Preparing approximate $N$-fold cat states with the phase space instruction set

arXiv:2608.07696v1 Announce Type: new Abstract: The phase space instruction set is a continuous-variable universal gate set involving single-qubit rotations and qubit-dependent displacements on a single boson. Using these gates, we prove that a circuit depth $\mathrm{\Omega}(\varphi(N))$ is necessa