In recent years, much work has been directed to the development of technologies to enable the long-term goal of scalable, universal quantum computers.This effort is motivated by the promise of quantum computational speed-up in tasks such as integer factoring, quantum simulation, and solving systems of linear equations.Despite the tremendous advances in quantum technologies reported in the last few years, the implementation of a large-scale universal quantum computer is still far from our current capabilities.Hence, intermediate milestones need to be identified in the long-term effort towards harnessing the computational potential of quantum systems.A first fundamental step in this direction is the achievement of the regime of quantum computational supremacy (also called quantum computational advantage) [1], i.e., the experimental demonstration of a quantum device capable of performing a computational task unambiguously faster than present-day classical computers.In order to achieve quantum advantage the following key ingredients are necessary: (1) to identify a computational problem whose complexity scales exponentially with classical hardware, but only polynomially when using quantum devices;(2) to address this problem with the best classical algorithm so as to find the threshold to be beaten for a claim of quantum advantage;(3) to implement the quantum instance on a system large enough to surpass the classical threshold;(4) to develop suitable tools to validate/certify the correctness of the output produced by the quantum system.