Its not meant to be an analogy. We also will not attempt to generate all quantum states on a quantum computer. As with classical monte carlo, we will only ever

Its not meant to be an analogy. We also will not attempt to generate all quantum states on a quantum computer. As with classical monte carlo, we will only ever generate a tiny fraction of the possible quantum states/distributions, and will also sample from a fixed distribution (whatever the quantum circuit outputs, we measure it in a fixed basis and always draw samples from that single, fixed distribution). We will also achieve robustness against the tyranny of the real numbers in our gate parameters in a very similar way that a classical computer does when it approximates some idealized Monte Carlo algorithm.