Undecidability of the Spectral Gap

Abstract

We treat the results of the 2015 paper by Cubitt et al. entitled “Undecidability of the Spectral Gap”, and the constructions required to arrive at these results. This paper showed that a specific quantum mechanical problem (the “spectral gap problem”) is algorithmically undecidable, using techniques from computer science. We also treat the theory from quantum mechanics and computer science that is required to understand these results and constructions.