Do we live in a [quantum] simulation? Constraints, observations, and experiments on the simulation hypothesis

The question "What is real?" can be traced back to the shadows in Plato's cave. Two thousand years later, Rene Descartes lacked knowledge about arguing against an evil deceiver feeding us the illusion of sensation. Descartes' epistemological concept later led to various theories of sensory experiences. The concept of "illusionism", proposing that even the very conscious experience we have is an illusion, is not only a red-pill scenario found in the 1999 science fiction movie "The Matrix" but is also a philosophical concept promoted by modern tinkers, most prominently by Daniel Dennett. Reflection upon a possible simulation and our perceived reality was beautifully visualized in "The Matrix", bringing the old ideas of Descartes to coffee houses around the world. Irish philosopher Bishop Berkeley was the father of what was later coined as "subjective idealism", basically stating that "what you perceive is real". With the advent of quantum technologies based on the control of individual fundamental particles, the question of whether our universe is a simulation isn't just intriguing. Our ever-advancing understanding of fundamental physical processes will likely lead us to build quantum computers utilizing quantum effects for simulating nature quantum-mechanically in all complexity, as famously envisioned by Richard Feynman. In this article, we outline constraints on the limits of computability and predictability in/of the universe, which we then use to design experiments allowing for first conclusions as to whether we participate in a simulation chain. Eventually, in a simulation in which the computer simulating a universe is governed by the same physical laws as the simulation, the exhaustion of computational resources will halt all simulations down the simulation chain unless an external programmer intervenes, which we may be able to observe.