quantum computing meghaditya
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Final Year Final Semester Seminar Slides.TRANSCRIPT
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Quantum Computing
Meghaditya Roy ChaudhuryBCSE – IV
Roll – 000810501052
Jadavpur University
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Overview
� Definition of Quantum Computing.
� Why Quantum Computing is necessary?
� Advantages over Classical Computation
� Quantum Algorithm: Shor’s Algorithm
� Current Developments and Future Prospects
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What is Quantum Computing?
� A quantum computer is a machine that performs calculations based on the laws of quantum mechanics,which is the behavior of particles at the sub-atomic level.
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Why Quantum Computing?
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Moore’s Law
Moore's law was a statement made in 1965 by Gordon Moore , one of the founders of Intel.
Moore noted that the number of transistors that could be squeezed on to a silicon chip was doubling every year . Over time, this has been revised to doubling every 18 months .
This has held true …….. So far
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Stretching the limits: But how far?
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Problems
� At current rate transistors will be as small as an atom.
� If scale becomes too small, Electrons tunnel through micro-thin barriers between wires corrupting signals.
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Quantum Computing Timeline
� The story of quantum computation started as early as 1982, when the physicist Richard Feynmanconsidered simulation of quantum-mechanical objects by other quantum systems
� 1985 when David Deutsch of the University of Oxford published a crucial theoretical paper in which he described a universal quantum computer.
� In 1994 when Peter Shor from AT&T's Bell Laboratories in New Jersey devised the first quantum algorithm.
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Nobody understands Quantum Mechanics
� “We always have had a great deal of difficulty in understanding the world view that quantum mechanics represents ”
� - Richard Feynman
("Simulating physics with computers" ,1982)
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Representation of Data - Qubits
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 λλλλ for time interval t
Electron
State |0> State |1>
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Properties Of Quantum Mechanics
� Quantum Superposition
� Quantum Entanglement
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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:
|ψψψψ> = αααα |0> + αααα |1>
Where αααα and αααα are complex numbers and |αααα | + | αααα | = 1
1 2
1 2 1 22 2
A qubit in superposition is in both of the states |1> and |0> at the same time
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Relationships among data -Entanglement
�Entanglement is the ability of quantum systems to exhibit correlations between states within a superposition.
�Imagine two qubits, each in the state |0> + |1> (a superpositionof the 0 and 1.) We can entangle the two qubits such that the measurement of one qubit is always correlated to the measurement of the other qubit.
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Classical computation vs. Quantum Computation
Classical Computation
Data unit: bit
x = 0 x = 1
0
1
0
1
Valid states:x = ‘0’ or ‘1’ |ψ⟩ = c1|0⟩ + c2|1⟩
Quantum Computation
Data unit: qubit
Valid states:
|ψ⟩ = |0⟩ |ψ⟩ = |1⟩ |ψ⟩ = (|0⟩ + |1⟩)/√2
=|1⟩ =|0⟩= ‘1’ = ‘0’
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Classical computation vs. Quantum Computation
Classical Computation
Measurement: deterministic
x = ‘0’
State Result of measurement
‘0’
x = ‘1’ ‘1’
Quantum Computation
Measurement: stochastic
|ψ⟩ = |0⟩
|ψ⟩ = |0⟩ + |1⟩
State Result of measurement
|ψ⟩ = |1⟩
√2
‘0’
‘1’
‘0’ 50%
‘1’ 50%
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Quantum Algorithm: Shor’s Algorithm
� Shor's algorithm is a quantum algorithm for factoring a number N in O((log N)3) time and O(log N) space, named after Peter Shor.
� The algorithm is significant because it implies that RSA, a popular public-key cryptographymethod, might be easily broken, given a sufficiently large quantum computer
� Like many quantum computer algorithms, Shor's algorithm is probabilistic
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Quantum Algorithm: Shor’s Algorithm
� Shor's algorithm consists of two parts:� A reduction, which can be done on a classical computer, of the factoring problem to the problem of order-finding.
f(x) = axmod(N)� A quantum algorithm to solve the order-finding problem
� The algorithm is dependant on� Modular Arithmetic� Quantum Parallelism� Quantum Fourier Transform
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# bits 1024 2048 4096factoring in 2006 105 years 5x1015 years 3x1029 yearsfactoring in 2024 38 years 1012 years 7x1025 yearsfactoring in 2042 3 days 3x108 years 2x1022 years
with a classical computer
# bits 1024 2048 4096# qubits 5124 10244 20484# gates 3x109 2X1011 X1012
factoring time 4.5 min 36 min 4.8 hours
with potential quantum computer
Quantum Algorithm: Shor’s Algorithm
In 2001, Shor's algorithm was demonstrated by a group at IBM, who factored 15 into 3 × 5, using an NMR implementation of a quantum computer with 7 qubits
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Quantum computing in computational complexity theory
� The class of problems that can be efficiently solved by quantum computers is called BQP, for "bounded error, quantum, polynomial time".
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Practical Implementations
� Ion Traps
� Nuclear magnetic resonance (NMR)
� Optical photon computer
� Solid-state
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Applications
� Factoring – RSA encryption
� Quantum simulation
� Spin-off technology – spintronics, quantum cryptography
� Spin-off theory – complexity theory, DMRG theory, N-representabilitytheory
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Thank You