debasis sadhukhan m.sc. physics, iit bombay. 1. basics of quantum computation. 2. quantum circuits...
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Debasis Sadhukhan
M.Sc. Physics, IIT Bombay
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1. Basics of Quantum Computation.
2.Quantum Circuits
3.Quantum Fourier Transform and it’s applications.
4.Quantum Search Algorithm
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WHAT WE NEED TO KNOW
1.Basic Quantum Mechanics &
2.A little Background of Computer Science
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*So, if the state can’t be written in the product state form, then they are Entangled. They are called to be Entangled State.
*Classical Analogy: No classical analog exists. But you can think of : Harry Potter and Voldemort
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Examples: Bell states or EPR pairs
Some of the very important applications are :1.Super-dense coding2.Quantum Teleportation3.Quantum Cryptography4.Quantum Games
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Represent a quantum state as a triangle with attached wires & do operation on quantum states just manipulating this picture
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*Execution of an classical algorithm require hardware, consist of many electrical circuits containing wires and logic gates.
*These logic gates are the basic building block of a classical computer.
*Similarly, to execute a quantum algorithm we must have a quantum computer where the building blocks are quantum gates.
*So, What are the Quantum Gates…?
*As the name suggests, the gates are quantum, the laws of quantum mechanics must be applicable here.
*So, they must be unitary operator and can be made reversible.
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*Note: The target and control qubit are not basis independent i.e. our target and control qubit may change if we use a different basis .
*In Classical Computation, we have seen NAND and NOR gate as universal quantum gate. A similar universality is true for quantum computation also.
*Every classical gates can be created using unitary quantum gates. In that sense quantum circuits include all the classical circuits.
*So, universality of quantum gates is obvious.
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*The final state of the 1st register:
Now, apply Inverse Fourier Transform on the 1st register.
Final state:
Overall Circuit:
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*The major applications are
1.Order finding
2.Prime factorization These can be used to break the
cryptosystem used in classical computer
3.Period Finding etc.
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*Examples:
C:\Users\DEBASIS\Desktop\GroversQuantumSearchAlgorithm.cdf
C:\Users\DEBASIS\Desktop\SimulatedQuantumComputerAlgorithmForDatabaseSearching.cdf
*Drawback:
1.Still, the problem remains in NP class.
2.If we don’t know the exact no of solution, we may not reach to our solution as no of iteration explicitly depends on M.
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References:
*[1] Michael A. Nielsen and Isaac I. Chuang, Quantum Computation and Quantum Information, Cambridge University Press(2002).
*[2] Phillip Kaye, Raymond Laflamme and Michele Mosca, An Introduction to Quantum Computing, Oxford University Press(2007).
*[3] Jamie Smith and Michele Mosca, arXiv:1001.0767v2 [quant-ph]
*[4] Lecture notes of John Preskill, California Institute of Technology: http://theory.caltech.edu/~preskill/ph229/