1. Distributed Quantum Computing Using the most precise description of our world to solve some of the hardest problems by Matthias Egli Based on the paper „Distributed Quantum Computing“ by Harry Buhrman and Hein Röhrig

2. These slides are just an addition to the math shown on the blackboard

3. Motivation

4. Communication Complexity n AliceBob

5. Communication Complexity ? AliceBob

6. Communication Complexity Classical ComputerQuantum Computer Disjointnessn Equality (Promise)nlog(n)

7. Speedup with Quantum Computers Classical ComputerQuantum Computer Factorization Searchn Deutsch-Jozsan1

8. Basics The qubit Superposition Entanglement Quantum Gate

9. Deutsch-Josza Algorithm Promise: Function is constant or balanced

10. Deutsch-Josza Algorithm nClasscial ComputerClassical randomizedQuantum Computer 2211 nnLog(n)1

11. Communication

12. Qubit Communication AliceBob

13. Communication Types Entanglement Communication

14. Classical bits with EPR Pairs Communication AliceBob

15. Communication Types Qubit with shared EPR Pairs Communication AliceBob

16. Deutsch-Jozsa Communication

17. Deutsch-Josza Communication Y: 00101100 AliceBob X: 00101100

18. Deutsch-Josza Communication AliceBob X = Y ? Y: 00101100X: 00101100

19. Deutsch-Josza Communication Y: 00101100 AliceBob X: 00101100 X = Y ? n

20. Deutsch-Josza Communication Y: 00101100X: 00101100 X = Y ? ? AliceBob

21. Deutsch-Josza Communication Y: 00101100X: 00101100 X = Y ? Promise: Hamming Distance = n/2 or 0 AliceBob

22. Deutsch-Josza Communication Y: 00101100X: 00101100 X = Y ? Promise: Hamming Distance = n/2 or 0 XOR AliceBob

23. Deutsch-Josza Communication Y: 00101100X: 00101100 X = Y ? Promise: Hamming Distance = n/2 or 0 AliceBob

24. Alice

25. Bob log(n)+1

26. Bob

28. Deutsch-Jozsa Algorithm

29. What else is possible? Leader Election Disjointness […]

30. Sources Caltech Introduction to Quantum Computing http://www.theory.caltech.edu/people/preskill/ph229/notes/chap1.pdf http://www.theory.caltech.edu/people/preskill/ph229/notes/chap1.pdf Distributed Quantum Computing Harry Buhrmann and Hein Röhrig Can quantum mechanics help distributed computing? Anne Broadbent and Alain Tapp Distributed Quantum Computing: A New Frontier in Distributed Systems or Science Fiction? Vasil S. Denchev and Gopal Pandurangan

31. Questions?