basic quantum system, 4.2 Observable, and others, IBM quantum experience, hello world example

Chapter 4

4.1. quatum states

particle and waves

basic quantum system: a particle at discrete positions on a line; single particle spin system

state

complex amplitudes

superposition

normalized state

spin

Transition amplitudes: In quantum mechanics, the transition amplitude is a complex number that encodes the probability amplitude for a system to evolve from one state to another.  Imagine you're flipping through radio stations. Each station you might land on can be thought of as a "state." Now, the transition amplitude tells you how likely it is for your radio to transition from one specific station to another as you flip through the channels. It gives you a complex number, and the square of its magnitude tells you the probability of making that specific transition.

Start here on 9/7

4.2 Observable

hermitian operator 

expected values of observing \Omega repeatly on the same state \psi

https://docs.quantum-computing.ibm.com/start/hello-world

variance

summary: observables are represented by hermitian operators. 

expected value of observing \Omega on |psi>