We study the stellar representation of quantum computations, based on holomorphic functions, which delineates the boundary between discrete- and continuous-variable quantum information theory. This representation provides an elegant characterization of non-Gaussian quantum states that are resourceful for bosonic quantum computing: in the single-mode case, the evolution of a single bosonic mode under a Gaussian Hamiltonian can be described using a dynamical system of classical particles corresponding to the non-Gaussian zeros of the holomorphic function; in the multimode case, this holomorphic representation also induces a faithful and robust non-Gaussian hierarchy of quantum states. From this representation, we obtain a classification of subuniversal bosonic models that are generalisations of Boson Sampling and Gaussian quantum computing.

arXiv:2111.00117, joint work with Saeed Mehraban.