On the Problem of Universality of Quantum Theory

Peter Mittelstaedt

William Icefield

It is often assumed that the complete physics theory of the universe is computable - in sense that it can provide meaningful theoretical predictions for every phenomenon of the universe. Against this view, it is argued that once quantum mechanics is understood as encompassing a novel concept of probability, thereby resolving the measurement problem in straightforward ways, the interpretation speaks for uncomputability of the complete physics theory. The reasons why a new theory of probability is needed are explored, along the lines of the principle of indifference and the sleeping beauty problem.

Arthur I. Fine

Lorenzo Mattioli, Adam Sawicki

We study the universality and membership problems for gate sets consisting of a finite number of quantum gates. Our approach relies on the techniques from compact Lie group theory. We also introduce an auxiliary problem called the subgroup universality problem, which helps in solving some instances of the membership problem and can be of interest on its own. The resulting theorems are mainly formulated in terms of centralizers and the adjoint representations of a given set of quantum gates.

Arthur I. Fine

Arthur I. Fine