Quantum machine learning over infinite dimensions

Machine learning is a fascinating and exciting field within computer science. Recently, this excitement has been transferred to the quantum information realm. 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.

Although the results of the study are purely theoretical, the physicists expect that the new algorithm for continuous variables could be experimentally implemented using currently available technology. The implementation could be done in several ways, such as by using optical systems, spin systems, or trapped atoms. Regardless of the type of system, the implementation would be challenging. For example, an optical implementation that the scientists outlined here would require some of the latest technologies, such as “cat states” (a superposition of the “0” and “1” states) and high rates of squeezing (to reduce quantum noise).

Previous all-photonic implementations are difficult to do experimentally but are still within current reach of the latest technological achievements. For instance, high rates of squeezing are now achievable, along with the generation of cat states. However, researchers note that their scheme is not limited to photonic demonstrations but a variety of substrates, including spin ensemble systems, such as trapped atoms and solid state defect centers.

They hope that the work presented here will lead to further avenues of research. Especially since there has been a substantial increase of results in discrete-variable machine learning. All of these would be interesting to be generalized to continuous variables as future work. Additionally, adapting our current work into the cluster-state formulism would also be interesting in order to take advantage of state-of-the-art experimental interest and the scalability that continuous variables can provide. Furthermore, they note another viable option that uses a ‘best-of-both-worlds’ approach to quantum
information processing, i.e., hybrid schemes. It would be interesting to adapt their scheme presented here to such hybrid architectures.

Arxiv – Quantum machine learning over infinite dimensions