In this question of a few days ago, it was raised the question about the similarities or differences between the notion of universality in discrete-variable (DV) quantum computers and continuous-variable (CV) computers. My question is in the same line and I think that the answer would include both questions: Is the continuous-variable quantum computing model a quantum universal Turing machine?
This doubt stems from the definition of universality in the CV quantum case (see for example the original article by Lloyd): Universality of the CV model is defined as the ability to approximate arbitrary transformations of the form $U_H = e^{−it H}$, where the generator $H = H (x, p)$ is a polynomial function of $(x, p)$ with arbitrary but fixed degree. If the CV model is a quantum universal Turing machine, it would mean that it is equivalent to the DV model, and therefore I can represent any unitary transformation as $e^{−it H(x,p)}$, but I'm not sure about this last point.
