Majorana dimer models of holographic quantum error correction

Holographic quantum error-correcting codes have been proposed as toy models describing key aspects of the AdS/CFT correspondence. In this talk, we introduce a versatile framework of Majorana dimers capturing the intersection of stabilizer and Gaussian Majorana states. This picture allows for an efficient contraction with a simple diagrammatic interpretation and is amenable to analytical study of holographic quantum error-correcting codes. Equipped with this framework, we revisit the recently proposed hyperbolic pentagon code (HyPeC) and demonstrate efficient computation of boundary state properties for generic logical bulk input. We show that the dimers characterizing boundary states of the HyPeC follow discrete bulk geodesics. From this geometric picture, properties of entanglement, quantum error correction, and bulk/boundary operator mapping immediately follow, offering a fresh perspective on holography. We also elaborate upon the emergence of the Ryu-Takayanagi formula from our model, which shares many properties of the recent bit thread proposal.
Our work thus elucidates the connection between bulk geometry, entanglement, and quantum error correction in AdS/CFT, and lays the foundation for new models of holography.
We close with an outlook on the boundary symmetries of holographic Majorana dimer models and discuss the connection to the strong disorder renormalization group.