Understanding quantum gravity is one of the biggest intellectual challenges of modern science. String theory and the related AdS/CFT correspondence provide a rigorous theoretical laboratory to address some aspects of quantum gravity, and a few semi-classical quantum gravity effects, notably the existence of Hawking radiation, are well-established and understood. However we are strongly handicapped by the inability to perform experiments that probe quantum gravity effects directly. In recent years a series of results have established a promising pathway towards exhibiting and exploring genuine quantum gravity effects in a laboratory setting. This pathway exploits what appears to be a fundamental relationship between the connectedness of spacetime and quantum entanglement, as well as the holographic duality between certain bulk gravity phenomena and non-gravitational quantum systems. Both ideas are realized in the phenomenon of traversable wormholes, which have been shown in the rigorous context of AdS/CFT to be a feature of semi-classical quantum gravity. Such wormholes are rendered traversable by a quantum effect involving a flux of negative energy, similar to the quantum phenomenon that enables Hawking radiation. Furthermore these wormholes have a holographic dual description as a new form of quantum teleportation, which can be explicitly realized in the dynamics of the SYK model with N interacting Majorana fermions. There is considerable evidence that N~100 should be good enough to exhibit the key properties of traversable wormholes in a laboratory setting, e.g., by producing the dynamics on a quantum processor. I will describe how such experiments might be performed and what we could learn from them.