A brief presentation on qunatum computing system & the material science related to it

Presented by:-
Md. Fahim Foysal
Registration No:2014338006
Goutam Sarder
Hasin Raihan Shovon
Md. Sakibul Islam

History
Classical computing system
Quantum computing system & difference with classical
computing system
Building a quantum computer, it’s algorithm & materials
science

In 1936, Alan Turing published a paper titled “On
Computable Numbers, with an Application to the
Entscheidungsproblem (A german word means Decision
Problem)”.In that paper Alan Turing described “universal
computing” that could solve any mathematical problem
represented by an algorithm.
In 1965, Gordon Moore stated a law, the number of
transistors per microchips doubles every year.That’s now
widely known as Moore’s law and now has become a
guideline for tech companies.

In 1980, Russian-German mathematician named Yuri
Manin first proposed the idea of Quantum Computing.
A year later, eminent physicist Richard Feynmann
presented a logical quantum computer model named
“Quantum Computer”.
In 1985, David Deutch presented the idea for “quantum
universal Turing Machine”.He realised that “universal
computing machine” described by Alan Turing was limited
as he had used the laws of classical physics to describe
it.Deutch subsequently redid Turing’s work using the law of
quantum mechanics and thus made the first description of a
true quatum computer.

In 1994, MIT professor named Peter Shor developed one of
the first algorithms that could be performed by a quantum
computer. Shor Algorithm determines the prime factor of an
integer. This algorithm demonstrate the true power of
quantum computers. Shor algorithm can be used in field of
cryptography.
Lov Grover devised an algorithm in 1996, widely known as
Grover’s algorithm that in a word can be described as
“searching a database”.Grover’s algorithm can be used to
cracked password.

In 1998, MIT, Stanford an IBM collaborated to develop a
functional quantum computer consisting of three qubits. This
computer was built at the Almaden Research Center.
In 1999, world’s first Quantum
Computing company was founded.
It’s founded by Haig Farris,Geordie
Rose,Bob Weins and Alexandro
Zagoskin.D-wave operated as an offshoot from University of
British Columbia,Burnaby,Canada. While maintaining ties
with department of Physics & Astronomy.It funded academic
research in quantum computing.

History
In 2001, IBM succeeded in developing a quantum
computer consisting of 7 qubits. It was able to successfully
find out prime factors of 15 into 5 & 3 using Shor’s
algorithm.
In 2012, Serge Haroche and David J. Wineland received
Nobel prize in Physics “ for ground-breaking experimental
methods that enable measuring and manipulation of
individual quantum systems”.

A brief presentation on qunatum computing system & the material science related to it

What is classical computing system?
•Classical computing system is such a system where we use 1
and 0. This system is widely known as binary language
system. This ‘1’ and ‘0’ referes to physical abstract light on and
off respectively.
 How we use this binary language to compute mathematical
operation?
•This computational works is done with the use of transistors.
Transistors process the information in the form of sequences
of various combinations of zeroes and ones. It means
transistors act as a switch which can be turned on, that
corresponds to binary 1, or it can be turned off, which
corresponds to binary 0.

•The group of transistors called logic gates that allows the computer to
perform calculations and make decisions in accordance with the
manmade programme.The computing processing powers depend on
the number of transistors is used.
•All digital data consists of zeros and ones.This binary information is
referred as binary code.
•Each binary digit is known as “bit”. One bit can be represent two
different values 0 and 1.
•Two bits combined four different values “00,01,10,11”.
•Three bits combined eight different values “000, 001, 010, 011, 100,
101, 110, 111”.
•In general, n bits can be used to represent 2^n different values.

Are we reaching in quantum state?
•Answer is yes.
But How?
•According to Moore’s law, use of transistors is doubling every year.
That’s how we have been able to enter in the era of smartphone and
laptop.
•But the more transistor we use the more current we need.That’s
why our laptop & smartphone get’s overheated quickly.
•As we reduced the computer size to our lap, it’s not possible to
increase it’s size due to both commercial and habituated
convenient.As we can’t increase laptop or smartphone size to speed
up these electronic devices and increase it’s feature we need more
transistors. That’s why we are now compelled to deduce the size of
transistors.
•And this smaller size transistors peering over the quantum
computing system.

Max Planck suggested that the energy of light is
proportional to it’s frequency , also showing that light exist
in discrete quanta of energy.This hypothesis made the
foundation of “Quantum Mechanics”.
For his contribution he received Nobel Prize in physics , by 1918.

How we can make the computation in the quantum physics realm?
•Due to the property of “superposition” it is possible to make
quantum computer.
How “superposition” property made it possible?
•Louis de Broglie a french physicist in 1924 proposed that
moving objects have wave as well as particle
characteristics.Each elementary paricle is subject to wave-
particle duality.
Young’s double slit experiment shows that a photon
“somehow” goes through both slits simultaneously and
interferes with itself. This “somehow goes” is the reason of
it’s superposition property.This experiment can in fact be
performed with electrons, atoms or other sub-atomic
particles instead of light.

The above figure shows that the double slit experiment is
also applicable for electron.And prove the superposition
property of electron.
If first slit open then we will get the electron intensity like
the leftmost portion of the pic.
For the second slit open we will get the electron intensity
like the middle part.
If both slits is opened we will get electron intesity like the
rightmost part.

Interesting fact of this experiment is that when both slits is open the
wave function of electron splits into two wave function, as if one wave
function can be posed in two wave function .
Superposition property is stated by Schrodinger equation.As physical
phenomena is different in quantum realm from our large objects.This
superposition paradox explained the way is widely known as
“Schrodinger Cat”.

Erwin Schrodinger proposed a scenario with a cat in sealed
box, where the cat’s life and death is dependent on the state
of a particular sub-atomic particle.
Problem of measuring superposition is known as
decoherence. Decoherence is results in the collapse of the
quantum wave function and the settling of a particle into it’s
observed state under classical physics.
Decoherence is the main obstacle to build quantum
computer.Because it is totally impossible to isolate anything
from interaction with it’s environment.It’s the interaction of
quantum objects with the environment that produces what
we understand as classical objects.

Due to decoherence phenomena an electron requires
extreme cold to prevent it from becoming “classical” rather
than “quantum”. As it’s totally absurd to work on temperature
near absolute zero.
In Schrondinger cat if we open up the lead of the sealed box
we can determine the state of cat.This is decoherence.Until
open up it’s uncertain “alive” or “death”.
In 1935, another remarkable features was described, known
as “EPR” papers of Einstein, Boris Podolsky, Nathan Rosen
and it is sometimes referred to as the EPR paradox.They
described the idea of nonlocality, what Einstein rather called
“spooky at a distance”.

How information will be expressed is quantum computers?
•In case of quantum computing, information is expressed
through a quantum bit called qubit which is described by
both 0 and 1 binary units simultaneously.
•Here | 0 ⟩ is the Dirac notation for the
quantum state that will always give
the result 0 when converted to
classical logic by a measurement.
Likewise | 1 ⟩ is the state that will always convert to 1.

What’s the advantages of quantum computer rather than
classical computer?
 In a 2-bit data system all possible combination of bit are
00, 01, 10, 11. A 2- bit classical computer can at the most
simultaneously perform one of these four possible
functions. In order to check of them the computer would
have to repeat each operation separately. That’s time
consuming!
But a 2-qubit quantum computer, due to phenomenon of
superposition is able to analyze all of these possibilities at
the same time in one operation. This is due to fact that two
qubits contains information about four states, while 2-bits
only contain information about one state.

•Thus a machine with n-qubits can be in the superposition of 2^n
states at the same time.
•A 4-qubit computer could analyze 16 parallel states in a
single operation. In comparison to a 4-bit classical computer
can only analyze one state. To achieve this solution classical
computer would have to repeat this operation 16 times.
To find the prime factors of 2048 bit number a classical computer
would take millions of years but a quantum computer would take just a
few minute!

How we can build a quantum computer?
•We can’t build quantum computer with transistors and
diodes. In order to build it a new technology is needed that
enables qubits to exists as coherent superpositions of 0 and 1
states.
We still don’t know how we can do this?
•Many methods are being experimented with and are proving
to have varying degrees of success.
•An example of implementation qubit is “quantum dot”
basically a single electron trapped inside a cage of atoms.

How quantum dot works?
•When the dot of pulse of laser light of precisely the right
wavelength and duration, the electron raised to an excited state, a
second burst of laser light causes the electron to fall back to its
ground state. The ground and the exited states of the electron can
be thought of as the 0 and 1 states of the qubits.
•But this has some practical problems.
oThe electron only remains in its exited
states for about a microseconds before
It falls to ground states.
Bearing in mind that the required duration of each laser pulse is
around 1 nanoseconds, there is a limit to the number of
computationals steps that can be made before information is lost.

oConstructing quantum computing is a very difficult process
because they are so small. The technology
needed to build a computer from these
dots doesn’t exist.
So quantum dot can’t be
implemented!!!!
Now we have to find out other techniques.

Early prototypes of quantum computers were comprised of
test tubes. Scientists Neil Gershenfeld, Issac Chuang and
Mark kubiniec made use of the phenomenon of nuclear
magnetic resonance to create the first quantum computer
model. The model was compromised of a test-tube, which
contained chloroform particles.
This apparatus was placed in a constant magnetic field.
That helped the scientists to focus
on the interaction between spins of
Hydrogen and Carbon that acted as a
logic gate.

The programming was conducted with the use of radio
impulses of particular frequencies, which resulted in the
various of spins.
Although these experiments were successful but these
were nothing but classical simulation of quantum
computing.
To develop a fully efficient quantum computer, certain
requirements must be fulfilled. One of the most important
is to create appropriate conditions under which it would be
possible to manipulate qubits while allowing them to
maintain their unique properties.

One of the biggest problem that faced by scientists is the
issue of “Decoherence”.
In 2012, scientists from University of New South Wales
created the first single atom transistor made of silicon.This
Australian research team led by Michelle Simmons have
gained worldwide recognition.
The first quantum computing
company is D-wave Systems Inc.The
basic elements of d-wave computer
processors are called “SQUIDS”.
“SQUIDS” stands for Super Conducting Quantum
Interference devices.

SQUIDS are one of the most sensitive devices used to
measure the intensity of magnetic field.
SQIUDS are certain kind of superconductor ring that is
divided by an area is known as Josephson Junction.
The entire computation process is based
on the probabilistic method which is
known as “Quantum Annealing”.
 Quantum annealing consists of finding the optimal value
among all possible solutions.

The first stage of the algorithm is to place a memory register into a
coherent superposition of all its possible states. The letter 'Q' will be
used denote a qubit that is in the coherent state.
When a qubit is in the coherent state, it can be thought of as existing
in two different universes. In one universe it exists as a '1' and in the
other it exists as a '0' (See Figure 1). Extending this idea to the 3 bit
register we can imagine that the register exists in 8 different universes,
one for each of the classical states it could represent (i.e. 000, 001, 010,
011, 100, 101, 110, 111). In order to hold the number 15, a four bit register is
required (capable of representing the numbers 0 to 15 simultaneously in
the coherent state).
A calculation performed on the register can be thought of as a whole
group of calculations performed in parallel, one in each universe. In
effect, a calculation performed on the register is a calculation
performed on every possible value that register can represent.

The second stage of the algorithm performs a calculation using the
register. The details of which are as follows:
•The number N is the number we wish to factorise, N = 15
•A random number X is chosen, where 1 < X < N-1
X is raised to the power contained in the register (register A) and then
divided by N
•The remainder from this operation is placed in a second 4 bit register
(register B).
The final stage is perhaps
most difficult to follow.
The frequency of repetition
, f, can be found using a quantum computer. This is done by performing
a complex operation on register B and then looking at its contents
which causes the results from every universe to interfere with each
other. The resulting value for f is then used in the following equation to
calculate a (possible) factor.

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
O ( sqrt{N}) evaluations of the function, where N is the size
of the function's domain. It was devised by Lov Grover in
1996.
Although the purpose of Grover's algorithm is usually
described as "searching a database", it may be more accurate
to describe it as "inverting a function". Roughly speaking, if
we have a function y = f ( x ) that can be evaluated on a
quantum computer, Grover's algorithm allows us to calculate
x when given y . Inverting a function is related to the
searching of a database because we could come up with a
function that produces one particular value of y ("true", for
instance) if x matches a desired entry in a database, and
another value of y ("false") for other values of x.

If classical mechanics is
George Eliot,
Quantum mechanics is
Franz kafka.

A brief presentation on qunatum computing system & the material science related to it

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