Frederik Hahn

@frederikhahn.bsky.social

90 Followers 121 Following

frederikhahn.eu https://orcid.org/0000-0002-9349-4075

Dave Chapelle meme of his character Tyrone Biggums. Caption: Y'all got anymore of them conjectures?
Meme of Sophie Cunningham's pointing gesture with the caption "That is a hallucinated reference."
The meme is a Mr. McMahon reaction. First panel: LU=LC for circle graph states Second panel: Circle graphs are vertex-minors of bipartite circle graphs Third panel: Bipartite circle graph states are just planar code states Fourth and final panel: MBQC on circle graph states is efficiently classically simulable Context: Circle graph states are graph states whose underlying graphs are intersection graphs of chords of a circle. Their entanglement is a priori high enough to be candidates for universal measurement-based quantum compu- tation (MBQC), yet MBQC on circle graph states turns out to be efficiently classically simulable. We prove that for circle graph states, local unitary (LU) equivalence reduces to the efficiently decidable local Clifford (LC) equivalence. We further establish a one-to-one correspondence between bipartite circle graph states and planar code states, and use it to give a new proof that MBQC on circle graph states is efficiently classically simulable. Finally, we show that counting the number of graph states LU-equivalent to a given graph state is #P-hard, even when restricted to circle graph states.