Abstract

The theory of the universal quantum computer has brought us rapid technological developments, together with remarkable improvements in how we understand quantum theory. There are, however, reasons to believe that quantum theory may ultimately have to be modified into a new theory: for instance, it will have to be merged with general relativity, to incorporate gravity; and some claim that it may be impossible to have quantum effects beyond a certain macroscopic scale. So what lies ahead of quantum theory, and of the universal quantum computer? To shed some light on these questions, we need a shift of logic in the way things are explained. Specifically, one can adopt the approach where the basic assumptions are general principles about possible/impossible transformations, rather than dynamical laws and initial conditions. This approach is called constructor theory. I will describe its application to a handful of interconnected problems, within information theory, thermodynamics, and even quantum gravity. This ’Science of Can and Can’t’ may be the first step towards the ultimate generalization of the universal quantum computer, which von Neumann called the ‘universal constructor’.