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.

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.

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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

Chalk: 😐

Chalk, Japan: w⁠(⁠°⁠ｏ⁠°⁠)⁠w

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

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