Our new paper contains two main results.

1) We demonstrate that these circuits are simulatable on a regular computer (these include Clifford circuits, i.e. simulatable qubit circuits, and beyond).

2) Adding imperfections, either in the form of a vacuum state or by using realistic (imperfect) GKP states makes these circuits capable of universal quantum computation

The circuits shown in the first picture are efficiently classically simulatable, meaning a classical computer will be able to do everything these circuits can do in a reasonable (polynomial) time. We demonstrated this using a twist of the stabilizer formalism. Adding access to the vacuum (a very simple and usually considered simulatable) or realistic GKP states unlocks the full power of the quantum computer and can run all quantum algorithms (including e.g. Shor’s algorithm).