Drew Connelly

All I thought when I saw this was periodic boundary conditions

Correcting a typo:
"Affine Equivalence in the Clifford Hierarchy" is the name of the preprint.

A table showing the number of affine equivalence classes of cycles in the clifford hierarchy for varying numbers of qubits and cycle structures.

Here's the TLDR version of the cycle structure result:

Affine Equivalence in the Clifford Hierarchy In this paper we prove a collection of results on the structure of permutations in the Clifford Hierarchy. First, we leverage results from the cryptography literature on affine equivalence classes of ...

We also use our algorithm to enumerate how many affine equivalence classes of particular cycle structures are in the hierarchy for small cycle structures. We then prove a structure theorem which lets us determine this for arbitrarily many qubits.

Check it out if interested:
arxiv.org/abs/2507.14370

@jonasanderson.bsky.social & I now have our preprint of Clifford Equivalence in the Clifford Hierarchy up! We use affine equivalence algorithms from the crypto literature to computationally show that the 3rd level of the hierarchy on 4 qubits is strictly Semi-Clifford. (1/2)

I tried to purge this TLS from the system but museum staff got very upset for some reason…

Oh I see, so I needed to add a random pi phase bit to the measure and then propagate that through to cancel it. Thanks

Ah I didn’t notice that it would need classical feedback, interesting

Poorly drawn ZX calculus on a page

Great use of a particular identity for the hadamard in ZX calculus

I don’t post too often but I’d love to join the pack!

I trusted you bro :(