What wasn't clear for me, and also made me think that it seems you have to know the answer during the process, was the symmetry in reference to the tilted axis. What's that operation ?
I understand that you can change the sign of the axis representing the correct answer. But obviously , if you repeat this step , there is no convergence and you just flip the x axis indefinitely.
So between each "sign change of the right answer vector " step , you make a rotation /symmetry of the current vector state , following a plane of symetry that seems to be known only by the "correct answer" but affecting all the vector components (it is not anymore only the correct answer that change sign, but all vector that change their value ).
How does this step can occur ? I have intuition that it may just be normalization , but I cannot understand.
As I (kinda) understood it, the two reflections are happing about separate axes. The first reflection flips the sign of only the answer axis contribution (Z Gate?) and then the second flips everything against the hidden state axis. So the answer axis magnitude gets amplified, since the last flip pushed it further away from the state axis. The two flips make the next state axis, that has an increased answer direction component, and the process can repeat.
Hopefully that’s close enough or someone can correct me 😅
What I understand is that the verification function does something that was programmed to do, or learned to do (like a classification model), and it is a "black-box" because we can't "see" what it does, as opposed to physical logic gates that we can trace their behaviour. So, in this case, the output being "true" or "false" is an assumption we are making because it could be any other output, right?
Thus, if we input some values that are wrong, the Grover's algorithm will "miss" the flippings because the vector is not there in the dimension it was supposed to be in order to make it collapse into 1 or 0?
Finally, in the Sudoku case, I would have to throw random solutions into the quantum function and check the result as we would normally do? How would that be faster?
I did follow the two operations in the first video, but I think the Z gate explanation did help crystallize it, compared to just taking it as a given. Interesting, as I feel either explanation should have been equivalent for the main question.
Hello, and thank you.
What wasn't clear for me, and also made me think that it seems you have to know the answer during the process, was the symmetry in reference to the tilted axis. What's that operation ?
I understand that you can change the sign of the axis representing the correct answer. But obviously , if you repeat this step , there is no convergence and you just flip the x axis indefinitely.
So between each "sign change of the right answer vector " step , you make a rotation /symmetry of the current vector state , following a plane of symetry that seems to be known only by the "correct answer" but affecting all the vector components (it is not anymore only the correct answer that change sign, but all vector that change their value ).
How does this step can occur ? I have intuition that it may just be normalization , but I cannot understand.
As I (kinda) understood it, the two reflections are happing about separate axes. The first reflection flips the sign of only the answer axis contribution (Z Gate?) and then the second flips everything against the hidden state axis. So the answer axis magnitude gets amplified, since the last flip pushed it further away from the state axis. The two flips make the next state axis, that has an increased answer direction component, and the process can repeat.
Hopefully that’s close enough or someone can correct me 😅
It probably would have helped to put a second 2D graph next to it, where the vertical axis was a random incorrect answer.
What I understand is that the verification function does something that was programmed to do, or learned to do (like a classification model), and it is a "black-box" because we can't "see" what it does, as opposed to physical logic gates that we can trace their behaviour. So, in this case, the output being "true" or "false" is an assumption we are making because it could be any other output, right?
Thus, if we input some values that are wrong, the Grover's algorithm will "miss" the flippings because the vector is not there in the dimension it was supposed to be in order to make it collapse into 1 or 0?
Finally, in the Sudoku case, I would have to throw random solutions into the quantum function and check the result as we would normally do? How would that be faster?
Thank you. I had this confusion, but I was going to wait for the next videos to drop before spending too much time on it.
I did follow the two operations in the first video, but I think the Z gate explanation did help crystallize it, compared to just taking it as a given. Interesting, as I feel either explanation should have been equivalent for the main question.