{"id":"doi:10.5281/zenodo.21480278","kind":"article","title":"The Rydberg Fano Array: Neutral-Atom Implementation of Non-Associative H2 Computing via G2 Blockade Geometry","authors":["Ian Richard C Buckley"],"author_count":1,"year":2026,"published":"2026-07-21","venue":"Zenodo (CERN European Organization for Nuclear Research)","cited_by":0,"doi":"10.5281/zenodo.21480278","arxiv_id":null,"nct_id":null,"source_url":"https://doi.org/10.5281/zenodo.21480278","archive_url":"https://space-kitty.com/papers/doi:10.5281/zenodo.21480278","updated":null,"pmid":null,"pmcid":null,"openalex_id":"W7169830761","pdf_url":null,"abstract":"We propose the Rydberg Fano Array: a neutral-atom quantum processor whose geometry is the Fano plane F_7 (7 sites, 7 blockade lines of 3 sites each), chosen so that the Rydberg blockade subspace carries the 7-dimensional irreducible representation of G2. The blockade subspace decomposes as 1 + 7 as a G2-module (Fano Blockade Theorem), and three blockade-CZ pulses around a Fano line implement a BIND gate with non-associative G2 holonomy. This makes the Rydberg Fano Array the first proposed physical implementation of a non-associative H2 quantum gate that does not require magic state distillation. The G2 quantum walk on the Fano graph has spectrum +hbar*Omega*sqrt(7), 0 (6-fold), -hbar*Omega*sqrt(7), matching the G2 decomposition 7 = 1 + 6. We give explicit pulse sequences, gate fidelity estimates (>99.5% achievable with current Rydberg hardware parameters), and discuss the room-temperature analogue using metal-organic frameworks (MOFs) with f-element nodes. The architecture is directly compatible with IonQ, Quantinuum, and neutral-atom platforms.","abstract_license":"CC-BY (publisher license, via OpenAlex)","license":"cc-by","is_open_access":true,"retracted":false,"peer_reviewed":null,"categories":["Quantum Computing Algorithms and Architecture"],"details":null,"provenance":"openalex","attribution":"Abstract of \"The Rydberg Fano Array: Neutral-Atom Implementation of Non-Associative H2 Computing via G2 Blockade Geometry\" by Ian Richard C Buckley, https://doi.org/10.5281/zenodo.21480278, used under its Creative Commons Attribution license (CC-BY); markup removed, otherwise unmodified.","topics":[{"slug":"atoms-and-ions","name":"Neutral-Atom & Trapped-Ion Quantum Computing","domain_slug":"quantum-computing"}],"cited_in_dossiers":[]}