bibkey: chandran2019rydberg title: Do Rydberg chains yield Fibonacci anyons? authors: Anushya Chandran, Fiona J. Burnell, Shivaji L. Sondhi year: 2019 url: https://arxiv.org/abs/1909.09652v1 doi: 10.1103/PhysRevB.101.075104 claim: Blockaded Rydberg and Fibonacci-anyon chains have corresponding constrained basis states in fixed boundary sectors, but the correspondence does not preserve generic operator locality or the anyonic topological symmetry. strata_touched: [] license: citation-only triage: anchor

Constrained states and the separate operation correspondence

Chandran, Burnell and Sondhi, arXiv:1909.09652v1, study the nearest-neighbor Rydberg blockade constraint $n_i{n}_{i+1}=0$, equation (1). Section III, equation (19), identifies occupation basis states with the Fibonacci fusion-tree basis in each fixed boundary-condition sector by $Z_i=1\leftrightarrow n_i=1$ and $Z_i=\tau \leftrightarrow n_i=0$. The journal publication is Physical Review B 101, 075104 (2020), with the DOI given above; the cited arXiv version is the 2019 source.

This vector-space correspondence does not preserve generic operator locality. Section III, equations (20)–(21), explains how a local Rydberg occupation or flip can involve net fusion outcomes of extended anyon subsets. The paper also gives the other direction: local anyonic operators map to local Rydberg operators. These are directional statements about the specified correspondence, not an assertion that every operator in either model is nonlocal.

Section IV.B, equation (30), discusses the additional topological symmetry obstruction in the $(\tau ,\tau )$ boundary sector. Generic local Rydberg operators need not commute with the total-charge projector; appropriately tuned combinations can preserve it. Sections V–VI explain why the Hilbert-space correspondence alone supplies neither generic anyon dynamics nor topological protection of a Rydberg qubit.

For a length-three binary window with the two outer neighbors fixed empty, the same nearest-neighbor exclusion has five allowed occupancy strings. That elementary combinatorial match does not identify an ordered FIB source tree, its high-to-low reader, or its quantities and seams with an anyon chain. In particular, it supplies no calibrated source-controlled probe, guard-testing instrument, phase reference, reset, copy, or acquisition-cost correspondence. Those require a separate mathematical or physical operation contract.

This note paraphrases the primary source and its scope. No article PDF, figure or extended excerpt is redistributed.