Notes: 

Quantum Systems are exponentially powerful

Based on particles: 2^500 – More particles in the universe

Challenges:

• Not all problems are well suited
• Need to understand Q Mechanics

Qubit – simplest quantum system

Entanglement-

• Bell Inequalities
• Teleportation

Lecture 1: Double Slit Experiment

• Is light a particle or a wave?
• If light was a particle, it would be like a bullet, and we would see the two beams overlap each other:

• Strange that if both holes are open why we get this strange interference pattern.
• Why did the count drop when both holes were open? From a decent amount, to nearly zero.
• If we use bullets, we would see a whole number of bullets that get through
• If we use water & waves, we get the same interference pattern.

If we add a measuring device just after the slits to track which slit the electron goes through, it “disrupts” the measurement and we get the 2nd pattern. If we use a very slight/dim light enough light, we get the 3rd “expected” pattern, but we also miss a lot of the electrons and may not capture the pattern.

= Hesienburgs uncertainty principle = Impossible to design apparatus which can detect which slit it went through without disturbing the interference pattern. read more

Traveling sales person problem

Solve problems which are NP hard – and they can’t be solved in polynomial time.

P versus NP problem: full polynomial versus nondeterministic polynomial problem

A P problem is one that can be solved in “polynomial time,” which means that an algorithm exists for its solution such that the number of steps in the algorithm is bounded by a polynomial function of n, where n corresponds to the length of the input for the problem. Thus, P problems are said to be easy, or tractable. A problem is called NP if its solution can be guessed and verified in polynomial time, and nondeterministic means that no particular rule is followed to make the guess. read more