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.

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

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

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