Wormhole spacetimes with SQUID arrays

Abstract

Quantum simulators are becoming increasingly popular as non-­universal quantum computers with the potential of proving the long­ -sought quantum supremacy. An alternate approach is to consider them as useful tools to explore the frontiers of quantum physics, ranging from open problems in well­-established theories such as quantum field theory to untested physics whose observability is hard or dubious. Wormholes or Einstein-­Rosen bridges are compelling mathematical objects appearing in some solutions of Einstein's General Relativity equations. Since they provide a bridge between distant regions of spacetime, they have attracted a great deal of attention from a foundational viewpoint as well as at a pedagogical level. They might contain closed timelike curves (CTCs), which are also interesting for Quantum Computing applications, since they would boost the capabilities of quantum computers. We present an analog quantum simulator of spacetimes containing traversable wormholes. A suitable spatial dependence in the external bias of a dc­SQUID array mimics the propagation of light in a 1D wormhole background. The impedance of the array places severe limitations on the type of spacetime that we can implement. However, we find that wormhole throat radius in the sub­-mm range are achievable. We show how to modify this spacetime in order to allow the presence of closed timelike curves. The quantum fluctuations of the phase due to the impedance might be seen as an analogue of Hawking's chronology protection mechanism.