Welcome to the presentation on Computational Capabilities with Quantum Computer

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Welcome to the presentation onComputational
Capabilities with Quantum Computer

• By
• Anil Kumar Javali

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Agenda

• Introduction
• Quantum Parallelism
• Quantum Algorithms
• NMR for Quantum Computer ( Q.C. )
• CNOT Gate for Q. C
• Obstacles
• References

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Introduction

• What is a Q.C.

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Classical Computer (C.C) vs. Q.C.
bit
qubit
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Power Potential of Q.C
500

• A system with 500 qubits gt 2 states
• Each state single list of 500 0s 1s
• 99 100th qubit
• Best know encryption method RSA, will no longer
  be the best

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Quantum Interference
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Quantum Interference (contd)
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CC vs QC

• Best know algorithm for classical computer runs
  in O(exp(64/3) (ln N) (ln ln N) ) steps
• For ex, in 1994, 129 digit number, factorized,
  1600 workstations, 8 months.
• Similarly, 800,000 years to factor a 250 digit
  number 10 years to factor a 1000 digit number

1/3
2/3
2/3
25
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CC vs QC (cont.)
2E

• Where as, Q.C takes O((log N) ) steps
• 1000 digit number would take only a few million
  steps.
• Public key cryptosystems based on factoring may
  be breakable

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Quantum Algorithms

• Shors Algorithm
• Grovers Algorithm

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Shors Algorithm

• Finds factors of a very large number
• For ex N 91,
• Choose a co-prime of 91 which is 729
• i.e., 729 1 (mod 91)
• gt 28 x 26 0 (mod 91)
• gt either gcd(28,91) or gcd(26,91) will give the
  factors of 91
• Here, both gives different factors, those are 7
  13
• 91 7 x 13

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Physical Implementation of Q.C

• NMR (nuclear magnetic resonance)-Based Q.C
• Heteropolymer-Based Q.C
• Ion Trap Based Q.C
• Cavity QED-Based Q.C

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NMR for Q.C
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How NMR works

• Takes pulse signal as input
• Acts on the qubit molecules
• Qubit changes its state
• Measure the density of the qubit to know its new
  state

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How NMR works (cont.)

• Qubits initial state is represented by its
  density which is represented in the form of
  matrix ( a )
• When input pulse signal x acts on a
• Density of qubit changes to final state b
• We can represent the above operation symbolically
  as a X x b

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Genetic Algorithm (G.A) to find the pulse signal

• Using GA, find the pulse signal x
• Train the network using GA for different test
  cases
• Test the network for new values

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My contribution towards NMR QC

• Implementing GA to find the pulse signal

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Basic gates for C.C

• AND, OR, NOT
• Original 2 inputs cant be restored
• Electronic circuits are not reversible

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Basic Gates for Q.C

• There are AND, OR and NOT gates for Q.C
• They are not the smallest units for Q.C
• Where as CNOT ( controlled NOT ) is
• CNOT represent AND, OR NOT operations

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Universal CNOT gate for Q.C
CONTROL
CONNECTION
TARGET
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How CNOT works
IN IN OUT OUT
CONTROL TARGET CONTROL TARGET
0 0 0 0
0 1 0 1
1 0 1 1
1 1 1 0
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Obstacles

• There are many obstacles to be resolved to make
  Q.C a reality like,
• Quantum Entanglement
• Quantum Teleportation
• Quantum Error Correction

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References

• Isaac L Chuang, M A Nielsen, Quantum Computation
  and Information, Dec 2000
• Center for Quantum Computation,
  http//www.qubit.com/
• Jacob West, The Quantum Computer,
  http//www.cs.caltech.edu/westside/quantum-intro.
  html April 28, 2000
• Samuel L. Braunstein, Quantum Computation,
  http//www.informatics.bangor.ac.uk/schmuel/comp/
  comp.html Aug 23, 1995

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Questions ?