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

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 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.