Alexey Uvarov

Congrats! I like that randomness is illustrated with a non-d6 die :)

3.

On the one hand, we have the connection "no barren plateaus ~ possible classical simulability", if I got it correctly. On the other hand, the averaging we do when arguing with BPs feels like something of a "zoomed out" view to me, so I can't decide just by looking at them

Combinatorial species are a bit hard to explain in a series of short posts, but quite fun when you get them. I learned about them in John Baez’s blog, where he uses them to study random permutations: math.ucr.edu/home/baez/pe...

Importantly, if G(x) describes the number of ways to impose some structure on a finite set, then exp(G(x)) describes the number of ways to split the set into subsets and impose this structure on each subset. That is, if you can count pairs and cycles, you can count perfect 2-matchings.

The article above may look scary at first because category theory, but really it just describes what structures you generate when you add, multiply, or compose the generating functions.

The thing is, you can construct a function whose m’th Taylor coefficient (times m!) is the desired sum for the 2m-vertex complete graph. This function can be built from simpler blocks using so-called combinatorial species: en.wikipedia.org/wiki/Combina...

However, only even-length cycles are allowed, and on top of that, each perfect 2-matching is counted with a weight equal to 6^(number of cycles). Turns out, you can still calculate this sum for a complete graph.

Pictures of a complete graph with 6 vertices. Vertices are connected into pairs, cycles, or both, so that all vertices are in some pair or cycle and no vertex is in two things at once.

For the adjacency matrix of a graph, the Hafnian function counts the number of perfect matchings, i.e. the number of ways to split vertices into pairs. For the randomized estimators we studied in the paper, the second moment is governed by the number of perfect 2-matchings, which also allow cycles.

The details of that are in the paper, but here I would like to talk more about the part which I found the most fun and which ended up being something of a side note.

Non-meme summary: there are ways to classically estimate the probability of seeing a given outcome in a GBS experiment if its “kernel matrix” is nonnegative. We ran numerical experiments and found that the estimators typically work very well if the kernel is an adjacency matrix of a random graph.

Kilgrave captioned "Classical estimators of the Hafnian" stares at Jessica Jones captioned "Gaussian boson sampling with a nonnegative kernel"

On the occasion of #QTML2024 I’d like to write a few words about the work I presented there. It’s been published in PRA some time ago:

doi.org/10.1103/Phys...

Following the suggestion from @dulwichquantum.bsky.social, I produced a meme summarizing its content

bsky.app/profile/andr...

I'd be glad to join

scholar.google.com/citations?us...

Does the feed pick specifically quantum posts though? E.g. in the science feed people mark their posts with a tube emoji when they want them to appear in the feed

By popular demand, here is a starter pack of all quantum PhD students on BlueSky that we could find.
go.bsky.app/AUTn1di

Chalk: 😐

Chalk, Japan: w⁠(⁠°⁠ｏ⁠°⁠)⁠w

Photo of a Hagoromo chalk stick

Someone left their Hagoromo chalk at the meeting room, so I tried writing with it. It's really neat and smooth but I don't think I've become a 10x mathematician while using it

Now that there seems to be another exodus from Twitter, people are sharing lists of researchers to follow in their field. Does anyone have such a list for quantum physics or quantum computing? Thx 🧪

A virtual certificate with text "Celebrating 10M users on Bluesky, #5,172,005, Alexey Uvarov ‪@alexuvar.bsky.social‬, joined on Mar 18, 2024"

Bluesky now has over 10 million users, and I was #5,172,005!

Hi! I work in quantum computing and would like to join the science feed

scholar.google.com/citations?us...

Hello world!

Recently decided to move away from twitter a little bit. I probably won't post much, but mainly it's going to be about science and quantum computing