Describes a simple quantum gate, the Hadamard gate. Part of a series on "Quantum computing for the determined". The full series is at: www.youtube.com...
Hi, this is one of the clearest lecture on the subject I have found, congrats! I would like to contribute with my two cents: Sometimes using the same notation for the operator and state vectors may help clarity for the students. My suggestion is to write H like: H = |0> = kronecker (l, m) = (1 for l = m and 0 otherwise) we simply replace = = 0, = = 1 So, by applying H to base states we get H |0>= |0> + |1> + |0> - |1> = (|0>+|1>) / square root of 2 symmetrically: H |1>= |0> + |1> + |0> - |1> = (|0>-|1>) / square root of 2 For those asking about the appearance of the square root, it has to appear so the results stays orthonormal. Sorry for my bad writing, I'm not a native speaker.
Yeah, this is a better notation, but he would have to explain all you explained in the first videos... But it is surely a clearer way of doing things. I'm also not a native speaker, but I can safely say I've read native speakers not writing as well as you did, so I think you surpassed the point of having to apologize for not writing the language properly - and I'm just saying that because eventually this will happen...
Oops, I didn't notice the parent asking about the Hadamard gate. Yes, you're quite right, in the alpha=beta case you go back to |0>. (Actually, a multiple of |0>, I guess, depending on the exact value of alpha.) Thanks for the correction.
Michael, your videos have helped my progress and understanding of quantum physics for years! Additionally, they (your videos on quantum computing) helped me refresh my knowledge as I conduct my research.
Great video. I watched a bunch of videos on the Hadamard gate, and although I understood what it was theoretically, your video helped me understand what it really did. Thanks for that.
Nothing happens with the NOT gate, but if you look at the equations you see that if alpha = beta and you apply the Hadamard gate you get the |0> state.
+Rish Fulmali The best I can suggest is the article by Eleanor Rieffel called 'An Introduction to Quantum Computing for Non-Physicists', it is free to download from arXiv, and includes introduction to the notation and mathematics of this. One help it doesn't give but I can give, is that when Tensor products are used in quantum computing, they typically speak of specifically the Kronecker product, as Tensor is more of an umbrella term.
I'm sure it can. It can probably be reduced even further. Keep in mind, though, that this is not the kind of course for people that already know all the concepts. It is for people with a background of linear algebra, so that the mathematical knowledge can be the least limiting factor. Also, it is harder to make a good short video than a good longer one.
VeteranVandal well said. My professor needs and hour and half hour to talk about this and only half of our classmates are able to get it. Therefore, 90mins vs 14mins
TING-CHIEH Huang And the reason for that is that when you have such a long time you add not the essential stuff to the subject - and this can be important, if done properly (of course it can be done in a bad manner, but... teaching an exact science is not an exact science). Of course when you strip something from an explanation you have to work with previous knowledge. Then, while two minutes might be enough to explain something, explaining it in two minutes with nobody understanding what you are saying is exactly what "not explaining" means. I believe it is generally better to have a talk in 90 minutes with 50% of the people understanding what you are explainig than one with 2 minutes with a similar 1% index.
Hi, this is one of the clearest lecture on the subject I have found, congrats! I would like to contribute with my two cents: Sometimes using the same notation for the operator and state vectors may help clarity for the students. My suggestion is to write H like:
H = |0> = kronecker (l, m) = (1 for l = m and 0 otherwise)
we simply replace = = 0, = = 1
So, by applying H to base states we get
H |0>= |0> + |1> + |0> - |1> =
(|0>+|1>) / square root of 2
symmetrically:
H |1>= |0> + |1> + |0> - |1> =
(|0>-|1>) / square root of 2
For those asking about the appearance of the square root, it has to appear so the results stays orthonormal.
Sorry for my bad writing, I'm not a native speaker.
Yeah, this is a better notation, but he would have to explain all you explained in the first videos... But it is surely a clearer way of doing things.
I'm also not a native speaker, but I can safely say I've read native speakers not writing as well as you did, so I think you surpassed the point of having to apologize for not writing the language properly - and I'm just saying that because eventually this will happen...
The most comprehensive source till now!
If |0> and |1> are the two values of spin...
What's the meaning of -|1> ?
Oops, I didn't notice the parent asking about the Hadamard gate. Yes, you're quite right, in the alpha=beta case you go back to |0>. (Actually, a multiple of |0>, I guess, depending on the exact value of alpha.) Thanks for the correction.
Michael, your videos have helped my progress and understanding of quantum physics for years! Additionally, they (your videos on quantum computing) helped me refresh my knowledge as I conduct my research.
Great video. I watched a bunch of videos on the Hadamard gate, and although I understood what it was theoretically, your video helped me understand what it really did. Thanks for that.
Note that the columns of H is orthogonal i.e. independent (unit) vectors in R2.
How do you make a Hadamard gate physically, on the laboratory? For example in a superconductor quantum circuit.
Nothing happens with the NOT gate, but if you look at the equations you see that if alpha = beta and you apply the Hadamard gate you get the |0> state.
Is H analogues to rotation of the vector in the complex plane !
Yes, that's right.
These are great! Thanks for making them!
hm, so NOT gate flips around 45º, H flips around 22.5º
Wouldn't the NOT flip it 90 and H flip it 45?
@@Decimated_By_A_Train Yep, I think you're right.
Very nice, thank you for making these excellent videos!
why square root 2?
What about through Constantinople??
in a 13 minute video about hadamard gates my man is asking about constantinople
Its name is currently Istanbul belongs to Turks
anyone know where i could get the background info to understand this
+Rish Fulmali The best I can suggest is the article by Eleanor Rieffel called 'An Introduction to Quantum Computing for Non-Physicists', it is free to download from arXiv, and includes introduction to the notation and mathematics of this. One help it doesn't give but I can give, is that when Tensor products are used in quantum computing, they typically speak of specifically the Kronecker product, as Tensor is more of an umbrella term.
SausageOfBirth Thanks, really want to get into all this stuff but had no idea where to start
college
what is the reason of that 1/ root2?
to normalize, a matrix represented by gate has to be a unitary matrix, A_transpose * A = I
One could use graphical interpretation of the Hadamard gate on a unit disk.
So far I haven't seen any complex vector.
Awesome! :D Thanks for the lecture :D
not a matrix but a spectrum of probability...but a matrix will have to do till you update the formula
Okay, guess I'm done with this series for now...
yeah that explains it if you already know the material. otherwise, not at all.
The whole talk can be reduced to 2 minutes.
I'm sure it can. It can probably be reduced even further.
Keep in mind, though, that this is not the kind of course for people that already know all the concepts. It is for people with a background of linear algebra, so that the mathematical knowledge can be the least limiting factor.
Also, it is harder to make a good short video than a good longer one.
VeteranVandal well said. My professor needs and hour and half hour to talk about this and only half of our classmates are able to get it. Therefore, 90mins vs 14mins
TING-CHIEH Huang And the reason for that is that when you have such a long time you add not the essential stuff to the subject - and this can be important, if done properly (of course it can be done in a bad manner, but... teaching an exact science is not an exact science). Of course when you strip something from an explanation you have to work with previous knowledge. Then, while two minutes might be enough to explain something, explaining it in two minutes with nobody understanding what you are saying is exactly what "not explaining" means.
I believe it is generally better to have a talk in 90 minutes with 50% of the people understanding what you are explainig than one with 2 minutes with a similar 1% index.
+Peng Wu It could but this is easy to follow. You can jump ahead. I like it a lot this way.