Quantum Computing CPSC 321

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Quantum ComputingCPSC 321

• Andreas Klappenecker

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Plan

• T November 16 Multithreading
• R November 18 Quantum Computing
• T November 23 QC Exam prep
• R November 25 Thanksgiving
• M November 29 Review ???
• T November 30 Exam
• R December 02 Summary and Outlook
• T December 07 move to November 29?

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Announcements

• Todays lecture 1245pm-130pm
• 1245pm-115pm Basic of QC
• 115pm-130pm Evaluation
• Bonfire memorial dedication

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In Memoriam
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Moores Law

• Gordon Moore observed in 1965 that the number of
  transistors per integrated circuit seems to
  follow an exponential law, and he predicted that
  future developments will follow this trend.
• Remarkably, he made his observation about 4 years
  after the production of the first integrated
  circuit.
• The number of transistors is supposed to double
  every 18-24 months.

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The End of Moores Law?

• Sometime in 2020-2030, computations will occur at
  an atomic scale.
• We have to deal with quantum effects
• Pessimists Noise
• Optimists New computational paradigm

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Quantum Bits
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Polarized Light
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Quantum Cryptography
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Quantum Algorithms

• Searching unsorted data
• Classical algorithms linear complexity
• Quantum algorithms O(n1/2)
• Factoring Integers
• Classical algorithms Exponential complexity
• Quantum algorithms Polynomial complexity

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Complexity Questions

• Can quantum algorithms really outperform
  classical algorithms?
• Can we solve NP-hard problems in polynomial time
  on a quantum computer?
• Can we solve problems in NP O coNP in polynomial
  time on a quantum computer?
• Can we solve distributed computing problems with
  lower message complexity?

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The Stern-Gerlach Experiment
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Quantum Bits
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Memory
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Quantum Computing in a Nutshell
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Operations on a Quantum Computer
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Example
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Teleportation
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Teleportation Its Simple!
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Background

• State of a quantum computer
• A complex vector of dimension 2n
• 00gt11gt (1,0,0,1)
• Operations
• Unitary matrices (linear operations)
• Measurements
• Probabilistic (amplify quantum effects)
• Classical Picture
• Calculate A00gt or A11gt, or both A(00gt11gt)

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Conclusion

• The basic model is simple
• Everyone can write a simulator of a quantum
  computer in a very short time
• The computational model is different you need
  time to absorb that!
• Numerous potential technologies!