Typical quantum simulation papers do not target 100% accuracy, they target "chemical accuracy [1]". That said, chemistry simulations do tend to be less tolerant of approximations because you are sampling an unknown distribution and so can't easily tell if a shot had a failure. But the linked article is about a subroutine for Shor's algorithm, where it is very obvious if you succeeded or not because you either recovered the private key or you didn't.
[1]: https://chemistry.stackexchange.com/questions/62001/why-is-c...