Don't tell me about numerical experiments. They are not experiments in the empirical sense.

Empirical observations are not completely reproducible. Each time you make an observation, you get a slightly different answer. You can try to eliminate the error as much as you can, but you can never exactly reproduce the same number. That's nature.

Numerical experiments are perfectly reproducible. Even the random number generators are perfectly reproducible. Therefore they are not really experiments. They are simply algorithm constructions that are too complex to be understood without the numerical results. Therefore they are at best mathematics.

Quantum computing as it is studied now is physics, not computer science.