1. Limits and Horizon of Computing
Post silicon computing

2. Limits
Theoretical limit: Some unsolvable problems Halting problem

3. Limits Theoretical limit: Some unsolvable problems Halting problem
Practical Limits: Too slow to be worth it

4. Example
Know there is a binary key of n digits that decrypts data… try every possible key …

5. Example
Know there is a binary key of n digits that decrypts data… try every possible key
O(2n) n
Possible keys 1 2 4 3 8 16 … 10
1024 20
~1,000,000 30
~1,000,000,000 40
~1,000,000,000,000

6. Example
Traveling Salesman Problem:

7. Example O(n!) Traveling Salesman Problem: Towns Routes 2 3 6 4 24 5
120 … 10
3,628,800 20
2,432,902,008,176,640,000

8. Classes
Exponential and factorial growth:

9. Impossible For Any Significant Size
Classes
Exponential and factorial growth:
Impossible For Any Significant Size
Doable

10. Classes
Polynomial: Work is O(nm) for some constant m O(1), O(logn), O(n), O(n*logn), O(n2), O(n3)
Non-polynomial: More time than polynomial O(2n), O(n!)

11. P vs NP

12. Other Hard Problems Factoring Integers – why RSA works!
Many optimization problems

13. But Moore's Law! Moore's Law "solves" polynomial problems
18 months, 2x as fast
3 years, 4x as fast
6 years, 16x as fast

14. But Moore's Law! Moore's Law "solves" polynomial problems
18 months, 2x as fast
3 years, 4x as fast
6 years, 16x as fast
O(n) : do 16x more work
O(n2) : do 4x more work

15. But Moore's Law!
More's law not much help with non- polynomial problems
2n doubles each time n increases by 1

16. But Moore's Law!
More's law not much help with non- polynomial problems
2n doubles each time n increases by 1
18 months do +1 units of work
3 years do +2 units of work
6 years do +4 units of work

17. Silicon
Reaching limits of ability to work with silicon…

18. Tiny tiny tiny Transistors are small http://htwins.net/scale2/
Modern chip: 14 nanometer scale
Transistor ~30 atoms across
30 atoms!!!

19. New Materials
Trick 1: New materials

20. Molecular Computation
Trick 2: Molecular computation
DNA Storage: 700 terabytes in one gram

21. Longer Term?
Moore's law is going to break…

22. Longer Term? Moore's law is going to break…
Even it can't help us with some problems…

23. Longer Term?
Need something completely different

24. Quantum Mechanics Trick 3: Quantum Mechanics
Rules that govern sub atomic physics
Particles can pass through solid objects
Particles can be entangled and read each other's "minds" across the universe
Everything is random until it is observed… then it changes to match observation

25. Video Quantum Computers:
What they are:
How they work:

26. Optimization Problem
Each switch is on or off – make the highest total:

27. Classical Approach 6 switches, each on or off
26 or 32 possible states… try them one by one

28. Scaling

29. Quantum Approach Switches can be both on and off…
Test all possible solution at once!
Observing forces qubits to one state…
…set up so desired answer is most likely state

30. 100 A problem space is represented by 100 bits 2100 possible answers
Conventional computer:
1,000,000,000 solutions checked per second
40 trillion years to solve

31. 100 A problem space is represented by 100 bits 2100 possible answers
Quantum computer with 100 bits
Try all states at once
Seconds (+ lots of setup time)
Answer is only probably correct – need multiple runs to confirm…

32. Reality
Solving 3 x 5 = 15 the hard way