# The Rydberg Fano Array: Neutral-Atom Implementation of Non-Associative H2 Computing via G2 Blockade Geometry

Article · Ian Richard C Buckley

- Archive id: doi:10.5281/zenodo.21480278
- Published: 2026-07-21
- Venue: Zenodo (CERN European Organization for Nuclear Research)
- DOI: https://doi.org/10.5281/zenodo.21480278
- Citations: 0
- Source URL: https://doi.org/10.5281/zenodo.21480278
- Provenance: openalex

## 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 reproduced under CC-BY (publisher license, via OpenAlex)._

Topics: [Neutral-Atom & Trapped-Ion Quantum Computing](https://space-kitty.com/topics/atoms-and-ions)

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