You're wrong, we do know that, and the paper you cite doesn't refute that in any way.
Integer factorization and quantum simulation would be two examples of commercially highly relevant applications where an exponential speed-up applies.
Integer factorization and quantum simulation would be two examples of commercially highly relevant applications where an exponential speed-up applies.
"Quantum simulation" is too vague to speak to applicability in any domain. There is no proven or empirically demonstrated exponential speedup on any simulation problem with known commercial applications.
https://arxiv.org/pdf/2011.06571.pdf
It does seems too good to be true.
The two caveats are
1. Only works for "mildly" nonlinear equations
2. Results are in quantum world and have to be translated back into normal deterministic world results, and this hasn't been figured out yet