Quantum Computing: Fundamentals (Superposition, interference, entanglement), Applications(Materials, medical, teleportation, data modeling, finance), and Challenges(scalability, decoherence, fault tolerance ).

1. Quantum Computing
Submitted By: Jai Sipani
Roll no. : 16/454

2. CONTENTS
• What is Quantum
Computing?
• Why Quantum Computing?
• Fundamentals of Quantum
Computing
• Application Areas in
Quantum Computing
• Limitations in Quantum
Computing

3. Quantum Computing
Quantum computing is an area of computing focused on developing
computer technology based on the principles of quantum theory,
which explains the behavior of energy and material on the atomic and
subatomic levels.
During a conference co-hosted by MIT and IBM, Nobel Prize winner
Richard Feynman challenges a group of computer scientists to develop
a new breed of computers based on quantum physics.

4. • Quantum computing is the study of how to use phenomena
in quantum physics to create new ways of computing.
• The basis of quantum computing is the Qubit. Unlike a
normal computer bit, which can be 0 or 1, a Qubit can be
either of those, or a superposition of both 0 and 1.
Quantum Supremacy?
On October 23, 2019 Google announced that it had achieved
"Quantum Supremacy," meaning that they had used a quantum
computer to quickly solve a problem that a conventional
computer would take an impractically long time (thousands of
years) to solve.

5. • Moore's Law refers
to Moore's perception that
the number of transistors on
a microchip doubles every
two years, though the cost
of computers is halved.
• Transistor cannot be made
smaller due to the laws of
Quantum mechanics starts
to take over (Already at
7nm ).
Why Quantum Computing?

6. Quantum Bit VS Classical Bit

7. Quantum Bits or Qubits
Information is stored in quantum bits, or qbits. A qbit can be in states
labelled |0} and |1}, but it can also be in a superposition of these states, a|0} + b|1},
where a and b are complex numbers. If we think of the state of a qbit as a vector, then
superposition of states is just vector addition.
For every extra qbit you get, you can store twice as many numbers. For example, with
3 qbits, you get coefficients for |000}, |001}, |010}, |011}, |100}, |101},
|110} and |111}.

8. Fundamentals Of Quantum Computing
Superposition
Superposition refers to a combination of states
we would ordinarily describe independently. To
make a classical analogy, if you play two musical
notes at once, what you will hear is a
superposition of the two notes.
An example of a physically observable
manifestation of the wave nature of quantum
systems is the interference peaks from an e-
beam in a double-slit experiment. The pattern
is very similar to the one obtained
by diffraction of classical waves.

9. Entanglement
Quantum entanglement is a quantum
mechanical phenomenon in which the
quantum states of two or more objects
have to be described with reference to
each other, even though the individual
objects may be spatially separated.
Entangled particles behave together as a
system in ways that cannot be explained
using classical logic.
For example, it is possible to prepare two
particles in a single quantum state such
that when one is observed to be spin-up,
the other one will always be observed to be
spin-down and vice versa

10. Interference
Finally, quantum states can undergo
interference due to a phenomenon known as
phase. Quantum interference can be
understood similarly to wave interference;
when two waves are in phase, their
amplitudes add, and when they are out of
phase, their amplitudes cancel.
Interference effects can be observed with all
types of waves, for
example, light, radio, acoustic, surface water
waves, gravity waves, or matter waves.

11. Applications Of Quantum Computing
Machine Learning
Using quantum systems to train and run machine learning algorithms could allow us
to solve complex problems more quickly, potentially improving applications like
disease diagnosis, fraud detection, and efficient energy management.
In Classical computing, CNN takes upto 2 days to train itself completely. While via
Quantum computers it can be done in a few minutes.
More computational power can bring enormous change, training and testing
petabytes of data in lesser time.

12. Materials
Simulating quantum mechanical systems is a promising early application of
quantum computing. This technique can be applied to fields such as chemistry,
materials science, and high energy physics.
Learning the size, properties of each and every molecule in making medicines will
Be observed easily and quickly via qubits.
IBM scientists simulated the bonding in H2, LiH and BeH2 molecules using a
quantum computer.

13. Finance
In the financial service sector, many computationally intensive problems exist,
such as optimization of financial portfolios or the risk analysis of such portfolios.
For some of these problems, quantum computing may have the potential to
achieve a significant advantage compared to classical computing.
Learning the size, properties of each and every molecule in making medicines will
Be observed easily and quickly via qubits.
IBM scientists simulated the bonding in H2, LiH and BeH2 molecules using a
quantum computer.

14. Cryptography
Quantum computers follows probabilistic approach unlike deterministic like
classical computing.
Using the fundamental of superposition, where it is always uncertainity about the
states of bits. We can use it to make private keys which will never be intercepted
by hacker. And It does get intercepeted he won’t be able to derive any conclusions
from it.
RSA Encryption which is the core of encryption schemes applied in real world can
be eaily broken by Quantum Computing.

15. Teleportation
Quantum teleportation provides a mechanism of moving a qubit from one
location to another, without having to physically transport the underlying particle
that a qubit is normally attached to.

16. Limitations in Quantum Computing
Scalability
Quantum Computers can never be scaled upto classical computers. Even If they were, they
won’t be able to sustain much longer. Change in temperature in surrounding may lead them
to become error prone.
Noise distortion can lead to information corruption. These are still evolving but we won’t
be able to use them at a scale of classical computers.

17. Decoherence
The decoherence theory is reverting a quantum system back to classical through interactions
with the environment which decay and eliminate quantum behavior of particles.
Due to decoherence qubits are extremely fragile and their ability to stay in superposition and
or entangle is severely jeopardized. Radiation, light, sound, vibrations, heat, magnetic fields or
even the act of measuring a qubit are all examples of decoherence.
Decoherence leads to errors in quantum computational systems where information is lost.

18. Fault Tolerance
A quantum computer should to able to derive the results we want or the patterns
predict from the confused state in superposition.
It is an another challenge in designing the algorithms to predict accurate results.
One of the key factors which makes development of algorithms and code on a classical
computer manageable is symmetry of resources:
A moderate number of registers — all alike.
Large amount of memory — and all alike.
which the quantum computers lack.

19. Conclusion
A quantum computer thus has the theoretical capability of
simulating any finite physical system and may even hold the
key to creating an artificially intelligent computer.

20. References
1. https://www.cs.virginia.edu/~robins/The_Limits_of_Quantum_Co
mputers.pdf
2. https://physics.stackexchange.com/questions/183179/are-there-
known-fundamental-limits-of-quantum-computer-scaling
3. https://medium.com/@jackkrupansky/the-greatest-challenges-for-
quantum-computing-are-hardware-and-algorithms-c61061fa1210
4. https://hackernoon.com/decoherence-quantum-computers-
greatest-obstacle-67c74ae962b6
5. https://www.ibm.com/quantum-computing/learn/what-is-
quantum-computing/