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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!

  1. $\langle\psi|U^{\dagger}MU|\psi\rangle$

  2. $|0\rangle\langle0|$ or $|0\rangle |0\rangle$

  3. $ {\oplus}$

  4. $|0\rangle^{\otimes n}$

  5. 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!

  6. 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.

  7. Is it a NOT gate? XOR gate? Or denoting any possible operation?

  8. 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?

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    $\begingroup$ It looks like you're having the age old issue of mathematicians and physicists having different notation for linear algebra. abstrusegoose.com/128 and the next 2 $\endgroup$ – AHusain Feb 10 at 2:20
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Get hold of a copy of the Nielsen and Chuang textbook and read the first few chapters. If you google it you'll find the PDF version easily, although, of course, I'd recommend buying it. Almost all the notation you mention is explained in chapters 1 and 2 of the textbook. Catching up with notation is no big deal if you have studied linear algebra before. Even if you haven't, the book has a whole chapter dedicated to linear algebra, which you can learn from scratch.

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