I think I found a few errors in Changing Perspective Errors in the Quantum Fourier Transform Module in the codebook.
Error 1:
I believe the roots of Unity in the Photo should be x_1 = 1, - x_1 = -1, x_2 = i, and -x_2 = -i. This is consistent with the rest of the section, which explicitly states the roots of unity in this case are [1,-1,i,-i].
Error 2:
I am not entirely sure if this is an error, because the math does end up coming to the right solution. The notation lists X_{ij}, where i denotes the row and j denotes the column. However, the summation shown switches i and j around. If i = the ith row and j = the jth column, then the summation would contain the term w^{ik}w^{-jk} , rather than w^{jk}w^{-ik} . However, it does still reach the same conclusion, (the matrix is unitary), so there is a good chance I am missing something. Thought I would post it here to see if you guys would take a look and see if there if you guys agree.
Also, thank you for the corrections to other errors pointed out in previous posts. I greatly appreciate it, and hope you guys continue to build out the codebook. It has been an invaluable resource in learning QIS.
Hi @connor_gambla !
Thanks for reporting this.
You are correct, there is a sign mistake in the third root, x_2=i and not i. However, I do think that the fourth should be -x_2=-i.
We recently redid the images for better looking and this mistake got through.
I fixed it and the change will be live later today or tomorrow.
1 Like
Hi Daniela,
No problem happy to help. I agree that x_2 = i and -x_2 = -i, I made a typo in my response. Just corrected it. Thank you again for the changes.
Best,
Connor
Mmm and with respect to your second question. I agree with the fact that it isn’t a mistake, I would probably say that the notation gets inconsistent with the expected indexing.
What I mean is that strictly speaking, those indices i, j refer to the new matrix X, the multiplication, and not the old matrices U and the conjugate. And this summation is just a way of writing that matrix so it is not necessary to maintain the same “expected” indexing.
However, you are right in saying that it would be more clear if we wrote w^{ik}w^{-jk} given that the matrix multiplication is the row times the column and the connection that we all make is that in order to write this summation, one should be referring to the multiplication of the U s and their indexed elements.
I don’t know if I was super clear, apologies if I wasn’t. I will consider making this change as well.
1 Like
Sound goods. I think a change to the index to better reflect index notation would be a good change, but I understand if that isn’t a priority right now.
