Currently, all proposals for the quantum version of machine learning utilize the finite-dimensional substrate of discrete variables. Here we generalize quantum machine learning to the more complex, but still remarkably practical, infinite-dimensional systems. Researchers present the critical subroutines of quantum machine learning algorithms for an all-photonic continuous-variable quantum computer that achieve an exponential speedup compared to their equivalent classical counterparts. Finally, they also map out an experimental implementation which can be used as a blueprint for future photonic demonstrations.

One of the biggest advantages of having a quantum machine learning algorithm for continuous variables is that it can theoretically operate much faster than classical algorithms. Since many science and engineering models involve continuous variables, applying quantum machine learning to these problems could potentially have far-reaching applications.