Quantum ComputingCPSC 321

Andreas Klappenecker

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?

Announcements

• Today’s lecture 12:45pm-1:30pm• 12:45pm-1:15pm Basic of QC• 1:15pm-1:30pm Evaluation • Bonfire memorial dedication

In Memoriam

Moore’s 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.

The End of Moore’s 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

Quantum Bits

Polarized Light

Quantum Cryptography

Quantum Algorithms

• Searching unsorted data• Classical algorithms: linear complexity• Quantum algorithms: O(n1/2)

• Factoring Integers• Classical algorithms: Exponential

complexity• Quantum algorithms: Polynomial

complexity

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 coNP in polynomial time on a quantum computer?

• Can we solve distributed computing problems with lower message complexity?

The Stern-Gerlach Experiment

Quantum Bits

Memory

Quantum Computing in a Nutshell

Operations on a Quantum Computer

Example

Teleportation

Teleportation – It’s Simple!

Background

• State of a quantum computer • A complex vector of dimension 2n

• |00>+|11> = (1,0,0,1)

• Operations• Unitary matrices (linear operations)

• Measurements• Probabilistic (amplify quantum effects)

• Classical Picture• Calculate A|00> or A|11>, or both A(|00>+|11>)

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!