The cost of simulating quantum mechanics on a quantum computer

One of the most commonly suggested applications for a quantum computer is simulating quantum systems. Although clearly promising in the limit of large quantum computers, we explore whether quantum simulations are a practical application area for small quantum computers. We show that, at least for the application of quantum chemistry, the standard algorithms in the worst case require significantly more resources then can be envisioned in the near-term. We discuss the potential way forward including recent suggestions for how to improve this situation and whether the worst case scenarios apply.