Computational physicists have been thinking about algorithms for simulating quantum systems essentially since computers were invented. We have decent algorithm

Computational physicists have been thinking about algorithms for simulating quantum systems essentially since computers were invented. We have decent algorithms for approximating ground states, or for systems in equilibrium (contingent on it being spin-balanced, or at half-filling, or at 0 density, ... depending on the model), or in other limited circumstances. But lift any of those special restrictions, and simulation methods hit a sign problem [sign]. In particular, real-time evolution of quantum systems, which is what a quantum computer does by its very nature, poses in some sense the most difficult sign problem for approaches leveraging classical computing. That's not a proof that classical algorithms can't become more capable, but it's almost certainly a question that must be answered system-by-system. The generic sign problem is NP-hard, so special-case reasoning is required. [sign]: https://en.wikipedia.org/wiki/Numerical_sign_problem https://en.wikipedia.org/wiki/Numerical_sign_problem