  The AdS/CFT correspondence stipulates a duality between conformal field
theories and certain theories of quantum gravity in one higher spatial
dimension. However, probing this conjecture on contemporary classical or
quantum computers is challenging. We formulate an efficiently implementable
multi-scale entanglement renormalization ansatz (MERA) model of AdS/CFT
providing a mapping between a (1+1)-dimensional critical spin system and a
(2+1)-dimensional bulk theory. Using a combination of numerics and analytics,
we show that the bulk theory arising from this optimized tensor network
furnishes excitations with attractive interactions. Remarkably, these
excitations have one- and two-particle energies matching the predictions for
matter coupled to AdS gravity at long distances, thus displaying key features
of AdS physics. We show that these potentials arise as a direct consequence of
entanglement renormalization and discuss how this approach can be used to
efficiently simulate bulk dynamics using realistic quantum devices.
