1. Quantum Computing CPSC 321 Andreas Klappenecker

2. 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?

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

4. In Memoriam

5. 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.

6. 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

7. Quantum Bits

8. Polarized Light

9. Quantum Cryptography

10. Quantum Algorithms Searching unsorted data Classical algorithms: linear complexity Quantum algorithms: O(n 1/2 ) Factoring Integers Classical algorithms: Exponential complexity Quantum algorithms: Polynomial complexity

11. 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?

12. The Stern-Gerlach Experiment

13. Quantum Bits

14. Memory

15. Quantum Computing in a Nutshell

16. Operations on a Quantum Computer

17. Example

18. Teleportation

19. Teleportation – It’s Simple!

20. Background State of a quantum computer A complex vector of dimension 2 n |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>)

21. 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!