But you have a problem when you want to compare two numbers (to see if the particles overlap). Or if you want to divide one number by another.

In theory, in classical physics if you start a simulation on a Turing machine, then all the initial states must be computable. And you can carry on using symbolic representation of numbers, even with transcendental functions (as long as you compute them to a precision necessary to carry out the next step of the simulation).

But with quantum mechanics, we might have true randomness, so precise classic simulation can become impossible after the first interaction.