Quantum computing is a new method of computing based on quantum mechanics that offers greater computational power than classical computers. Quantum computers use quantum bits or qubits that can exist in superpositions of states allowing massive parallelism. Several approaches like ion traps, quantum dots and NMR have demonstrated quantum computing. However, challenges remain around errors from decoherence and a lack of reliable reading mechanisms. If these obstacles can be overcome, quantum computers may solve problems in artificial intelligence, cybersecurity, drug design and more exponentially faster than classical computers.

1. Quantum Computing
Submitted to: Submitted By:
Dr. Rohit Kumar Keshav(2K19/EC/091)

2. Outline
Introduction
What is Quantum Computer ?
Need of Quantum Computer
Representation of Data- Q bits
Representation of Data- Superposition
Quantum Gates
Demonstration of Quantum Computing
Obstacles & Research
Future Application

3. Introduction to Quantum Computers
As the making of transistors smaller and smaller is continued ,the width of a wire in a computer chip is no
longer than a size of a single atom. These are sizes for which rules of classical physics no longer apply. If the
transistors become much smaller, the strange effects of quantum mechanics will begin to hinder their
performance.
▪ 1985 - David Deutsch developed the quantum Turing machine, showing that quantum
circuits are universal.
▪ 1994 - Peter Shor came up with a quantum algorithm to factor very large numbers in
polynomial time.
▪1997 - Lov Grover develops a quantum search algorithm with O(√N) complexity
▪ “I think I can safely say that nobody understands quantum mechanics” - Feynman
▪ 1982 - Feynman proposed the idea of creating machines based on the laws of quantum
mechanics instead of the laws of classical physics.

4. What is Quantum Computer ?
Quantum computing is a modern way of computing
that is based on the science of quantum mechanics
and its unbelievable phenomena. It is a beautiful
combination of physics, mathematics, computer
science and information theory. It provides high
computational power, less energy consumption and
exponential speed over classical computers by
controlling the behaviour of small physical objects
i.e. microscopic particles like atoms, electrons,
photons, etc.

5. Need of Quantum Computer
➢ The Potential and Power of Quantum Computing
Quantum computer with 500 qubits gives 2500 superposition states. Each state would be classically equivalent
to a single list of 500 1's and 0's. Such computer could operate on 2500 states simultaneously. Eventually,
observing the system would cause it to collapse into a single quantum state corresponding to a single answer,
a single list of 500 1's and 0's, as dictated by the measurement axiom of quantum mechanics. This kind of
computer is equivalent to a classical computer with approximately 10150processors.
➢ Moore's Law for Quantum Computers
If we use an analogue of Moor’s law for quantum computers, the number of quantum bits would be double in
every 18 months. But adding just one qubit is already enough to double a speed. So, the speed of quantum
computer will increase more than just doubling it.
➢ The Major Difference between Quantum and Classical Computers
. The memory of a quantum computer is a quantum state that can be a superposition of
different numbers. A quantum computer can do an arbitrary reversible classical computation on all the
numbers
simultaneously.
➢ Superiority of Quantum Computer over Classical Computer

6. Representation of Data
❑ Quantum computers, which have not been built yet, would be based on the strange principles of
quantum mechanics, in which the smallest particles of light and matter can be in different places at the
same time.
❑ In a quantum computer, one "qubit" - quantum bit - could be both 0 and 1 at the same time. So with
three qubits of data, a quantum computer could store all eight combinations of 0 and 1 simultaneously.
That means a three-qubit quantum computer could calculate eight times faster than a three-bit digital
computer.
❑ Typical personal computers today calculate 64 bits of data at a time. A quantum computer with 64
qubits would be 2 to the 64th power faster, or about 18 billion billion times faster. (Note: billion billion
is correct.)

7. Representation of Data-Qbits
➢ A bit of data is represented by a single atom that is in one of two states denoted by |0> and |1>. A
single bit of this form is known as a qubit.
➢ A physical implementation of a qubit could use the two energy levels of an atom. An excited state
representing |1> and a ground state representing |0>.
Excited
State
Ground
State
Nucleus
Light pulse of
frequency  for
time interval t
Electron
State |0> State |1>

8. Representation of Data- Superposition
A single qubit can be forced into a superposition of the two states denoted by the addition of the state
vectors:
|> =  1 |0> +  2 |1>
Where  1 and  2 are complex numbers and | 1 |2 + |  2 |2 = 1
A qubit in superposition is in both of the
states |1> and |0 at the same time

9. Light pulse of
frequency  for time
interval t/2
State |0> State |0> + |1>
Consider a 3 bit qubit register. An equally weighted superposition of all possible states
would be denoted by:
|> =
𝟏
√𝟖
|000> +
𝟏
√𝟖
|001> + . . . +
𝟏
√𝟖
|111>

10. Quantum Gates
▪Quantum Gates are similar to classical gates, but do not have a degenerate output. i.e. their original
input state can be derived from their output state, uniquely. They must be reversible.
▪This means that a deterministic computation can be performed on a quantum computer only if it is
reversible. Luckily, it has been shown that any deterministic computation can be made
reversible.(Charles Bennet, 1973)
▪Simplest gate involves one qubit and is called a Hadamard Gate (also known as a square-root of NOT
gate.) Used to put qubits into superposition.
H
State
|0>
State
|0> + |1>
H
State
|1>
Note: Two Hadamard gates used in
succession can be used as a NOT gate

11. Quantum Gates - Controlled NOT
A gate which operates on two qubits is called a Controlled-NOT (CN) Gate. If the bit on the control
line is 1, invert the bit on the target line.
A - Target
B - Control
Input Output
Note: The CN gate has a similar
behavior to the XOR gate with some
extra information to make it reversible.
A’
B’

12. A Universal Quantum Computer
▪ The CCN gate has been shown to be a universal reversible logic gate as it can be used as a NAND gate.
A - Target
B - Control 1
C - Control 2
Input Output
A’
B’
C’
When our target input is 1, our target
output is a result of a NAND of B and C.

13. Démonstrating Quantum Computing
❑ Nuclear Magnetic Resonance :- The latest development in quantum computing takes a radical new approach.
When held in a magnetic field, each nucleus within a molecule spins in a certain direction, which can be used
to describe its state; spinning upwards can signify a 1 and spinning down, a 0. Nuclear Magnetic Resonance
(NMR) techniques can be used to detect these spin states and bursts of specific radio waves can flip the nuclei
from spinning up (1) to spinning down (0) and vice-versa.
❑ Ion Trap :- An Ion Trap quantum computer is also based on control of nuclear spin (although using vibration
modes or "phonons" has also been considered). In this approach the individual ions are, as the name implies,
trapped or isolated by means of an electromagnetic field which is produced by means of an electromagnetic
chamber. They are then manipulated by laser pulses and a qubit arises from the superposition of lower and
higher energy spin states.
❑ Quantum Dot :- A quantum dot is a particle of matter so small that the addition or removal of an electron
changes its properties in some useful way. When the dot is exposed to a pulse of laser light of precisely the
right wavelength and duration, the electron is raised to an excited state: a second burst of laser light causes the
electron to fall back to its ground state. The ground and excited states of the electron can be thought of as the 0
and 1 states of the qubit and the application of the laser light can be regarded as a controlled NOT function as
it knocks the qubit from 0 to 1 or from ' to 0

14. Obstacles & Research
The field of quantum information processing has made numerous promising advancements since its conception,
including the building of two- and three-qubit quantum computers capable of some simple arithmetic and data
sorting. However, a few potentially large obstacles still remain that prevent us from "just building one", or more
precisely, building a quantum computer that can rival today's modern digital computer.
➢ Decoherence
Consider a qubit that is in the coherent state.As soon as it measurable interacts with the environment it will
decohere and fall into one of the two classical states.
➢ Error Correction
Those errors that arise as a direct result of decoherence, or the tendency of a quantum
computer to decay from a given quantum state into an incoherent state as it interacts, or entangles, with the state
of the environment.These interactions between the environment and qubits are unavoidable, and induce the
breakdown of information stored in the quantum computer, and thus errors in computation.
➢ Lack of Reliable Reading Mechanism
The techniques that exist till date have a big problem that trying to read from a superpositioned qubit would
invariably make it to lose its superpositioned state and make it to behave just as a classical bit – i.e. it would
store only one among the values of 0 and 1.

15. Future Benefits of Quantum Computer
❖ Artificial Intelligence & Machine Learning
❖ Computational Chemistry
❖ Drug Design & Development
❖ Cybersecurity & Cryptography
❖ Financial Modelling
❖ Logistics Optimisation
❖ Better Batteries
❖ Cleaner Fertilization
❖ Traffic Optimization
❖ Weather Forecasting and Climate Change
❖ Solar Capture
❖ Electronic Materials Discovery

16. References
➢ https://www.technologyreview.com/2019/01/29/66141/what-is-quantum-computing/
➢ https://giapjournals.com/ijsrtm/article/view/108/102
➢ https://www.intechopen.com/online-first/introduction-to-quantum-computing
➢ https://www.technologyreview.com/2019/01/29/66141/what-is-quantum-computing/
➢ https://builtin.com/hardware/quantum-computing-applications

17. ❖ Where a classical computer would take 5 trillion years to factor a 5,000 digit number, a
quantum computer could finish in 2 minutes.
❖ According to Chuang a supercomputer needs about a month to find a phone number from the
database consisting of world's phone books, where a quantum computer is able to solve this task
in 27 minutes.
❖ In fact a quantum computer capable of performing Shor's algorithm would be able to break
current cryptography techniques in a matter of seconds.