Quantum Computing - Basic Concepts

04/12/2023Quantum Computing(Fundamental Concepts)-Sendash Pangambam 1

(SOME INTRODUCTORY CONCEPTS)

Presented by:Pangambam Sendash

SinghM.Sc. Computer Science


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:


Some Common Quantum Gates


Hadamard Gate(SRN gate):

acts on a single qubit.

transforms |0 to (|0 +|1)/2 And |1 to (|0 -|1)/2


Pauli-X gate:

acts on a single qubit. Quantum equivalent of NOT gate. Transforms |1 to |0 and |0 to |1


Pauli-Y gate:

acts on a single qubit. Transforms |1 to -i|0 and |0 to i|1


Pauli-Z gate:

acts on a single qubit. Transforms |1 to -|1 and |0 remains

unchanged.


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 .


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


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.


HEROES OF QUANTUM COMPUTING:

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


HEROES OF QUANTUM COMPUTING: 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 called Orion

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

One of its Noise Filtering Stage

Orion chip’s sample holder, ready to begin a cooldown. It works at 0.005ºC above absolute zero (-273ºC)

Chip constructed by D-Wave Systems


Applications:

PhysicsChemistry

Material Science&

Engineering

Biology&

Medicine

Nanotechnology

Business&

CommerceCryptography

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


Thank You…