryogen-free dilution refrigerator systems from specialist Blufors (A Finnish company specializing in supercooling). This works in stages cooling more at each stage. They use a mixture of Helium isotopes as the refrigerant.
January 2021 Google has a cryogenic control circuit that operates at 4 K.
2020 IBM is developing a refrigerator named GoldenEye that can reach temperatures of around 15 mil i-kelvins. The device is 10' tall and 6' wide.
QUBITS AND GATES
Into the qubit
Quantum Computing – Quantum Gates
A quantum circuit is essentially a sequence of quantum gates. It is reversible and is the analog of an n-bit register, called an n-qubit register.
A qubit is a two-state quantum-mechanical system. Spin or polarization work well.
The qubit, unlike a bit, need not be in one state or the other, but is in a superposition of states.
The Bloch sphere representation of a qubit
—- 61
QUBITS
Quantum Computing – Qubit
A qubit can be represented by the spin of an electron or the polarization of a photon.
Quantum Computing – Qubit
A single quantum “bit” which is 1 with probability p and 0 with probability 1-p.
When measured, outcome is either 0 or 1.
Measuring a qubit changes its value! If outcome is 0, p is set to 0, if outcome is 1, p is set to 1.
A qubit could be implemented using a photon to carry a horizontal or vertical polarization.
PAGE 63
QUBIT REPRESENTATION
Quantum Computing – Qubit
This is typically written as
bra-ket notation also called Dirac notation is used to represent vectors. In this case the two states ]] | and | are both kets. If one wishes to represent two qubits then there are four states to be represented: ---- QUBIT REPRE QSE uaNT nt ATION um Computing – Qubit Keep in mind that these are the states you will have once you have measured the qubit. Until such measurement occurs, the qubit is in a superposition of possible states. Therefore, to describe a qubit the following formula is useful. The values α and β are the probability amplitudes. Usually, these probabilities are complex numbers. ---- Quantum Computing – Qubit Date represented in a qubit is in one of two states denoted by | and | . A physical implementation of a qubit could use the two energy levels of an atom, polarization of a photon, etc. Using states of an atom, an excited state representing | and a ground state representing | . Light pulse of frequency λ for Excited State | State | time interval t State Nucleus Ground State Electro n ---- Quantum Computing – Superposition Light pulse of frequency λ for time interval t/2 State | State | + | Consider a 3-bit qubit register. An equally weighted superposition of all possible states would be denoted by: | ψ> = | + | + . . . + | 1 1 1 √8 √8 √8 ---- Photons Quantum Computing – Storing Qubit Photons are commonly used, with the data (1 or 0) determined by the polarization. The horizontal polarization is | and vertical is | . The polarization method is a common method for using photons for qubits. Another method used with photons is to encode the qubit using time-bin encoding. The process involves having a single photon be processed through a Mach-Zehnder interferometer. This interferometer is a device that takes two beams that are derived from splitting a single light source and determines the relative phase shift variations between them. When a photon enters the interferometer, it will be guided along one of two paths. One path is longer than the other, and the difference between the two paths must be longer than the coherence length of the photon. For those readers not well versed in physics, coherence length is the propagation distance over which a coherent electromagnetic wave can maintain a particular degree of coherence. The photon takes one of the two paths. The shorter path (i.e. the earlier arrival of the photon) designates the state | and the longer designates state | . ---- 68 Quantum Computing – Storing Qubit Electron Electrons and photons are two of the most obvious ways to implement a qubit. Electron qubits use some property such as electron spin to indicate the state of the qubit. For example, an up spin can designate state | and a down spin designating | . Some researchers have focused on quantum states of electrons in particular mediums. For example, the Okinawa Institute of Science and Technology has worked on using electrons in liquid helium. Data suggests that electron spin states in liquid helium would maintain coherence longer. ---- 69 Quantum Computing – Storing Qubit IONS (used for quite some time) A trapped ion quantum computer uses ions that are confined using electromagnetic fields. The Qubits are stored in stable states of each ion. Lasers are frequently used to manipulate the qubits. The first implementation of a controlled-NOT quantum gate was proposed in 1995 by Ignacio Cirac and Peter Zoller and used the trapped ion system. ---- 70 Quantum Computing – Storing Qubit Neutral Atoms (newer approach) “Several research groups trap neutral atoms using either magnetic fields or light, but light traps have received the most attention for quantum computing. Atoms are polarizable, and the oscil ating electric field of a light beam induces an oscil ating electric dipole moment in the atom.” -Weiss, D. S., & Saffman, M. (2017). Quantum computing with neutral atoms. Physics Today, 70(7), 44. ---- 71 Quantum Computing – Storing Qubit NMRQC Nuclear magnetic resonance quantum computing is a very interesting approach to physically implementing quantum computers. This approach uses spin states of nuclei within molecules to represent the qubits. The states are probed using nuclear magnetic resonances, thus the name. Nuclear magnetic resonance quantum computing is a very interesting approach to physically implementing quantum computers. This approach uses spin states of nuclei within molecules to represent the qubits. The states are probed using nuclear magnetic resonances, thus the name. ---- 72 Quantum Computing – Bose-Einstein Condensate Quantum Computing The concept is similar to current multicore processors. A Bose-Einstein condensate (BEC) is a state of matter formed when a gas consisting of bosons is cooled to temperatures quite close to absolute zero. Bosons are particles that can be either elementary particles or composite particles. Bosons are particles that carry a force and have a whole number spin. There are four gauge bosons in the standard model that carry specific forces: Photon Gluon (there are actually different types of gluons) Charged weak bosons (there are two types of these) Neutral weak bosons ---- 73 Quantum Computing – Bose-Einstein Condensate Quantum Computing The concept in this approach to quantum computing is to divide computational problems among multiple small quantum computers. Each individual quantum computer communicates information using Bose-Einstein condensate BEC clouds. This approach is believed to ameliorate the decoherence problem. The interested reader can dive deeper into Bose-Einstein Condensate BEC computing at the following sources: https://physics.gatech.edu/news/bose-einstein-condensates-evaluated-communicating-among-quantum-computers https://physicsworld.com/a/citizen-scientists-excel-at-creating-bose-einstein-condensates/ https://cds.cern.ch/record/403945/files/9910073.pdf ---- 74 Quantum Computing – Storing Qubit GaAS Gallium arsenide (GaAs) is often used to create quantum dots. A quantum dot is a device that is nanoscale in all three dimensions. The electron spin in the GaAs quantum dot is subject to an effective magnetic field. This field is called an Overhauser field. The Overhauser effect is a nuclear effect that occurs when the nuclear spin polarization of one population of nuclear is transferred to another. This is accomplished via cross-relaxation. The details of cross-relaxation are beyond the scope of our current discussion; however the general process is an RF pulse or series of pulses is applied to some sample in a homogeneous magnetic field and the resonance frequency of the nuclei. ---- 75 Quantum Computing – Summary Method Brief Description Photons The horizontal polarization is | and vertical is | . The polarization method is a common method for using photons for qubits. Linear Optical Quantum This is a system rather than a single qubit, and it uses photon Computing (LOQC) detectors along with other optical instruments such as mirrors and waveplates. The photons are stil the carriers of information Electrons Electron qubits use some property, such as electron spin, to indicate the state of the qubit. For example, an up spin can designate state | , and a down spin can designate | . Ions The qubit value is stored as an electronic state for each ion. Nuclear magnetic resonance This approach uses spin states of nuclei within molecules to represent quantum computing the qubits. The states are probed using nuclear magnetic resonances, thus the name. Bose-Einstein condensate quantum Bose-Einstein condensates are used to communicate among multiple computing smal quantum computers, much like a multiprocessor computer. GaAs quantum dots A quantum dot is a device that is nanoscale in all three dimensions. The electron spin in the GaAs quantum dot is subject to an effective magnetic field. ---- 76 Quantum Computing – Storing Qubit Other Methods Electron on Helium: qubits are spin states of an electron trapped by liquid helium. Nitrogen vacancy centers: these are defects in a diamond, and the electron spin of such defects can be used to store qubits. Nonlinear optics: this approach uses a nonlinear optics crystal. https://physicsworld.com/a/nonlinear-optical-quantum-computing-scheme-makes- a-comeback/ ---- 77 Quantum Computing – Manipulating Qubits Manipulating qubits with lasers Manipulating qubits with microwave Using both (Penn State) ---- 78 TRADITIONAL GATES Quantum Computing – Gates And Or xor ---- TRADITIONAL GATES Quantum Computing – Gates nand nor ---- Quantum Computing – Hadamard Simplest gate involves one qubit and is called a Hadamard Gate ( also known as a square-root of NOT gate.) Used to put qubits into superposition. H H State State State | | + | | Note: Two Hadamard gates used in succession can be used as a NOT gate ---- Quantum Computing – Controlled Not A gate which operates on two qubits is called a Controlled-NOT (CN) Gate. If the bit on the control line is 1, invert the bit on the target line. Input Output A -Target A’ A B A’ B’ 0 0 0 0 0 1 1 1 B - B’ 1 0 1 0 Control 1 1 0 1 Note: The CN gate has a similar behavior to the XOR gate with some extra information to make it reversible. ---- Quantum Computing – Multiplication We can build a reversible logic circuit to calculate multiplication by 2 using CN gates arranged in the fol owing manner: Input Output Carry Ones Carry Ones Bit Bit Bit Bit 0 0 0 0 0 1 1 0 0 Carry Bit Ones Bit H ---- Quantum Computing – CCN A gate which operates on three qubits is called a Controlled Controlled NOT (CCN) Gate. If the bits on both of the control lines is 1,then the target bit is Input Output inverted. A B C A’ B’ C’ A -Target A’ 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 B - Control B’ 0 1 1 1 1 1 1 1 0 0 1 0 0 1 0 1 1 0 1 C - Control C’ 1 1 0 1 1 0 2 1 1 1 0 1 1 ---- Quantum Computing – NAND The CCN gate has been shown to be a universal reversible logic gate as it can be used as a NAND gate. A -Target Input Output A’ A B C A’ B’ C’ 0 0 0 0 0 0 B - Control B’ 0 0 1 0 0 1 1 0 1 0 0 1 0 0 1 1 1 1 1 C - Control C’ 1 0 0 1 0 0 2 1 0 1 1 0 1 1 1 0 1 1 0 1 1 1 0 1 1 When our target input is 1, our target output is a result of a NAND of B and C. ---- NOTATION Quantum Computing – Dirac Notation While it is all about vectors, normally Dirac notation is used. < | 0 is called a bra and | is a ket (yes that is like bra-ket or bracket) ---- TWO-QUBITS Quantum Computing –Two Qubits Two qubits would be represented like this ---- Quantum Computing – QASM Example ---- Quantum Computing – Q# Example ---- WHAT DOES IT ALL MEAN Quantum Computing – Implications Understanding the implications ---- Quantum Computing – Cybersecurity The problem is that quantum computing wil render most current asymmetric cryptography obsolete and there will be a need for cryptographic algorithms that are able to maintain security, even in light of quantum computing based attacks . ---- Quantum Computing – Cybersecurity RSA – Factoring DH – Discrete Logarithm ECC - The discrete logarithm problem with respect to an elliptic curve. Quantum computers can solve these problems in practical time. ---- Quantum Computing – How does RSA Work? Key generation Generate two large random primes, p and q, of approximately equal size such that their product n = pq is of the required bit length (such as 2048 bits, 4096 bits, and so on): Let n = pq Let m = (p – 1)(q – 1) Choose a small number e, co-prime to m. (Note: Two numbers are co-prime if they have no common factors.) Find d, such that de mod m ≡ 1 Publish e and n as the public key. Keep d as the secret key. ---- 94 RSA CON Q TI ua N nt UED um Computing – How does RSA Work? Encrypt Ciphertext= Plaintexte mod n Put another way Computes the cipher text c = me mod n Decrypt Plaintext = Ciphertext d mod n Put another way Uses his private key (d,n) to compute m = cd mod n. ---- 95 Quantum Computing – How does RSA Work? 1. Select primes: p=17 & q=11 2. Compute n = pq =17×11=187 3. Compute ø( n)=( p– 1)( q- 1)=16×10=160 4. Select e=7 1. Find d, such that de mod m = 1, d = 23 5. since 23×7=161 mod M (160) = 1 6. Publish public key 7,187 7. Keep secret private key 23,187 ---- 96 Quantum Computing – How does RSA Work? Now use the number 3 as the plain text. Remember e =7, d=23, and n =187 Ciphertext= Plaintexte mod n or Ciphertext = 37 mod 187 Ciphertext =2187 mod 187 Ciphertext = 130 Decrypt Plaintext = Ciphertext d mod n Plaintext = 13023 mod 187 Plaintext = 4.1753905413413116367045797e+48 mod 187 Plaintext = 3 ---- DIFFIE-H Q ELLM uant AN um Computing – Diffie-Hellman Diffie-Hellman is a cryptographic protocol that allows two parties that have no prior knowledge of each other to establish a shared secret key jointly over an insecure communication channel. ---- DIFFIE-H Q ELLM uant AN um C ( o CONTI mputi N ng U ED) – Diffie-Hellman The system has two parameters, called p and g. Parameter p is a prime number, and parameter g (usually called a generator) is an integer less than p, with the following property: for every number n between 1 and p – 1 inclusive, there is a power k of g such that n = gk mod p. 1. Alice generates a random private value a and Bob generates a random private value b. Both a and b are drawn from the set of integers. 2. They derive their public values using parameters p and g and their private values. Alice’s public value is ga mod p and Bob’s public value is gb mod p. 3. They exchange their public values. 4. Alice computes gab = ( gb) a mod p, and Bob computes gba = ( ga) b mod p. 5. Since gab = gba = k, Alice and Bob now have a shared secret key k. ---- Quantum Computing – Cryptocurrency Quantum computing also poses a problem for cryptocurrency. Cryptocurrencies (Bitcoin, Dogecoin, etc.) depend on asymmetric cryptography to determine ownership. There are multiple approaches being considered to address this issue. I have in fact submitted a paper to an IEEE conference on this issue. ---- Quantum Computing – NIST Post quantum cryptography standards working group. NIST has initiated a process to solicit, evaluate, and standardize one or more quantum-resistant public-key cryptographic algorithms. Full details can be found in the Post-Quantum Cryptography Standardization page. The submission deadline of November 30, 2017 has passed. Please see the Round 1 Submissions for the listing of complete and proper submissions. In recent years, there has been a substantial amount of research on quantum computers – machines that exploit quantum mechanical phenomena to solve mathematical problems that are difficult or intractable for conventional computers. If large-scale quantum computers are ever built, they will be able to break many of the public-key cryptosystems currently in use. This would seriously compromise the confidentiality and integrity of digital communications on the Internet and elsewhere. The goal of post-quantum cryptography (also called quantum-resistant cryptography) is to develop cryptographic systems that are secure against both quantum and classical computers, and can interoperate with existing communications protocols and networks. The question of when a large-scale quantum computer will be built is a complicated one. While in the past it was less clear that large quantum computers are a physical possibility, many scientists now believe it to be merely a significant engineering challenge. Some engineers even predict that within the next twenty or so years sufficiently large quantum computers wil be built to break essentially all public key schemes currently in use. Historically, it has taken almost two decades to deploy our modern public key cryptography infrastructure. Therefore, regardless of whether we can estimate the exact time of the arrival of the quantum computing era, we must begin now to prepare our information security systems to be able to resist quantum computing. ---- Quantum Computing – NIST Round 3 Asymmetric Cryptography Alternate Public Key Classic McEliece BIKE FrodoKEM CRYSTALS-KYBER HQC NTRU NTRU Prime SABER SIKE Digital Signature Alternate Digital Signature CRYSTALS-DILITHIUM GeMSS FALCON Picnic Rainbow SPHINCS+ ---- MA Q JOR A uant PPR um C O o ACHE mputi S ng – Quantum Resistant Algorithm Lattice based algorithms Multi-variate cryptography Super singular el iptic curve isogeny cryptography Hashed based algorithms Code based algorithms ---- LATTI QuaCE nt BASE um Co D CR mputiYPT ng –OG L RA attic PHY e Based Cryptography Lattice based cryptography involves the construction of cryptographic primitives based on lattices. A lattice is represented by a standard matrix, familiar to anyone who has taken an introductory course in linear algebra. The vectors that constitute the lattice are known as the basis vectors for the lattice. A formal definition of a lattice is shown in the figure below. ---- Quantum Computing – Lattice Based Cryptography Lattice based cryptography is simply cryptographic systems based on some problem in lattice-based mathematics. One of the most commonly used problems for lattice-based cryptography is the Shortest Vector Problem (SVP). Essentially this problem is that given a particular lattice, how do you find the shortest vector within the lattice? More specifically, the SVP problem involves finding the shortest non-zero vector in the vector space V, as measured by a norm, N. A norm is a function that assigns a strictly positive length or size to each vector in a vector space. ---- LEARNING WI Q TH uant ERRORS um Co (L mputWE ing )– PROB LWE LEM This is a problem from the field of machine learning. It has been proven that this problem is as difficult to solve as several worst-case lattice problems. Put simply, this means that the LWE problem is very difficult to solve. The LWE problem has been expanded to use algebraic rings with Ring-LWE. ---- GGH ALGORI Q THM uantum Computing – GGH The GGH algorithm, named after its inventors Glodreich, Goldwasser, and Halevi (Peikert, 2016), is a lattice based crypto system. This algorithm was first published in 1997 and uses the closest vector problem (CVP). This problem is summarized as: given a vector space V, and a metric M for a lattice L and a vector v that is in the vector space V, but not necessarily in the lattice L, find the vector in the lattice L that is closest to the vector v. ---- NTRU ALGORITHM Quantum Computing – NTRU NTRU is another lattice-based cryptosystem. It was invented by Hoffstien, Pipher and Sil verman. NTRU has been shown to be resistant to Shor's algorithm. Shor's algorithm is named after the inventor, Peter Shor, and it is a quantum algorithm for integer factorization. It is effective at factoring large numbers, thus breaking cryptography based on factorization problems. Another important fact about NTRU, is that even without concern about quantum computers, NTRU is more efficient than RSA. That makes it a viable option for classical computing. ---- OVERVIEW Q OF uant ALG um C ORI o THM mputingS – Summary ---- OVERVIEW OF Qua C nt URRE um CoNT C mputiRYPT ng – A S NALY umma SI ry S GGH has solid mathematics but has been the target of multiple, successful cryptanalytical attacks. The math is sound, but variations should be explored. NTRUEncrypt appears to be robust as far as current cryptanalytical studies can determine. LWE key exchange protocols have been found to be susceptible to several attacks. Further research is needed. ---- QUANTUM COMPUTING AND AI What about quantum computing and machine learning/AI? ---- THERE ARE TWO PRIMARY ISSUES Can AI/ML Help Develop QC Will QC Provide better AI/ML ---- Quantum Computing/ML – Grover's Grover's algorithm is a quantum algorithm that finds with high probability the unique input to a black box function that produces a particular output value, using just is the size of the function's domain. It was devised by Lev Grover in 1996 There are approaches to ML to improve it with quantum information processing uses amplitude amplification method. ---- QUANTUM MACH Qua INE nt LE um C A o RNING mputing/ML Quantum-enhanced machine learning refers to quantum algorithms that solve tasks in machine learning The term "quantum machine learning" is often associated with classical machine learning methods applied to data generated from quantum experiments. This includes hybrid methods that involve both classical and quantum processing, where computationally difficult subroutines are outsourced to a quantum device. Quantum analogues of classical neural nets are often referred to as quantum neural networks. Hidden Quantum Markov Models (HQMMs) are a quantum-enhanced version of classical Hidden Markov Models (HMMs), which are typical y used to model sequential data in various fields like robotics and natural language processing. ---- QUANTUM MACH Qua INE nt LE um C A o RNING mputing/ML A number of quantum algorithms for machine learning are based on the idea of amplitude encoding, that is, to associate the amplitudes of a quantum state with the inputs and outputs of computations. Many quantum machine learning algorithms in this category are based on variations of the quantum algorithm for linear systems of equations. Another approach to improving classical machine learning with quantum information processing uses amplitude amplification methods based on Grover's search algorithm, which has been shown to solve unstructured search problems with a quadratic speedup compared to classical algorithms. ---- QUANTUM NEURAL NETWORKS Quantum Computing/Neural Networks Quantum Neural Networks are essentially ANN's based on quantum mechanics. There are primarily two major avenues of QNN research. One is the application of quantum information processing to improve neural network models. The to other approach involves looking for quantum effects in natural neural networks. The latter is most related to work by Roger Penrose. One common goal is a quantum equivalent for the perceptron unit. The perceptron is an algorithm for supervised learning of binary classifiers. ---- NOTEWORTHY Qua PR nt OJE um C C o TS IN mputi QU ng/M A L-NTU Pro M jec-AI ts Google AI https://ai.google/research/teams/applied-science/quantum-ai/ "Quantum Entanglement in Deep Learning Architectures," was published this in March 2019 in the journal Physical Review Letters. As early as 2018 scientists were reporting exciting results with Neural networks enabling learning of error correction strategies for computers based on quantum physics. Accenture, a global professional services company, has been granted a US patent for a “quantum computing machine learning module” that trains artificial intel igence (AI) to determine when and how computational tasks would be best handled by quantum computing versus classical computing methods, and route them to the appropriate option. US patent number 10,275,721 granted April 30, 2019 ---- NOTEWOR Q THY uant PROJ um Co ECTS I mputi N ng/ QU ML - AN Ad TU van M ce-sAI “My col eagues and I instead hope to build the first dedicated neural network computer, using the latest ‘quantum’ technology rather than AI software,” wrote Michael Hartmann, a professor at Heriot-Watt University who’s leading the research, in a new essay for The Conversation. “By combining these two branches of computing, we hope to produce a breakthrough which leads to AI that operates at unprecedented speed, automatically making very complex decisions in a very short time.” ---- NOTEWOR Q THY uant PROJ um Co ECTS I mputi N ng/ QU ML - AN Ad TU van M ce-sAI Speaking during a keynote at DesignCon 2019, Dr. Irfan Siddiqi, a professor of physics at the Quantum Nanoscience Laboratory and the Department of Physics at the University of California Berkeley, proposed artificial intelligence as a possible solution to the complexity of creating quantum computers. In September 2019 researchers at Harvard published work on a quantum circuit-based algorithm inspired by convolutional neural networks (CNNs). "The resultant quantum circuit involves only log(n) number of parameters to be optimized for n-qubit input data, which is double exponential improvement compared to a naive approach, in which exp(n) number of parameters are optimized," ---- NOTEWOR Q THY uant PROJ um Co ECTS I mputi N ng/ QU ML - AN Ad TU van M ce-sAI In October 2019 it was announced that the Wisconsin Quantum Institute Awarded Grant from the Department of Energy to Advance Quantum Computing Machine Learning. Schuld, M., & Kil oran, N. (2019). Quantum machine learning in feature Hilbert spaces. Physical review letters, 122(4), 040504. Their work is in reference to encoding inputs in a quantum state as a nonlinear feature map that maps data to quantum Hilbert space Cárdenas‐López, F. A., Sanz, M., Retamal, J. C., & Solano, E. (2019). Enhanced Quantum Synchronization via Quantum Machine Learning. Advanced Quantum Technologies, 1800076. Uses machine learning to improve quantum synchronization. O’Driscol , L., Nichols, R., & Knott, P. A. (2019). A hybrid machine learning algorithm for designing quantum experiments. Quantum Machine Intel igence, 1(1-2), 5-15. Their work is on using machine learning to improve the design of quantum expiriments ---- Artificial Consciousness • Awareness • Learning • Anticipation • Subjective Experience (Qualism) ---- Artificial Consciousness • Not exactly intended as a general test for consciousness, but a specific test for self-consciousness, and more exactly self-recognition. • Who passed : – Humans (over 2 years old) – Great apes (bonobos, chimps, orangutans, and goril as) – Rhesus monkeys – Elephants – Bottlenose dolphins ---- COGNITIVE SCIEN Ar C tif E ic : HO ial CoW DO M nsciousneIN ss DS WORK? What would an answer to this question look like? What is a mind? What is intelligence? How do brains work? Neurons Brain structure What’s the difference between the brain and the mind? ---- Artificial Consciousness Cognition – from Latin base cognitio – “know together” The collection of mental processes and activities used in perceiving, learning, remembering, thinking, and understanding and the act of using those processes ---- WHAT IS CONSC Ar IOU tific SNESS ial Consciousness Blackmore (2013) states that consciousness has no generally accepted definition in science or in philosophy. This statement, while accurate, does not address the problem encountered in artificial intelligence research. Blackmore’s commentary is more applicable to a complete definition of consciousness for the purposes of cognitive science and psychology. For the purposes of furthering research into artificial consciousness, it is not necessary to derive a broadly applicable, generally accepted definition of consciousness. ---- Artificial Consciousness Synthetic consciousness would be operationally defined as any artificial device or software that is self-aware. This is a minimalistic definition and does not attempt to address issues regarding emotions, other related cognitive functions ---- EMERGENCE AND Ar CO tific NSCI ial Con O sc US iou NE sneSsS s Emergence in any system consists of those properties and behaviours that cannot be accounted for as the sum of the constituent parts. There is a significant body of research that opines that consciousness even in human beings is an emergent property (Fingelkurts & Fingelkurts, 2018; Lagercrantz & Padil a, 2016; Railo, Revonsuo, & Koivisto, 2015). Thus, utilizing emergent self-direction as an indicator of at least nascent consciousness is appropriate. ---- PENROSE AND HAMEROFF Artificial Consciousness Essentially Penrose and Hameroff proposed that microtubules were suitable candidates for quantum processing. Microtubules contain hydrophobic pockets that can contain delocalized electrons. Hameroff further posited that these electrons can become quantumly entangled and would form a Bose-Einstein condensate. Penrose and Hameroff' s theories have been widely criticized in the neuroscientific community. Among the criticisms have been arguments that a biological system cannot avoid quantum de-coherence due to the environment of the biological system. However, advances in quantum computing have cast doubt on this criticism as researchers have achieved quantum states for several seconds at room temperature (Neumann, et al., 2013; Saeedi, et al., 2010). Furthermore, evidence suggests that plants routinely use quantum-coherent electron transport mechanisms as part of photosynthesis (Lambert, et al., 2013; Panitchayangkoon, et al., 2010). ---- PREVAILING NEUR Ar O tif S ic CIENCE ial Consc V io IE us W ness Many neuroscientists disagree with Penrose, Hameroff, and Lucas. Instead, the prevailing opinion in neuroscience is that consciousness is an emergent property that is predicated on meeting a certain threshold of neurological complexity (Krieger, 2013; Laurys, Gosseries, & Tononi, 2015; Tononi, Boly, Gosseries, & Laureys, 2016; Penfield, 2015). In this view, consciousness wil emerge when the neurology reaches a particular level of complexity ---- FRANCIS CRICK Artificial Consciousness Yet another neurobiological view of consciousness was posited by Nobel Laurate Francis Crick. Crick posited that consciousness in inextricably associated with how the brain uses short-term memory processes to facilitate sensory input (Crick & Koch, 2003). Crick focused primarily on visual input, but his work is applicable to any sensory input. His focus was on the neurological correlates of visual processing. Not merely detecting an object, but processing that sensory input (Baker, 2010). ---- RESOURCES - SIMULATORS http://www.quantumplayground.net/#/home https://algassert.com/quirk https://www.ibm.com/quantum-computing/technology/simulator/ ---- CONCLUSIONS Questions?? ---- RESOURCES – QUANTUM COMPUTERS D-Wave https://www.dwavesys.com/take-leap IBM https://www.ibm.com/quantum-computing/ ---- REFERENCES Albash, T., Rønnow, T. F., Troyer, M., & Lidar, D. A. (2015). Reexamining classical and quantum models for the DWave One processor. The European Physical Journal Special Topics, 224(1), 111-129. Bernstein, D. J., & Lange, T. (2017). Post-quantum cryptography. Nature, 549(7671), 188-194. Chen, L., Chen, L., Jordan, S., Liu, Y. K., Moody, D., Peralta, R., . . & Smith-Tone, D. (2016). Report on post-quantum cryptography. US Department of Commerce, National Institute of Standards and Technology. Chi, D. P., Choi, J. W., San Kim, J., & Kim, T. (2015). Lattice based cryptography for beginners. IACR Cryptology ePrint Archive, 2015, 938 Fano, G., Blinder, S. (2017). Twenty-First century quantum mechanics: Hilbert space to quantum computers: Mathematical methods and conceptual foundations. New York City, New York: Springer. Imre, S., & Balazs, F. (2013). Quantum computing and communications: An engineering approach. Hoboken, New Jersey: John Wiley & Sons. Kumar, R., Maurya, S. G., Chugh, R., & Manoj, P. V. (2014). Current refuge trends using classical and quantum cryptography. International Journal of Computer Science and Information Technologies, 5(3), 2974-77. Mariano, A., Laarhoven, T., Correia, F., Rodrigues, M., & Falcão, G. (2017). A practical view of the state-of-the-art of lattice-based cryptanalysis. IEEE Access, 5, 24184-24202 Monteiro, R. T. (2016). Post-quantum cryptography: lattice-based cryptography and analysis of NTRU public-key cryptosystem (Doctoral dissertation). University of Lisbon, Portugal. ---- REFERENCES Moret-Bonillo, V. (2017). Adventures in computer science: From classical bits to quantum bits. New York City, New York: Springer. Peikert, C. (2016). A decade of lattice cryptography. Foundations and Trends in Theoretical Computer Science, 10(4), 283-424. Raychev, N. (2015). Quantum computing models for algebraic applications. International Journal of Scientific & Engineering Research, 6(8), 1281-1289. Rieffel, E., Polak, W. (2011). Quantum computing: A Gentle introduction. Boston, Massachusetts: MIT Press. Shenoy-Hejamadi, A., Pathak, A., & Radhakrishna, S. (2017). Quantum cryptography: Key distribution and beyond. Quanta, 6(1), 1-47 Stanescu, T. (2016). Introduction to quantum matter & quantum computation. Boca Raton, Florida: CRC Press. Trabesinger, A. (2017). Quantum computing: towards reality. Nature, 543(7646), S1-S1. Wang, D. S., Hill, C. D., & Hollenberg, L. C. (2017). Simulations of Shor’s algorithm using matrix product states. Quantum Information Processing, 16(7), 176-183. Easttom, C. (2019). "An Analysis of Leading Lattice-Based Asymmetric Cryptographic Primitives". 2019 IEEE 9th Annual Computing and Communication Conference. ---- Document Outline Slide Number 1 This workshop Introduction section Classical physics Slide Number 5 Particles and waves The beginnings of quantum physics Quantum-wave duality Uncertainty Wave Function Hamiltonian Operator Hamiltonian Operator Slide Number 13 Schrödinger’s Equation Entanglement Bell’s Inequality Bell’s Inequality Quantum mechanics Quantum Mechanical Model Slide Number 20 Will we get there Slide Number 22 Slide Number 23 Slide Number 24 Slide Number 25 Slide Number 26 Lev Grover Slide Number 28 Slide Number 29 Two branches Quantum key distribution (QKD) Quantum key distribution (QKD) Quantum Key Exchange Slide Number 34 Slide Number 35 In the “real world” In the “real world” In the “real world” Slide Number 39 Slide Number 40 Slide Number 41 But what do we need Current exciting trends Current exciting trends Current exciting trends Current exciting trends Current exciting trends A lot of work done recently Slide Number 49 Slide Number 50 Slide Number 51 The major players * [[Quantum programming Supercooling Methods * [[Qubits and gates
Slide Number 61
Traditional gates
Notation
Slide Number 89
What does it all mean
RSA Continued
Major approaches
- Learning With Errors (LWE) problem
- Overview of quantum computing algorithms
Overview of current cryptanalysis
There are two primary issues
Slide Number 112
Quantum machine learning
Quantum neural networks
Noteworthy projects in Quantum-AI
Noteworthy projects in Quantum-Ai
Noteworthy projects in Quantum-Ai
Noteworthy projects in Quantum-Ai
Slide Number 120
Slide Number 121
Cognitive Science: How do minds work?
Slide Number 123
What is Consciousness
Slide Number 125
Emergence and Consciousness
Penrose and Hameroff
Prevailing Neuroscience View
Francis Crick
Resources - simulators
Conclusions
Fair Use Sources
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- Snippet from Wikipedia: Quantum computing
A quantum computer is a computer that exploits quantum mechanical phenomena. On small scales, physical matter exhibits properties of both particles and waves, and quantum computing takes advantage of this behavior using specialized hardware. Classical physics cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations exponentially faster than any modern "classical" computer. Theoretically a large-scale quantum computer could break some widely used encryption schemes and aid physicists in performing physical simulations; however, the current state of the art is largely experimental and impractical, with several obstacles to useful applications.
The basic unit of information in quantum computing, the qubit (or "quantum bit"), serves the same function as the bit in classical computing. However, unlike a classical bit, which can be in one of two states (a binary), a qubit can exist in a superposition of its two "basis" states, a state that is in an abstract sense "between" the two basis states. When measuring a qubit, the result is a probabilistic output of a classical bit. If a quantum computer manipulates the qubit in a particular way, wave interference effects can amplify the desired measurement results. The design of quantum algorithms involves creating procedures that allow a quantum computer to perform calculations efficiently and quickly.
Quantum computers are not yet practical for real-world applications. Physically engineering high-quality qubits has proven to be challenging. If a physical qubit is not sufficiently isolated from its environment, it suffers from quantum decoherence, introducing noise into calculations. National governments have invested heavily in experimental research aimed at developing scalable qubits with longer coherence times and lower error rates. Example implementations include superconductors (which isolate an electrical current by eliminating electrical resistance) and ion traps (which confine a single atomic particle using electromagnetic fields).
In principle, a classical computer can solve the same computational problems as a quantum computer, given enough time. Quantum advantage comes in the form of time complexity rather than computability, and quantum complexity theory shows that some quantum algorithms are exponentially more efficient than the best-known classical algorithms. A large-scale quantum computer could in theory solve computational problems that are not solvable within a reasonable timeframe for a classical computer. This concept of additional ability has been called "quantum supremacy". While such claims have drawn significant attention to the discipline, near-term practical use cases remain limited.
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