This simple explanation of the 1-qubit QFT as Hadamard gate deserves the prize of the best short QFT explanation ever ! First time I can finally intuitively understand what is going on ! Excellent video.

oh god! the best QFT explanation ever on KZfaq that I can find. Thank you so much professor!

Explained perfectly. - limited to the essentials - only the math that is necessary - Explicit reference to the important parts of the content - very clear, as far as this is possible with quantum computing This also applies to the following videos in the series.

Abraham, I'm a 78 years old student. I Fully agree with Gerardo Moscatelly, Your explanation of the notation used is just brilliant.

I watched 100 different videos to understand QFT and this is exactly what I was looking for. Thank you so much !

I LOVEEEE the guy explaining Shor's algo, 1000000 times better than my prof:)

This has saved my pre-QC exam evening, thank you so so much for these videos!

The lecturer does an amazing job! I can follow everything easily. The way he explains and breaks down things is simply great!

Understood the entire quantum Fourier transform and it’s amazing how a qubit encodes amplitude as well as relative phase at the same time

I have seen, read and study the QFT a lot, finally I understand it, Abraham is amazing. I'll keep with this series, thanks a lot.

Appreciate all the work and knowledge you're putting out there! While I may not fully comprehend the knowledge given, it's surely being absorbed over time as exposure to the material happens. Hope to keep motivated in this exciting upcoming field, thank you again

Abraham Asfaw is a qisikit gift

While watching the lecture. When I was 15 minutes in, I had the urge to listen to Mr Tambourine man by Bob Dylan. I’ll be back in 5 minutes.

At 43:15, after step 1, I believe Abraham meant we apply a Hadamard to get the exp(2.pi.i.x1/2) phase instead of having applied a URot. Is this a minor slip of the tongue? One could argue that the Hadamard is a special case of the URot though, where k = 1.

now i actually understood QFT including mathematics and physical realization ❤ thank u so much sir you are amazing

Very well done. Superb explaination simply awesome stuff and thank you for saving me lots of time trying to figure QFT on my own

@MudahnyaFizik Asked "At 45:40, you claimed that the phase change for |1> of the first qubit in the circuit is the same but in reversed order of the |1> in the QFT. I don't get it. In the QFT, we have only a single phase shift due to the nth qubit. However, in the circuit, we have phase change due to all other qubits. How is the two state the same? " I had the same question until I realized the x in the expanded version shown at 45:40 is the full x, not x_n. Using what we saw for the expanded y: x = sum(k=1 to k=n) x_k * 2^(n-k) = 2^(n-1) * x_1 + 2^(n-2) * x_2 + ... + 2^(n-n) * x_n Therefore expanding out the term shown at 45:40 (|0> + exp(i2pi x/2^n) |1>) = (|0> + exp(i2pi * [2^(n-1) * x_1 + 2^(n-2) * x_2 + ... + 2^(n-n) * x_n] /(2^n)) |1>) Canceling out the numerators using the (1/2^n) we find: (|0> + exp(i2pi x/2^n) |1>) = (|0> + exp(i2pi * [2^(-1) * x_1 + 2^(-2) * x_2 + ... + 2^(-n) * x_n]) |1>) Which is the exact expression shown at 45:37

simplest explanation on this topic. Cheers

Thank you so much for such a simple explanation......

Thanks! You are a good teacher

something i completely understand whow! ty!

All I can say is Best presentation 👍

At 45:40, you claimed that the phase change for |1> of the first qubit in the circuit is the same but in reversed order of the |1> in the QFT. I don't get it. In the QFT, we have only a single phase shift due to the nth qubit. However, in the circuit, we have phase change due to all other qubits. How is the two state the same?

In the example (green) till 26:24 - 3 Qubits are used; N is 2^3 = 8 but QFT|x> takes it's decimal value x="five" into account (in the exponent), while building the 3 parts contianing scalar product and ignores the binary representation of the number - which says: my middle term is zero... That looks like an error atm.

These videos are amazing! I really appreciate you guys posting these lectures as I could not participate in the class this summer. I have a quick question I ran into during the notes on the QFT. At 16:25, Abe writes a y^{k} (superscript k). Should this term be a y_{k} (subscript k)? I think he might have been distracted by explaining the cancelation of the 2^{n} because he writes it as y_{k} later on. I don't blame him... not an easy topic to cover so quickly and he did an amazing job👍

Hi, this course has been amazing so far! but it would be of great help for us who couldn't attend the live lectures and doing the course now, if we could see those live chats. it would be helpful because we can also look for some great questions apart from those which were being answered on the lectures. Also, I don't know if it is technically possible or not but if it is, I will be highly obliged if the team looks after this matter. Thank you.

At 43.16, you have applied the rotation matrix conditioned on x2 but if that rotation matrix rotates the state by e^((2(pi) i)/ 4), why does the coefficient of the power of e becomes multiplied by x2 if we do that? Shouldn't it be just x1 ?

When we change the basis, what we essentially get is smaller and smaller rotation. I assume this has physics interpretation. My concern is the follows: If we try to make fourier basis of let's say 1000 bits, wouldn't we required phase that (if it has physical meaning, I suppose it does) is smaller than the planck's constant, making it practically unimplementable? Therefore not much more useful, than classical computer (cuz we will be capped at basis with cardinality let's say 200-300). I want to clarify, that my physics background is nonexistent. I'm sure I didn't state my question as one competent in the field do, but I hope it's understandable.

Thank you! Please! Which software do you use for those lectures?

Can anyone explain what the swap gate was for in the end?

at time stamp 45:38 how the first expression is exactly equal to the derivation. It has more terms in the form of exp multiplied to the original term that we are looking for.

Fantastic explanation. May I know the name of the presenter so I can search for other videos he has created.

QFT에서는 n번째 큐비트로 인해 단일 위상 변이만 발생합니다. 47:00 회로에서는 다른 모든 큐비트로 인해 위상 변화가 있습니다. 두 상태가 어떻게 동일합니까?

I heard Peter Shor's actually a really bad lecturer - you're never Shor what he's talking about

I am trying to draw this circuit but got an attribute error “QuantumCircut has no cu1”, how can I fix it please help asap.

where can we get the code mentioned in the end that was posted in the discord. I’m not in the discord

Wait. Y= |4> is a state in the lab frame

Not to complain (again) about " A Rose by any other name will smell as Sweet" and QM-TIMESPACE is the Engineering of Spacetime, a phase-locked substantion shaping of Math-Phys-Chem and Geometry here-now-forever formatting of /by e-Pi-i sync-duration, ie lines of sight projection-drawing (E=mC²) density-intensity superposition quantization of time-timing Superspin, In-form-ation. The Measurement Problem, or Uncertainty Principle consequence of simultaneous Duality of multiphase-locked holographic photon-phonon universally is probably a jargon for Amateur Observer's compositions of coherence-cohesion objectives, so the dominant Nomenclatures of Scientific Analysis are in a state of confusion, which can only be sorted out by talented Artists who have a natural appreciation of macro-micro Quantum-fields Perspective. Eg the common sensing of phenomena is directly related to Neurological arrangements in Brains, and Computational Information is Quantum Chemistry. So reference Sir Rodger Penrose, and Robert Sapolsky etc, before guessing about the logarithmic probability dominant resonance conglomeration connection..? This same does not apply to Computational Methodologies Sciencing, but thanks for the attempt to make the subject more accessible.

Where can we get the demo-2.ipynb . The MYQFT is very different from the one used by qiskit in the qiskit book

Can you please help me with the tensor product part from 19:25 timestamp? I didn't understand how the instructor introduced those tensor product...

In all the derivation in blue through 19:54, due to the product xy in the exponent of the exponential function, the formulas only make sense for x a scalar. After 19:54 you suddenly claim that "we went from |x> = |x1 x2... xn>". What would be the meaning of the product xy in the exponent if |x> really was |x1 x2 ... xn>? And then you go on and use green arrows to map each one of the factors of the tensor product |x> to the tensor factors of |x_tilde>, even though the whole derivation of |x_tilde> is only meaningful if x is assumed to be a scalar. You lose me here...