UC Berkley – Lecture Notes from Vazirani on Quantum Computing

Posted on by paschmann

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.

  • Electrons are delicate
  • We can make the light faint, but we may miss the measurement

Lecture 2: Qubits

“The energy of an atom is quantized” … The energy of the electron is put into a discrete state. (Essentially limiting the energy of the electron)

Hydrogen Atom, can be in the ground or 1st excited state, but not any higher.

Ground state = 0, Excited state = 1

Can be “partly” in one state or the other. Probability of one state or the other.

Electron can end up in a “superposition” state where it has a complex amplitude of being 

Alpha | 0> + Beta | 1 > 

The reason we do one of 1/Sq2 is that we need the state “normalized” … = | Alpha | ^2  + | Beta | ^2 must = 1
This is because we need the probabilities to add up to one.

When you are “not measuring” the electron is in the super position, when you do measure, it decides which position and you get the measurement back.

Alpha and Beta are complex numbers, because they are normalized, they add up to 1 and are considered Unit vectors

| 0 > =  (1/0)
| 1 > = (0 /1)

Qubits allow you to work with a much simpler setting.

Lecture 3: 

 Go through again and make notes