Undecidability in tensor network states

摘要

Recent work has examined how undecidable problems can arise in quantum-information science.We augmentnthis by introducing three undecidable problems stated in terms of tensor networks. These relate to ideas ofnPenrose about the physicality of a spin network representing a physical process, closed timelike curves, andnBoolean relation theory. Seemingly slight modifications of the constraints on the topology or the tensor familiesngenerating the networks lead to problems that transition from decidable to undecidable to even always satisfiable.