Laboratory Realization of an Analogue AdS - CFT Duality in a Cold-Atom Hyperbolic Lattice

We present a comprehensive experimental proposal to realize a toy model ofthe AdS/CFT correspondence in a cold‑atom quantum simulator. Atwo‑dimensional hyperbolic optical lattice, generated by a combination ofstructured laser beams, hosts ultracold bosonic atoms whose hoppingamplitudes are engineered to reproduce the metric of anti‑de Sitter space(AdS$_{2+1}$). The boundary of the lattice is a one‑dimensional ring ofatoms that plays the role of the conformal field theory (CFT). Byexploiting synthetic gauge fields and Raman‑assisted tunneling, theeffective speed of light in the bulk becomes locally tunable, enablingthe simulation of the Malament–Hogarth effect---an infinite proper timewithin a finite boundary time. We detail the construction of thehyperbolic lattice, the mapping of bulk fields to boundary operators, theencoding of a universal Turing machine as a bulk defect, and the readoutof the computational halt state via boundary correlation measurementswith exponential suppression of errors. Our blueprint provides themissing laboratory platform for the PV‑crystallographic hypercomputerand opens a new paradigm for table‑top holographic quantum computation.