Summer of Math Exposition

Not understandable for someone that does not have basics in quantum computing. I see that the author chose only graduate as tag, and not undergrads, so difficulty may not be a problem but here the author really assume too much prior knowledge, even for computer science Ph.D. this is not easy to understand.

When I watched the video I was confused. I did not know what to make of it. since I can’t understand it , it is very hard for me to grade it properly, but I will try my best.

String points:

• Genuine curiosity and initiative. You noticed a real asymmetry — circuit→matrix is straightforward, matrix→circuit is not — and instead of shrugging, you tried to build tools to probe it. That instinct is good science.

-The unitary test itself is legitimate. Checking whether a matrix times its conjugate transpose gives the identity matrix is exactly how you verify a matrix is physically realizable as a quantum operation.

• Intellectual honesty. They openly admit uncertainty, invite pushback, and pose their own unresolved questions at the end rather than overclaiming. That’s a healthy scientific attitude.

Suggestions for improvements:

Make it easier to understand. Easier said than done, but I honestly say what could improve your piece.

Terminology is at times imprecise at least to me. Try to make it more precise.

The cryptography section is difficult to grasp. Encrypting inside a family as an analogy to a secret carrier frequency isn’t tied to any concrete protocol, security proof, or threat model. As stated, it reads (at least to me) as speculative metaphor rather than a testable cryptographic scheme.

I like your piece and I like your enthusiasm and effort to build your own map of a field. I wish you the best.

I think I am the target audience (I took a very physics-light course in quantum information as an undergrad, and later in my studies I was far from these ideas) for the paper; and as a piece of entertainment, I found the video quite good. To wit: your animation style is memorable, the mascot and its eye movements really work for me, it’s a short overall and snappy when it should be, and the conclusion is very sweet. I also think it’s well-sequenced; I suspect think some folks will complain that the proofs should have been moved later, but I like your choice.

Still, I have to give a fairly substantial penalty because of those proofs. It’s clear your aim in that section of the video is to convey some specific technicalities of the paper, and despite pausing and rewinding quite a bit, I am still confused by them. I think I reduced the main trouble to fitting the definitions of Sets A and B into the figure that is on screen at 5:00. This picture tripped me up for a long time, and after about 5 watches of this portion of the video I still don’t feel I understood it enough to critique it; it feels like you’re using some notational shorthand that’s harmless to experts but is really tripping me up as an outsider. (For instance: A and B are first described to be (disjoint?) sets of qbits, but immediately afterward A and B are described to contain quantum states (of those qbits?), which I thought were more general than the qbits themselves. Then families are described as power sets— though I think that doesn’t mean literally all subsets of some set but just that the elements of families are sets like A and B?— but the elements of the families are supposed to also supposed to be quantum states? So then A and B are supposed to be subsets of the families rather than elements, but this doesn’t make sense because Family 1 and Family 2 are clearly disjoint, so am I supposed to intersect A and B with each family? )

I also don’t know what you mean by “can be compared”, and this time I’m more confident this was a missing definition in your script. This felt like a less significant narrative confusion because the lack of comparability across families, whatever that means, seemed to allow us to just focus on one family at a time. So that was fine by me.

Finally, for a sticking point that you handled very well: I don’t know what it means for an algorithm, to exist inside a family— I think that the narration is trying to explain that, but it didn’t land for me. This is the only time when I felt something was explained completely enough that I should understand, but still didn’t. Since “an algorithm” is playing the role of A or B, something about its input-output pairs…? Still, you did signpost (on a first watch, even) that it wasn’t too important for me to understand that to proceed, which was very much appreciated.

Too technical, especially at the start, for anyone not familiar with the topic; and a bit too shallow for anyone who is familiar with it.

And you don’t link your paper in the description which is sketchy.

This is more an advertisement for your paper than a video trying to explain a topic, which I think is not the spirit of this contest. It was more trying to promote your paper to expert than trying to explain a topic to someone.

The video is well done. But it does not explain what a quantum computer can do. I understand that a quantum algorithm is a transformation on a vector of qubit which can be express as a unitary matrix and that from this matrix more than one circuit can represent the same transformation. Is there always a circuit ? You should take more time explaining the family concept, it when too fast, and I did not understand what exactly define a family.

I think the art style is quite nice although with my background in TCS/Cryptography I have come across some quantum computing.

It was hard to understand exactly what the problem you were trying to solve was. The problems of which matrices are representable by quantum circuits is a solved problem: The unitary ones are the standard model and every unitary matrix can be approximated to exponential precision by elementary quantum gates.

I think it would be worth spending some time with basics of quantum computing and or trying to take a course on it. The impression I get that you are overestimating your understanding of the topic.