There is a vast amount of new notations which would be new even to Ph.D. in math. How on Earth can I catch up with all of this? Is there a place online which is devoted to the QC syntax? I would like to show a few examples, if someone can explain even just them, it would be of much help!
$|0\rangle\langle0|$ or $|0\rangle |0\rangle$
I have no clue it looks like some sort of inner product. I saw somewhere this equals the probability of $U$. (Where M is a measurement matrix?) Have no idea!
The first I saw something like it's a projection of any vector on zero. So this is an operator, not a vector. On the other hand, not sure about $|0\rangle |0\rangle$. Thought saw them somewhere.
Is it a NOT gate? XOR gate? Or denoting any possible operation?
Vector zero, and composition of subscript n appearing above like a 'power'.
Can someone clear up the confusion? Or offering a place to look them all and their definitions up?