Quantum computing and resampling techniques Maybe I miss interpreted how does quantum computing work.
If I understood well it would allow to perform extreme parallelization by making using a single qubit to perform many calculations at the same time by exploiting superposition.
I though that maybe calculation based on resampling or iteration could particularly benefit from it. For example one could perform bootstrap or cross validation using all possible combinations instead of relying on chance, hoping to find the right compromise between sampling bias and computation time. 
Or even if you don't investigate all possible sample, one could perform montecarlo techniques instantly.
Now, I know we are talking about something that won't become mainstream in at least 50 years, but I just wanted to know if this intuition regarding parallelization is correct.
Thanks
 A: In theory...Maybe?
In our bootstrap method there is n^n possible resamples. When we do classical monte carlo we pick B random resample and pick B so that it is large enough to represent all the possible resamples. For each monte carlo simulation we just calculate the test-statistic.
In quantum monte carlo we would start with M independent quantum states, each of which are a superposition of the n^n possible resamples. When we measure a quantum state it will converge to one of the superposition states. If we want some quantum advantage we need to keep the M states in superposition while performing the next step in the bootstrap method. How you do this next step in the bootstrap method will determine if quantum monte carlo would be better or not. This is still a growing field, no one has proven whether you can this next step such that you gain an advantage.
My guess would be that bootstrap may not benefit from quantum monte-carlo. Even if you had a super-postion of all the possible test-statistics measuring this state would collapse it to one of the test-statistics, making it no diffrent from the classical case.
