Towards Holography in Trapped Ions

We show that coherent noise and over-rotations native to ion trap quantum computers can transform holographic stabilizer codes, previously not linked to any emergent gravitational effects, into approximate quantum error correcting codes that exhibit behaviors analogous to those predicted by the quantum extremal surface formula. By injecting bulk entanglement, we support this claim through numerical simulations of holographic toy models representing both single-sided AdS and two-sided AdS connected by a wormhole. To quantify the effects of such coherent circuit noise, we provide noise estimates from entropy measurements based on quantum state tomography, showing that these setups can be verified on current NISQ devices. This work opens up new opportunities for experimentally probing quantum gravity in the lab using NISQ technology.