Quantum Computing - Basic Concepts

(SOME INTRODUCTORY CONCEPTS)
Presented by:
Pangambam Sendash
Singh
M.Sc. Computer Science
5/10/2014Quantum Computing(Fundamental Concepts)-Sendash Pangambam 1

Overview:
 Introduction
 Quantum properties
 Data Representation
 Some Basic Quantum Gates
 Heroes of Quantum Computing
 Conclusion
 Reference

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.

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.

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..

Quantum properties used:
 Superposition
 Decoherence
 Entanglement
 Uncertainty principle
 Linear algebra
 Dirac notation

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.

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, ...)

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.

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.

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.

Linear algebra:
 Quantum mechanics depends heavily on
linear algebra.
 Some of the Quantum Mechanical concepts
come from the mathematical formalism, not
experiments.

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†

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.

 Classical bit: {0, 1}
 Qubit: {0, 1, superposed states of 0 and 1}
Classical bit Vs Qubit:

Physical representation of qubits:
 A single atom that is in either Ground or
Excited state.
 Ground state representing |0 .
 Excited state representing |1 .

Physical representation of qubits:

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.

Qubits in Superposed state:

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:

Hadamard Gate(SRN gate):
 acts on a single qubit.
 transforms |0 to (|0 +|1)/2
 And |1 to (|0 -|1)/2

Pauli-X gate:
 Quantum equivalent of NOT gate.
 Transforms |1 to |0 and |0 to |1

Pauli-Y gate:
 Transforms |1 to -i|0 and |0 to i|1

Pauli-Z gate:
 Transforms |1 to -|1 and |0 remains
unchanged.

Phase shift gate:
 Transforms |1 to ei |1 and |0 remains
unchanged.
 Modifies(rotates) the phase of quantum state
by .

 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.

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.

 1985, David Deutsch,
publishes a theoretical
paper describing a Universal
Quantum Computer.

 1994, Peter Shor-Used
Entanglement and
Superposition
methods to find the
Prime Factors of
Integer(useful in
quantum encryption
technology).

 1996 -Lov Grover(Indian American
Computer Scientist, born at
Meerut), invented Quantum
Database Search Algorithm, very
much faster one.

 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…..

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.

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

Applications:
Physics
Chemistry
Material Science
&
Engineering
Biology
&
Medicine
Nanotechnology
Business
&
Commerce
Cryptography Large DBMS

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.

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.

Conclusions:
 Quantum computer has more to offer.
 Advantages outweighs disadvantages.
 Wide range of applications.

Conclusions:
 “My students don’t understand Quantum Mechanics,
because I don’t understand it. Nobody understand
Quantum Mechanics.”
Richard Feynman

References:
 http://www.qubit.org
 http://en.wikipedia.org/wiki/Quantum_computers
 http://en.wikipedia.org/wiki/Quantum_gate
 http://en.wikipedia.org/wiki/Timeline_of_quantum_computing
 http://en.wikipedia.org/wiki/Quantum_mechanics
 http://phys.educ.ksu.edu

Quantum Computing - Basic Concepts

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