The paradigm of quantum computational advantage (also known as supremacy) aims to demonstrate that a programmable quantum device can solve a problem that no classical computer can solve in any feasible amount of time (irrespective of the usefulness of the problem). In this talk, we shortly describe two such schemes: Fermion Sampling and Boson Sampling. We present an overview of the recent developments concerning the Fermion Sampling scheme [1], and also review some of the parallel developments for Boson Sampling. In particular, we discuss hardness guarantees, experimental feasibility, certification and actual experimental results. Finally, we assess the potential of practically useful sampling schemes (for many-body, network theory and machine learning problems) based on Fermion and Boson Sampling [2].

 

[1] M. Oszmaniec, N. Dangniam, M. Morales, Z. Zimborás,

Fermion Sampling: a robust quantum computational advantage scheme 

using fermionic linear optics and magic input states

arXiv: 2012.15825

 

[2] D. Nagy, Z. Tabi, P. Hága, Z. Kallus, Z. Zimborás, 

Photonic Quantum Policy Learning in OpenAI Gym, 

IEEE Quantum Computing and Engineering 2021, pp. 123-129 (2021).