Limits and Horizon of Computing Post silicon computing

Limits Theoretical limit: Some unsolvable problems Halting problem

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

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

Example Know there is a binary key of n digits that decrypts data… try every possible key nPossible keys …… O(2 n )

Example Traveling Salesman Problem:

Example Traveling Salesman Problem, Brute Force: TownsRoutes …… O(n!)

Classes Exponential and factorial growth:

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

Classes Polynomial: Work is O(n m ) for some constant m O(1), O(logn), O(n), O(n*logn), O(n 2 ), O(n 3 ) Worse than polynomial: More time than polynomial O(2 n ), O(n!)

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

P vs NP

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

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(n 2 ) : do 4x more work

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

But Moore's Law! More's law not much help with non- polynomial problems – 2 n 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

Silicon Reaching limits of ability to work with silicon…

Tiny tiny tiny Transistors are small Modern chip: 14 nanometer scale Transistor ~30 atoms across 30 atoms!!!

Single Atom Transistor? Built in lab… not real practical

3D Gates Trick 1: Fancier ways of building with silicon

3D Gates Trick 2: New materials

Molecular Computation Trick 3: Molecular computation DNA Storage: 700 terabytes in one gram

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

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

Longer Term? Need something completely different

Quantum Mechanics Trick 4: 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

Video Quantum Computers: – What they are: – How they work:

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

Classical Approach 6 switches, each on or off 2 6 or 32 possible states… try them one by one

Scaling

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

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

100 A problem space is represented by 100 bits 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…

Reality Solving 3 x 5 = 15 the hard way