I can't tell how much of this is "quantum physics" and how much is "mathematical theory that also arises in quantum physics". As in, I doubt their construction

I can't tell how much of this is "quantum physics" and how much is "mathematical theory that also arises in quantum physics". As in, I doubt their construction allows "building something" which then allows solving a conventionally unsolvable problem. With new physics you may be able to build machines that can compute more; however I don't think they are talking about such physics here. But, they do quote: Marian B. Pour-El and Jonathan I. Richards. Computability in Analysis and Physics. Springer, 1989. M. B. Pour-El and J. Richards have earlier results: http://www.sciencedirect.com/science/article/pii/0001870881900013 http://www.sciencedirect.com/science/article/pii/00018708819...: The wave equation with computable initial data such that its unique solution is not computable (1981) http://philpapers.org/rec/POUTWE http://philpapers.org/rec/POUTWE: The wave equation with computable initial data whose unique solution is nowhere computable (1997) The Spectral Gap authors seem to call these results "easier" (page 8 at http://arxiv.org/pdf/1502.04573v2.pdf http://arxiv.org/pdf/1502.04573v2.pdf)