Your SlideShare is downloading. ×
0
Quantum Computation: Is RSA All Factored Out
Quantum Computation: Is RSA All Factored Out
Quantum Computation: Is RSA All Factored Out
Quantum Computation: Is RSA All Factored Out
Quantum Computation: Is RSA All Factored Out
Quantum Computation: Is RSA All Factored Out
Quantum Computation: Is RSA All Factored Out
Quantum Computation: Is RSA All Factored Out
Quantum Computation: Is RSA All Factored Out
Quantum Computation: Is RSA All Factored Out
Quantum Computation: Is RSA All Factored Out
Quantum Computation: Is RSA All Factored Out
Quantum Computation: Is RSA All Factored Out
Quantum Computation: Is RSA All Factored Out
Quantum Computation: Is RSA All Factored Out
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

Quantum Computation: Is RSA All Factored Out

1,324

Published on

Published in: Technology
0 Comments
2 Likes
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total Views
1,324
On Slideshare
0
From Embeds
0
Number of Embeds
5
Actions
Shares
0
Downloads
93
Comments
0
Likes
2
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. Quantum ComputationIs RSA All Factored Out?
    J. Caleb Wherry
    Austin Peay State University
  • 2. Outline
    Introduction to ClassicalComputing
    • Classical Bits & Logic Gates
    • 3. ComputationalComplexity Classes
    Introduction to Quantum Computing
    • History
    • 4. Qubits, Quantum Logic Gates, & BQP Complexity Class
    • 5. Entanglement, Teleportation, & SuperdenseCoding
    • 6. Applications of Quantum Computers
    • 7. ExponentiallyFaster Factoring
    Future of Quantum Computers
    • Advantages & Disadvantages
  • Introduction to ClassicalComputing
    How do classical computers work?
    • Classical Bits:
    0 or 1
    Low Voltage High Voltage
    • UniversalLogic Gates:
  • Introduction to ClassicalComputing
    ComputationalComplexity Classes
  • 8. Introduction to Quantum Computing
    History
    • Paul Benioff (1980)
    • 9. Arrays of spins (atoms) couldperformreversablecomputing
    • 10. Richard Feynman (1982)
    • 11. Proposed first non-trivial application for quantum computing (simulating quantum systems)
    • 12. Seth Lloyd (1993)
    • 13. Showed how quantum computers couldbeconstructed
    • 14. Peter Shor (1994)
    • 15. Discovered first « killer app » for quantum computers
    • 16. Factor numbersexponentiallyfasterthanclassical computers
  • Introduction to Quantum Computing
    How do quantum computers work?
    • Quantum Bits (Qubits):
    |0 or |1
    Superposition
    |0 + |1
    • Quantum Logic Gates:
    Allows us to compute 2n bits of information!!!
  • 17. Introduction to Quantum Computing
    Entanglement
    • « Spookinessat a distance. » - Einstein
    • 18. No seen interactions betweenparticles
    Teleportation
    • Like Star Trek!
    Superdensecoding
    • Multiple bits of information with one bit
  • Introduction to Quantum Computing
    New ComputationalComplexity Classes
    Image Source: http://en.wikipedia.org/wiki/Quantum_computer
  • 19. Applications of Quantum Computers
    Factoring
    • Public-keycryptography (RSA)
    ClassicalMeans
    • r = m*q wherem,q are prime
    • 20. Ways to computefactors?
    • 21. Brute force
    • 22. GCD
    • 23. Exponentionally hard
  • Applications of Quantum Computers
    Factoring by quantum means:
    • Exponentaillyfasterthanclassical computers
    • 24. ~O(N2)
    • 25. Double-slitexperiment
    • 26. Use of entanglement & destructive interference
    • 27. Poses a major threat to toclassicalmethods
    • 28. New types of cryptographycanbeused
    • 29. Lattice-based
  • Applications of Quantum Computers
    UnorderedDatabaseSearching
    • Based on Grover’salgorithm
    • 30. Probabilisticalgorithm
    • 31. ~O(√N)
    Simulating quantum systems
    • Ability to simulate quantum systemsefficiently
  • Future of Quantum Computers
    Moore’s Law
    • ~10-20 years, currentcomputingwillbe on the nano scale
    • 32. Quantum forces willbeatwork
    • 33. New research shows promise
    • 34. Ability to solvesystems of trillions of equations
    Advantages
    • Bring about new encryption techniques
    • 35. Accuratlysimulate quantum systems
    Disadvantages/Shortcomings
    • Cannot (as of yet) solve NP problems
    • 36. Extremeenvironmentsneeded to work in
  • References
    Bernstein, E., Vazirani, U., « Quantum ComplexityTheory. »
    Chuang, I., « Quantum Algorithms and theirimplementations: QuISU – An Introduction for Undergraduates. »
    Lloyd, S., « Quantum Information Science. »
    Nielson, M., Chuang, I., « Quantum Computation and Quantum Information. »
  • 37. SpecialThanks
    MIT QuISU
    Quantum Information Science for Undergraduates
    http://www.rle.mit.edu/quisu
  • 38. Questions?
    Comments?

×