2.
Overview:
Introduction
Quantum properties
Data Representation
Some Basic Quantum Gates
Heroes of Quantum Computing
Conclusion
Reference
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3.
Introduction:
What is Quantum Computing?
Calculation based on the laws of Quantum
Mechanics.
Uses Quantum Mechanical Phenomena to
perform operations on data.
Operations done at an atomic/sub-atomic
level.
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4.
Beauty of Quantum Theory:
Quantum Mechanical theories are totally
different from the point of common sense.
But it agrees fully with experimental facts..
This is the beauty of Quantum Mechanics.
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5.
Why Quantum Theory in Computing???
Classical(Newtonian) Mechanics deals with
macroscopic system while Quantum Mechanics
deals with microscopic system-atomic and
subatomic level.
Computer system/components are becoming
smaller and smaller from mechanical computer
to vacuum tubes, to transistors then to IC’s that
Classical theory fails to explain.
Thus Quantum theory becomes essential..
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7.
Superposition:
Property to exist in multiple states.
In a quantum system, if a particle can be in
states |A and |B, then it can also be in the
state 1|A + 2|B ; 1 and 2 are complex
numbers.
Totally different from common sense.
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8.
Decoherence:
The biggest problem.
States that if a coherent (superposed) state
interacts with the environment, it falls into a
classical state without superposition.
So quantum computer to work with
superposed states, it has to be completely
isolated from the rest of the universe (not
observing the state, not measuring it, ...)
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9.
Schrödinger's cat-a thought experiment:
(Gives an idea about Superposition and Decoherence)
A cat and a flask of poison together in a shielded box.
Classically cat’s state: alive or dead.
Quantum Mechanical Interpretation:Cat is simultaneously alive or
dead-Superposed State.
Yet, when one looks in the box, one sees the cat either alive or dead,
not both alive and dead-decoherence.
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10.
Entanglement:
Most important property in quantum
information.
States that two or more particles can be
linked, and if linked, can change properties
of particle(s) changing the linked one.
Two particles can be linked and changed
each other without interaction.
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11.
Uncertainty Principle:
Quantum systems are so small.
It is impossible to measure all properties of a
Quantum system without disturbing it.
As a result there is no way of accurately
predicting all the properties of a particle in a
Quantum System.
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12.
Linear algebra:
Quantum mechanics depends heavily on
linear algebra.
Some of the Quantum Mechanical concepts
come from the mathematical formalism, not
experiments.
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13.
Dirac Notation:
Dirac notation is used for Quantum
Computing.
States of a Quantum system are represented
by Ket vectors(Column Matrix).
Example: |0, |1
Other notation: Bra notation-Complex
conjugate of Ket vectors(Row Matrix).
Example: 0|, 1|; 0|=|0†, 1|=|1†
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14.
Data representation:
Quantum Bit(Qubit) is used.
Qubit, just like ‘classical bit‘, is a memory
element, but can hold not only the states |0
and |1 but also linear superposition of both
states, α1|0+α2|1.
This superposition makes Quantum
Computing fundamentally different.
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15.
Classical bit: {0, 1}
Qubit: {0, 1, superposed states of 0 and 1}
Classical bit Vs Qubit:
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16.
Physical representation of qubits:
A single atom that is in either Ground or
Excited state.
Ground state representing |0 .
Excited state representing |1 .
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17.
Physical representation of qubits:
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18.
More about qubits:
By superposition principle, a Qubit can be forced
to be in a superposed state.
i.e. | = 1|0+ 2|1
Qubit in superposed state occupies all the states
between |0 and |1 simultaneously , but
collapses into |0 or |1 when observed
physically.
A qubit can thus encode an infinite amount of
information.
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19.
Qubits in Superposed state:
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20.
Operations on qubits:
Quantum logic gates are used.
Quantum logic gates are represented by
Unitary Matrices-U†U=UU†=I.
States are also represented by matrices as:
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22.
Hadamard Gate(SRN gate):
acts on a single qubit.
transforms |0 to (|0 +|1)/2
And |1 to (|0 -|1)/2
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23.
Pauli-X gate:
acts on a single qubit.
Quantum equivalent of NOT gate.
Transforms |1 to |0 and |0 to |1
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24.
Pauli-Y gate:
acts on a single qubit.
Transforms |1 to -i|0 and |0 to i|1
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25.
Pauli-Z gate:
acts on a single qubit.
Transforms |1 to -|1 and |0 remains
unchanged.
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26.
Phase shift gate:
acts on a single qubit.
Transforms |1 to ei |1 and |0 remains
unchanged.
Modifies(rotates) the phase of quantum state
by .
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27.
There are also other quantum gates including
Quantum Universal Gates which acts on two
or more qubits.
viz: SWAP gate, CONTROLLED gates,
TOFFOLI gates, FREDkiN gates, etc., etc.
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29.
HEROES OF QUANTUM COMPUTING:
1981 -Richard Feynman
determines that it is
impossible to efficiently
simulate an evolution of
a quantum system on a
classical computer.
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30.
HEROES OF QUANTUM COMPUTING:
1985, David Deutsch,
publishes a theoretical
paper describing a Universal
Quantum Computer.
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31.
HEROES OF QUANTUM COMPUTING:
1994, Peter Shor-Used
Entanglement and
Superposition
methods to find the
Prime Factors of
Integer(useful in
quantum encryption
technology).
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32.
HEROES OF QUANTUM COMPUTING:
1996 -Lov Grover(Indian American
Computer Scientist, born at
Meerut), invented Quantum
Database Search Algorithm, very
much faster one.
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33.
HEROES OF QUANTUM COMPUTING:
1997 , David Cory, A.F. Fahmy,Timothy Havel, Neil
Gershenfeld and Isaac Chuang publish the first papers
on quantum computers based on bulk spin resonance,
or thermal ensembles.
AND MANY MORE…..
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34.
World's first Quantum Computer:
In 2007, a computer calledOrion was
presented by D-Wave.
Technology in Orion, called “Adiabatic
Quantum Computing", is based on
superconducting electronics.
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35.
A 16-qubit processor
Some of the components of Orion
OneofitsNoiseFilteringStage
Orion chip’s sample holder,
ready to begin a cooldown. It
works at 0.005ºC above
absolute zero (-273ºC)
ChipconstructedbyD-WaveSystems
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36.
Applications:
Physics
Chemistry
Material Science
&
Engineering
Biology
&
Medicine
Nanotechnology
Business
&
Commerce
Cryptography Large DBMS
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37.
Advantages:
Could process massive amount of complex
data.
Ability to solve scientific and commercial
problems.
Process data in a much faster speed.
Capability to convey more accurate answers.
More can be computed in less time.
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38.
Disadvantages and Problems:
Security and Privacy Issues:
Ability to crack down password (s).
Capability to break every level of encryption.
Moral, ethical, social, and economic issues:
Growing too much dependency on machines.
Economic division: who can/cannot afford technology.
Not suitable for word processing and email.
Problem of Decoherence, the need of a noise free environment.
Complex hardware schemes like superconductors.
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39.
Conclusions:
Quantum computer has more to offer.
Advantages outweighs disadvantages.
Wide range of applications.
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40.
Conclusions:
“My students don’t understand Quantum Mechanics,
because I don’t understand it. Nobody understand
Quantum Mechanics.”
Richard Feynman
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