Quantum Computing

Quantum Computing
Deepankar Sandhibigraha
1625107011
CIME, Bhubaneswar

Deepankar Sandhibigraha MCA 4th
Semester CIME, BBSR 2017
CERTIFICATE
This is to certify that Mr. Deepankar Sandhibigraha bearing
Reg. No. 1625107011 Of MCA 2nd
year has done a seminar
on “Quantum Computing” Under the guidance of Mr.
Susanta Kumar Behera in the academic session 2015-18 for
the partial fulfillment of his post graduate degree course
curriculum. To the best of my knowledge he has not submitted
this seminar work anywhere else till date.
Signature of the candidate Signature of the
Deepankar Sandhibigraha HOD
Mrs. Rajalaxmi Mishra
Signature of the Guide
Mr. Susanta Ku. Behera Date: - 09.03.2017

ACKNOWLEDGEMENT
I want to express my gratitude to all the people who
have given their heart whelming full support in making this
compilation a magnificent experience. With deep sense of
gratitude, I’m very thankful l to Mrs.Rajalaxmi Mishra,
H.O.D. of MCA department for his continuous
encouragement and help. I am extremely grateful for the
guidance of Mr.Susanta Kumar Behera and Mr.SSGN Mishra
for his adept and adroit guidance and incessant
encouragement throughout the work. At the same time I am
indebted to him for providing the necessary and highly useful
information on such a demanding subject. Last but not the
least, I thank Almighty God for reasons too numerous to
mention.

Overview
 Introduction
 Understanding Classical Computers
 How A Computer Works
 Bit
 Logic Gates
 Quantum Mechanics
 Superposition
 Tunnelling
 Entanglement
 Quantum Computing
 Qubit
 Quantum Gates
 Quantum Computer
 Building A Qubit
 D-Wave Systems
 Applications
 Quantum Cryptography
 Optimisation Problem Solving
 Conclusion
 References

Introduction
Quantum computing is the area of study focused on developing
computer technology based on the principles of Quantum Mechanics.
The power of the quantum computer is that it is based on a logic that
is not limited merely to on-or-off, true-or-false scenarios. Quantum
computing uses Qubits. It can represent a zero, a one and both, which
is known as Superposition. It uses phenomenon such as Quantum
Tunnelling, Quantum Entanglement to solve more complex
calculations. From optimization problems to simulation, machine
learning, weather forecasting all will be possible with accurate
outcomes with this technology. The superposition that occurs in a
quantum system is so different to that which occurs in classical
systems that it can allow two of these qubits to behave in ways that
cannot be explained by the individual components. This is called
entanglement. These more complex calculations can be used to re-
imagine computing.

What Is Computing ?
The process of utilizing computer technology to complete a task. Computing may involve
computer hardware and/or software, but must involve some form of a computer system.
Most individuals use some form of computing every day whether they realize it or not.
Swiping a debit card, sending an email, or using a cell phone can all be considered forms of
computing.
What Is A Computer ?
Computer is an electronic device that is designed to work with Information. The term
computer is derived from the Latin term ‘Computare’, this means to calculate or
programmable machine. Computer cannot do anything without a Program
How A Computer Works ?
A classical computer basically works its functions using bits, logical gates, transistors and pre-
defined algorithms which are programmed into machine codes. All the data from text to
graphic files and media files are stored in binary digits. The operations are made using logic
gate combinations. It processes information using all these methods.
Information
In computer, information, in its most basic form, can be represented as a sequence of bits.
What Is A Bit ?
Bit refers to binary digit. It is the basic unit of data in computers. Computer understands
binary instead of decimal. All the data in computers are presented in form of bits.
A bit can in one of the two states, i.e. either be zero or one at a time. Two classical bits can
represent four possible states, each state at a time.
Numbers can be represented in binary using decimal to binary conversion. Similarly words
using ASCII/UTF-8, graphics using jpeg, png, mpeg, etc. These are all just sequence of bits.

Logic Gates
A logic gate is an elementary building block of a digital circuit. Most logic gates have two
inputs and one output. At any given moment, every terminal is in one of the two binary
conditions low (0) or high (1), represented by different voltage levels.
Quantum Mechanics
Quantum mechanics (also known as quantum physics or quantum theory), is a branch of
physics which is the fundamental theory of nature at small scales and low energies of atoms
and subatomic particles. Quantum mechanics differs from classical physics in that energy,
momentum and other quantities are often restricted to discrete values (quantization), objects
have characteristics of both particles and waves (wave-particle duality), and there are limits
to the precision with which quantities can be known (Uncertainty principle).It also explains
quantum annealing, quantum superposition, quantum tunnelling, and quantum
entanglement.
Quantum
In physics, a quantum (plural: quanta) is the minimum amount of any physical entity
involved in an interaction. For example, a photon is a single quantum of, and can be referred
to as a "light quantum".

Quantization
It is the process of converting a continuous range of values into a finite range of discreet values.
This is a function of Analog-to-digital converters, which create a series of digital values to
represent the original Analog signal.
Superposition
It states that, much like waves in classical physics, any two (or more) quantum states can be
added together ("superposed") and the result will be another valid quantum state; and
conversely, that every quantum state can be represented as a sum of two or more other
distinct states. Because quantum mechanics is weird, instead of thinking about a particle
being in one state or changing between a varieties of states, particles are thought of as
existing across all the possible states at the same time. If you’re thinking in terms of particles,
it means a particle can be in two places at once. However, once a measurement of a particle
is made, and for example its energy or position is known, the superposition is lost and now
we have a particle in one known state. For example a qubit can be 1, 0 or both 0&1 at same
time.
Quantum tunnelling
Quantum tunnelling refers to the quantum mechanical phenomenon where a particle tunnels
through a barrier that it classically could not surmount. For example a ball trying to roll over
a hill, Classical mechanics predicts that particles that do not have enough energy to classically
surmount a barrier will not be able to reach the other side. Thus, a ball without sufficient
energy to surmount the hill would roll back down. Or, lacking the energy to penetrate a wall,
it would bounce back. In quantum mechanics, these particles can, with a very small
probability, tunnel to the other side. This plays an essential role in several physical
phenomena, such as the nuclear fusion that occurs in main sequence stars like the Sun. It has
important applications to modern devices such as the tunnel diode, quantum computing, and
the scanning tunnelling microscope. Tunnelling is often explained using the Heisenberg
uncertainty principle and the wave–particle duality of matter.
Quantum entanglement
Quantum entanglement is a physical phenomenon that occurs when pairs or groups of
particles are generated or interact in ways such that the quantum state of each particle
cannot be described independently of the others, even when the particles are separated by a
large distance (billions of miles)—instead, a quantum state must be described for the system
as a whole. Measurements of physical properties such as position, momentum, spin, and
polarization, performed on entangled particles are found to be appropriately correlated. For
example, if a pair of particles are generated in such a way that their total spin is known to be
zero, and one particle is found to have clockwise spin on a certain axis, the spin of the other
particle, measured on the same axis, will be found to be counter clockwise, as to be expected
due to their entanglement. Einstein referring to it as "spooky action at a distance".

Wave particle duality
Wave–particle duality is the concept that every elementary particle or quantic entity may be
partly described in terms not only of particles, but also of waves.
Uncertainty principle
It states that the more precisely the position of some particle is determined, the less precisely
its momentum can be known, and vice versa. As you proceed downward in size to atomic
dimensions, it is no longer valid to consider a particle like a hard sphere, because the smaller
the dimension, the more wave-like it becomes. It no longer makes sense to say that you have
precisely determined both the position and momentum of such a particle.
Quantum Computing
Qubit
In quantum computing, a qubit or quantum bit (sometimes qbit) is a unit of quantum
information—the quantum analogue of the classical bit. A qubit is a two-state quantum-
mechanical system, such as the polarization of a single photon: here the two states are
vertical polarization and horizontal polarization. In a classical system, a bit would have to be
in one state or the other. However, quantum mechanics allows the qubit to be in a
superposition of both states at the same time, a property that is fundamental to quantum
computing. An important distinguishing feature between a qubit and a classical bit is that
multiple qubits can exhibit quantum entanglement. Entanglement is a nonlocal property that
allows a set of qubits to express higher correlation than is possible in classical systems. A
number of qubits taken together is a qubit register. Quantum computers perform calculations
by manipulating qubits within a register. A qubyte (quantum byte) is a collection of eight
qubits. It is possible to fully encode one bit in one qubit. However, a qubit can hold even more
information, e.g. up to two bits using superdense coding.
Physical
support
Name
Information
support
| 0 > | 1 >
Photon
Polarization encoding
Polarization
of light
Horizontal Vertical
Number of photons Fock state Vacuum Single photon state
Time-bin encoding
Time of
arrival
Early Late
Coherent state of
light
Squeezed light Quadrature
Amplitude-
squeezed state
Phase-squeezed state
Electrons
Electronic spin Spin Up Down
Electron number Charge No electron One electron
Nucleus
Nuclear spin addressed
through NMR
Spin Up Down
Optical lattices Atomic spin Spin Up Down

Josephson
junction
Superconducting charge
qubit
Charge
Uncharged
superconducting
island (Q=0)
Charged superconducting
island (Q=2e, one extra
Cooper pair)
Superconducting flux
qubit
Current Clockwise current Counter clockwise current
Superconducting phase
qubit
Energy Ground state First excited state
Singly
charged quantum
dot pair
Electron localization Charge Electron on left dot Electron on right dot
Quantum dot Dot spin Spin Down Up
Quantum gates
In quantum computing and specifically the quantum circuit model of computation, a quantum
gate (or quantum logic gate) is a basic quantum circuit operating on a small number of qubits.
They are the building blocks of quantum circuits, like classical logic gates are for conventional
digital circuits. Unlike many classical logic gates, quantum logic gates are reversible.
 Commonly used gates are
 Hadamard gate
 Pauli-X gate (= NOT gate)
 Pauli-Y gate
 Pauli-Z gate
 Square root of NOT gate (√NOT)
 Phase shift gates
 Swap gate
 Square root of Swap gate
 Controlled gates
 Toffoli gate
 Fredkin gate
 Universal quantum gates

Quantum Computer
Building a qubit
Electron or nucleus can be used where spin is considered. Spin up is 1 and spin down is 0.
Photon can also be used where vertically polarized photon is 1 and horizontally polarized
photon is 0. Like a magnet in classical bit but its 3rd measurement other than 0 and 1 is it can
be in both state at one time.
Taking a phosphorous atom which contains one electron on outer cell we can build a qubit.
The phosphorous atom is embedded into silicon crystal followed by tiny transistors. To
differentiate the energy states of an electron when it’s spin up and spin down we need a
strong magnetic field. For this a super conducting magnet is used which is a large solenoid
coil inside liquid helium which is 150 times colder than outer universe. Because at room
temperature electron will spin up by thermal energy. Now the electron will line up with its
spin pointing down which is its lowest energy state. It’ll need some energy to put up into spin
up state. We can spin it up by hitting very specific frequency’s pulse of microwaves according
to the magnetic field in which electron is kept. Since magnetic fields can affect the spin, we
need to eliminate all the spin nearby. So we use an isotope of silicon, which is 28Si14
which has no spin of its own.
Where a 2-bit register in an ordinary computer can store only one of four binary
configurations (00, 01, 10, or 11) at any given time, a 2-qubit register in a quantum computer
can store all four numbers simultaneously, because each qubit represents two values. If more
qubits are added, the increased capacity is expanded exponentially.
Quantum algorithms
In quantum computing, a quantum algorithm is an algorithm which runs on a realistic model
of quantum computation, the most commonly used model being the quantum circuit model
of computation. A classical (or non-quantum) algorithm is a finite sequence of instructions, or
a step-by-step procedure for solving a problem, where each step or instruction can be
performed on a classical computer. Similarly, a quantum algorithm is a step-by-step
procedure, where each of the steps can be performed on a quantum computer. Although all
classical algorithms can also be performed on a quantum computer, the term quantum
algorithm is usually used for those algorithms which seem inherently quantum, or use some
essential feature of quantum computation such as quantum superposition or quantum
entanglement.
Problems which are undecidable using classical computers remain undecidable using
quantum computers. What makes quantum algorithms interesting is that they might be able
to solve some problems faster than classical algorithms.
The most well-known algorithms are Shor's algorithm for factoring, and Grover's algorithm for
searching an unstructured database or an unordered list. Shor's algorithms runs exponentially

faster than the best known classical algorithm for factoring, the general number field sieve.
Grover's algorithm runs quadratically faster than the best possible classical algorithm for the
same task.
 Algorithms based on the quantum Fourier transform
o 2.1Deutsch–Jozsa algorithm
o 2.2Simon's algorithm
o 2.3Quantum phase estimation algorithm
o 2.4Shor's algorithm
o 2.5Hidden subgroup problem
o 2.6Boson sampling problem
o 2.7Estimating Gauss sums
o 2.8Fourier fishing and Fourier checking
 Algorithms based on amplitude amplification
o 3.1Grover's algorithm
o 3.2Quantum counting
 Algorithms based on quantum walks
o 4.1Element distinctness problem
o 4.2Triangle-finding problem
o 4.3Formula evaluation
o 4.4Group commutativity
 BQP-complete problems
o 5.1Computing knot invariants
o 5.2Quantum simulation
D-Wave Systems
D-Wave Systems, Inc. founded in 1999, is a quantum computing company, based in Burnaby,
British Columbia, Canada. D-Wave is the first company in the world to sell quantum
computers. The D-Wave One was built on early prototypes such as D-Wave's Orion Quantum
Computer. The prototype was a 16-qubit quantum annealing processor, demonstrated on
February 13, 2007 at the Computer History Museum in Mountain View, California.
On May 11, 2011, D-Wave Systems announced D-Wave One, described as "the world's first
commercially available quantum computer", operating on a 128-qubit chipset[4] using
quantum annealing (a general method for finding the global minimum of a function by a

process using quantum fluctuations) to solve optimization problems. In May 2013, a
collaboration between NASA, Google and the Universities Space Research Association (USRA)
launched a Quantum Artificial Intelligence Lab based on the D-Wave Two 512-qubit quantum
computer that would be used for research into machine learning, among other fields of study.
Comparison of D-Wave systems
D-Wave
One
D-Wave Two D-Wave 2X D-Wave 2000Q[45][46]
Available May 2011 May 2013 August 2015 January 2017
Code-name Rainier Vesuvius
Qubits 128 512 1152 2048
Couplers 352 3000 5600
Josephson junctions 24,000 128,000
I/O / control lines 192
Operating
temperature
0.02 K 0.015 K
Power consumption 15.5 kW 25 kW
Buyers
Lockheed
Martin
Lockheed Martin
Google/NASA/USRA
Lockheed Martin
Google/NASA/USRA
Los Alamos National
Laboratory
Temporal Defense
Systems Inc.
The D-Wave 2000Q™ System
The Quantum Computer
 Exploits quantum mechanical effects to provide an entirely new type of
computational resource
 Built around “qubits” rather than “bits”
 Operates in an extreme environment
 Enables quantum algorithms to solve very hard problems
Power and Cooling

 “The Fridge” is a closed cycle dilution refrigerator
 The superconducting processor generates no heat
 Cooled to 180x colder than interstellar space (0.015 Kelvin)
A Unique Processor Environment
 Shielded to 50,000× less than Earth’s magnetic field
 In a high vacuum: pressure is 10 billion times lower than atmospheric pressure
 200 I/O and control lines from room temperature to the chip
 The system consumes less than 25 kW of power
 Power demand won’t increase with successive processor generations
Processing with D-Wave
 A lattice of 2000 tiny superconducting devices, known as qubits, is chilled close to absolute
zero to harness quantum effects
 A user models a problem into a search for the “lowest energy point in a vast landscape”
 The processor considers all possibilities simultaneously to determine the lowest energy
and the values that produce it
 Multiple solutions are returned to the user, scaled to show optimal answers
Applications
 Machine Learning & Computer Science • Detecting statistical anomalies • Finding
compressed models • Recognizing images and patterns • Training neural networks •
Verifying and validating software • Classifying unstructured data • Diagnosing circuit faults
 Security & Mission Planning • Detecting computer viruses & network intrusion •
Scheduling resources and optimal paths • Determining set membership • Analysing graph
properties • Factoring integers
 Healthcare & Medicine • Detecting fraud • Generating targeted cancer drug therapies •
Optimizing radiotherapy treatments • Creating protein models
 Financial Modelling • Detecting market instabilities • Developing trading strategies •
Optimizing trading trajectories • Optimizing asset pricing and hedging • Optimizing
portfolios
Software and Programming
Just as the classical computing world needed a software ecosystem to build a broad
community of application developers and users, the quantum computing world does as well.
The D-Wave 2000Q system provides a standard Internet API, with client libraries available for
C/C++, Python, and MATLAB. This interface allows users to access the system either as a cloud
resource over a network, or integrated into their high-performance computing environments
and data centres. Access is also available through D-Wave’s hosted cloud service. Using D-
Wave’s development tools and client libraries, developers can create algorithms and
applications within their existing environments using industry-standard tools.

Users can submit problems to the D-Wave quantum computer in several ways:
• Using a program in C, C++, Python, or MATLAB to create and execute quantum machine
instructions
• Using a D-Wave tool such as:
• QSage, a translator designed for optimization problems
• ToQ, a high level language translator used for constraint satisfaction problems and designed
to let users “speak” in the language of their problem domain
• qbsolv, an open-source, hybrid partitioning optimization solver for problems that are larger
than will fit natively on the QPU
• dw, which executes QMIs created via a text editor
• By directly programming the system via QMIs
D-wave system is not a universal quantum computer but it’s based on subset of quantum
mechanics called quantum annealing. Quantum annealing is a computational paradigm to
search for the minimum of a cost function (multivariable function to be minimized) through
a control of quantum fluctuations. Quantum annealing is used mainly for combinatorial
optimization problems with discrete variables. Many practically important problems can be
formulated as combinatorial optimization, typically machine learning for pattern recognition,
natural language processing, medical diagnosis, etc. Finding efficient methods to solve
combinatorial optimization problems is therefore very important, and this is one of the
reasons why quantum annealing attracts much attention.
Application
Teleportation
Quantum teleportation is a process by which quantum information (e.g. the exact state of an
atom or photon) can be transmitted (exactly, in principle) from one location to another, with
the help of classical communication and previously shared quantum entanglement between
the sending and receiving location. Because it depends on classical communication, which can
proceed no faster than the speed of light, it cannot be used for faster-than-light transport or
communication of classical bits. While it has proven possible to teleport one or more qubits
of information between two (entangled) atoms, this has not yet been achieved between
molecules or anything larger.
Although the name is inspired by the teleportation commonly used in fiction, there is no
relationship outside the name, because quantum teleportation concerns only the transfer of
information. Quantum teleportation is not a form of transport, but of communication; it
provides a way of transporting a qubit from one location to another, without having to move
a physical particle along with it.

Optimization problems
In mathematics and computer science, an optimization problem is the problem of finding the
best solution from all feasible solutions. Optimization problems can be divided into two
categories depending on whether the variables are continuous or discrete. An optimization
problem with discrete variables is known as a combinatorial optimization problem. In a
combinatorial optimization problem, we are looking for an object such as an integer,
permutation or graph from a finite (or possibly countable infinite) set. Problems with
continuous variables include constrained problems and multimodal problems.
Drug and Materials Discovery: Untangling the complexity of molecular and chemical
interactions leading to the discovery of new medicines and materials;
 Supply Chain & Logistics: Finding the optimal path across global systems of systems for
ultra-efficient logistics and supply chains, such as optimizing fleet operations for deliveries
during the holiday season;
 Financial Services: Finding new ways to model financial data and isolating key global risk
factors to make better investments;
 Artificial Intelligence: Making facets of artificial intelligence such as machine learning much
more powerful when data sets can be too big such as searching images or video; or
 Cloud Security: Making cloud computing more secure by using the laws of quantum physics
to enhance private data safety.
There is no imagination to the applications of quantum computers till date.
Security threat
The current RSA is based on prime factors of large numbers such as a 2048 bit number. The
current classical computer will take nearly 3biilion years to break this using the public key
provide with hit and trial method. But now with the use of quantum computers and Shor’s
quantum algorithm for factoring numbers using quantum computers it can be factored and
break the security of maximum current security on the internet.
But to overcome this threat a new cryptography is being developed called Quantum
Cryptography.
Quantum cryptography
As qubits can be made of polarized photons, say we transfer photons from sender to receiver
using fibre optics cables and the receiver will measure those photons into bits and read the
message.
Key to the original message is sent using this method. In this way a completely random key is
generated. The receiver needs to match the filter using which the sender has sent the key.
Because according to quantum mechanics ”if receiver uses a diagonal detector on photon sent

in vertical or horizontal photon, it’ll have a 50-50 chance of measuring either vertical or
horizontal. i.e. 1 or 0.”
Mathematician has proven that if you can make a really random key called one time pad,
theoretically it is impossible to break it.
Making the filters used in sender side public wont effect security, because only order of the
filters are being shared. You still need the photons to decrypt the key.
Still photons are sent randomly it’ll be impossible to guess it according to quantum mechanics.
And if someone tries to detect the photons using wrong detector, it’ll change its state as
mentioned above in italics.
And if you are thinking someone will just copy the photons and get the key using detectors,
this is not possible due “no clone theorem” which states qubits cannot be copied and it’s
impossible to listen to qubits without disturbing them.
It’ll still take a lot to do it practically because small disturbances can change polarization of
photons.
Strong light beam can change the state of a detector. Scientists are only abled to send it
across 200km till now. And most of IoTs needs to change to bring it commercially.
Also recently 3 way secure quantum communication has been demonstrated using quantum
entanglement.
Quantum teleportation can also be used for security purposes.

Conclusion
The power of the quantum computer is that it is based on a logic that
is not limited merely to on-or-off, true-or-false scenarios. It will use
practical ways to solve practical problems on large scale. It will change
how we use computers and secures them now. It can break most of
current cyber securities we currently use in just seconds. On the other
it will help us solving current unsolvable problems like optimization
problems to simulation, machine learning, weather forecasting all will
be possible with accurate outcomes with this technology. It also come
up with solution to security threat with quantum encryption method.
It will be only in our hands whether to use it for good or bad. Recently,
on 6th march 2017, IBM has announced world’s first “Universal
Quantum Computer” for business and science will be commercialised
this year.

References
http://www.dwavesys.com/d-wave-two-system
http://www.dwavesys.com/quantum-computing
http://www.dwavesys.com/resources/tutorials
http://computer.howstuffworks.com/quantum-computer1.htm
https://en.wikipedia.org/wiki/Quantum_information_science
Wikipedia – Annealing, Superposition, Qubit, Entanglement.
QUANTUM COMPUTING EXPLAINED By David McMahon
D-Wave-brochure-Mar2016B Research white paper.
https://www.youtube.com/user/minutephysics YouTube - Minute Physics
https://www.youtube.com/user/1veritasium YouTube – Veritasium
https://www.youtube.com/user/Kurzgesagt YouTube – Kurzgesagt – In a
Nutshell
https://www.youtube.com/user/frameofessence YouTube – Frame of Essence

Quantum Computing

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