Why do you think the simulators, if there be such, are limited to classical computers? Why do you think they have limits of any kind?
It is impossible in principle to have any evidence about simulationism. All knowledge about everything from logic up is from inside the simulation. Just accept that it's an epistemological tarpit and give up.
This form of world-as-simulation is effectively identical to strong theism. The world exists in the mind of God or runs on some supernatural "hardware" is basically the same thing as saying the world is a beyond-classical simulation.
I don't mean dismiss simulation, but I see now how it could be read that way. The key is the second part of the and-clause: quantum stuff being a side effect of a lazy simulator. That's what doesn't hold water.
It is impossible in principle to have any evidence about simulationism. All knowledge about everything from logic up is from inside the simulation. Just accept that it's an epistemological tarpit and give up.