Quantum complexity, Emergence and Computation by Measurement : On what computers reveal about physical laws, and what physical laws reveal about computers

Any computation is facilitated by some physical process, and the observable quantities of any physical process can be viewed as a computation. These close ties suggest that the study of what universal computers are capable of may lead to additional insight about the physical universe, and vice versa. In his thesis, we explore three lines of research that are linked to this central theme. The first partition shows how notions of non-computability and undecidability eventually led to evidence of emergence, the concept that even if a ‘theory of everything’ governing all microscopic interactions were discovered, the understanding of macroscopic order is likely to require additional insights. The second partition proposes a physically motivated model of computation that relates quantum complexity, quantum optimal control, and Riemannian geometry. Thus insights in any one of these disciplines could also lead to insights in the others. The remainder of this partition explores a simple application of these relations. The final partition proposes a model of quantum computation that generalizes measurement based computation to continuous variables. We outline its optical implementation, whereby any computation can be performed by single mode measurements on a resource state that can be prepared by passing a collection of squeezed states through a beamsplitter network