The document provides an overview of quantum computing, explaining key concepts such as superposition, entanglement, and quantum algorithms like Shor's and Grover's algorithms. It discusses the potential advantages of quantum computers over classical computers, particularly in fields like cryptography and optimization, while highlighting their transformative impact on industries such as pharmaceuticals and material science. The document also addresses concerns regarding security and the implications of quantum computing on data privacy.

1. Data Structure in Quantum
Computing
Guide: Kapil Mundada
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Students Names :
1.Shwetark Deshpande
2.Omkar Gadge
3.Preshit Ghode
4.Devesh Gugale
5.Ajinkya Gunjkar

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Content
• Introduction
• Why Quantum
Computer
• Shor’s Algorithm
• Grover’s Algorithm
• Reference

3. Introduction
• Quantum mechanics is a field of physics that studies the
behavior of the most basic and smallest parts of our
universe at the subatomic level.
• So this quantum computer is based on the principle of
quantum mechanics some of them are superposition and
entanglement.
• Currently computers use bits which are either a 0 or a 1 to
process information but if we use quantum particles as data
something interesting happens by using quantum particles
called qubits and the property of superposition they can read
both as a 0 or a 1 at the same time.
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4. Superposition
• Superposition is the phenomenon where particles can be in
two states at the same time.
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6. Why Quantum Computers
• Classical computers are now just fully developed and
reached at its physical limits.
• Need to simulate quantum behaviour ,so why not to
stimulate it by using actual quantum physics?
• By looking at high speed can create a great threat to
security if developed by bad mans and vice versa .
• These computers can bring a great revolution in chemical
and pharmaceutical industry.
• These can give birth to fabulous inventions that can change
ones perspective to look at world around us.
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7. Entaglement
• Unintuitive property of qubits.
• They can influence each other without physical connection.
• Only described by the joined state.
• On the reference of the observation of first entangled
particle another entangled particle changes its state
accordingly at the same instant.
• Irrespective of distance and fails theory of relativity.
• It's still being doubted but entangled particles could mean
that communication could be instant regardless of the
distance between the particles.
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8. Encryption
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10. Shor’s
Algorithm
But this work can be done with
surprisingly fast speed in
quantum computers hence one
whose possessing the large
enough quantum computer in
todays world can cause
immediate threat to privacy of
whole internet. By simply using
algorithm called SHOR’s
Alogorithm.
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11. • The Only Known way to decrypt the data is to guess any
number and do trial and error unless we get the right
number.
• Basically what Shor’s algorithm does is it transforms a bad
guess that we have made into a much better guess.
• There’s nothing quantum mechanical in turning this bad
guess into much better guess but it takes huge amount of
time in normal computer but it happens at ridiculosly fast
rate in quantum computer.
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So the question arises now is……
1.} How shor’s algorithm turns bad guess into
much better guess ?
2.} how quantum computer make this process
ridiculously fast.

13. Mathmatics
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Here the p is how many times we have to multiply g with g for decrypting
data we just need to find the value of p.
Only method exist for this process is to try different values of P.
This process seems very simple for small numbers but during decryption
the number we face are suppose 1000 digit numbers and g is 500 digit
number
So how many time g *g calculating that is tough task for normal
computers.
Here Quantum Mechanics comes into play

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But because of principal of super position in quantum computers the quantum computer
can simultaneously take large number of input and same time gives values of outputs.
Setting up quantum computer which automatically destroying all wrong values
and giving only one value of p . This task is done by using frequency
visualization in fourier transform.

16. • By using setting up a quantum fourier transform we can get
the output value of p which can be the factor of given
number.
• Hence once the one factor is know the data can be easily
decrypted.
• Hopefully quantum computers with this much capacity are
not available yet so our data is safe as of now……………
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17. Grover’s Algorithm
• Algorithm of Grover it's a database search algorithm. It still has the
same implications one obvious application is a search of an
unstructured database.
• Which is what this algorithm was originally intended for this is useful
when you have a large amounts of unordered data coming in and you
need to find items in this.
• This algorithm will be potentially useful when the Internet of Things
gets bigger and the whole world has more and more data coming in.
• A qubit is either a 0 or a 1 represented by a column matrix or
somewhere in between and that matrix the Hadamard matrix you see
puts the state of the qubit into a superposition .
• Hadamard matrix you see puts the state of the qubit into a
superposition.
• So this Hadamard matrix is basically the first part of this algorithm and
a bunch of these Hadamard matrices applied to register which is
basically a circuit of qubits it's called a Hadamard transform.
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• What this basically does is put the quantum computer into an
equal superposition of all the possible states of the register.
So say you had a eight qubit register 2 to the 8th there would
be 64 entries shade of 128 superimposed States.

19. • Next Grover iteration and the first part of the grover iteration is the
oracle and the oracle is basically a black box function that modifies the
entry you're looking for depending on its value this basically means
that if the item is in the correct state then the oracle rotated but
otherwise it'll do nothing.
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• Next part of the algorithm basically consists of a Hadamard transform then a phase
shift then another Hadamard transform, the way that the state is isolated is through a
lot of these transformations that take advantage of the difference in amplitude to
single out that single state that you're looking for increasing the probability of that
state.

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22. Future of Quantum Computing
• The qubit (quantum) data structures and computational
processes are proposed to significantly improve the
performance in solving problems of discrete optimization and
fault-tolerant design.
• Quantum computing can be a game-changer in such fields
as cryptography and chemistry, material science, agriculture,
and pharmaceuticals when the technology becomes more
mature.
• Encryption methods have been designed to take centuries to
solve even for supercomputers.
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23. • More complex problems are arising: As technology
advances, the problems encountered are getting more
complex. Quantum computing offers a solution for complex
problems like protein modeling.
• Supercomputers are limited to solving nonlinear
problems:
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24. References
• https://en.m.wikipedia.org/wiki/Quantum_algorithm
• https://www.geeksforgeeks.org/introduction-quantum-
computing/
• https://www.ibm.com/quantum-computing/learn/what-is-
quantum-computing/
• https://qiskit.org/textbook/ch-algorithms/shor.html
• https://qiskit.org/textbook/ch-algorithms/grover.html
• https://youtu.be/w1V3gZv0ebY
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