Quantum many-body physics involves problems with a unique combination of computational complexity and practical importance. Therefore, they are well-positioned to be one of the most promising present-day applications of present day quantum computers. While we can intuitively recognise that many state of the art quantum simulations of many-body systems have implicity achieved a practical quantum advantage, the nature of this advantage is vague and unquantified. The goal of this project is to formulate and implement concrete and quantifiable practical quantum advantages in many-body physics. I propose the following roadmap:
Characterise the current practical limitations in approximate classical simulation of many-body systems.
Develop and benchmark error models to quantum devices in order to estimate.
Develop approximation ansatze which can then be benchmarked using quantum devices (see this paper).
More generally, develop approximate theories with large number of free parameters, which can be learnt by training on data from quantum computers.