Quantum Gravity in the Lab: Magic-enriched Holographic Codes on Trapped-Ion Quantum Computers

We present results from quantum circuits on an ion-trap quantum computer that relate to holographic error-correcting codes and the AdS/CFT correspondence. Toy models like the HaPPY code (Pastawski et al, JHEP 2015) allow us to study the relationship between geometry and entanglement, as predicted by the holographic principle, but they do not have emergent gravity, an important feature of AdS/CFT. But the magic-enriched HaPPY code changes this paradigm by coupling "matter" to "gravity". In our experiments, magic is injected in the form of coherent gate over-rotations during logical encoding. We report progress on experiments on models of single-copy AdS and two-sided wormhole on the IonQ-Forte trapped-ion system. Preliminary experiments on a reduced two-sided wormhole confirm that injecting magic produces a bigger deformation of the quantum extremal surface entropy when two codes are entangled.