Théorique, numérique
Sampling problems are of crucial importance for demonstrating the quantum devices can efficiently perform tasks that no classical computer can efficiently simulate. Various groups have claimed the realisations of such so-called quantum advantages, but many of these experiments have ultimately been simulated on classical computers by exploiting experimental imperfections. This clearly shows the difficulty of translating highly idealised theoretical protocols to real experiments. In this internship, we will actively develop techniques to simulate optical sampling problems based on phase space representations of the quantum states, quantum operations, and quantum measurements. These phase space techniques are useful to explicitly construct hidden variable models for sampling problems. We will investigate which physical properties hinder us from using such hidden variables to efficiently simulate a sampling problem on a classical computer. In the past this approach was used to identify Wigner negativity as a required physical property [1]. However, other methods have recently emphasised the role of other physical properties [2]. The goal of this internship is to either identify new necessary properties or acquire a better understanding of how the different known properties combine to make the sampling problem hard to simulate. [1] Mari and Eisert, Phys. Rev. Lett. 109, 230503 (2012). [2] Chabaud and Walschaers Phys. Rev. Lett. 130, 090602 (2023).