  It is known that quantum computers yield a speed-up for certain discrete
problems. Here we want to know whether quantum computers are useful for
continuous problems. We study the computation of the integral of functions from
the classical Hoelder classes with d variables. The optimal orders for the
complexity of deterministic and (general) randomized methods are known. We
obtain the respective optimal orders for quantum algorithms and also for
restricted Monte Carlo (only coin tossing instead of general random numbers).
To summarize the results one can say that (1) there is an exponential speed-up
of quantum algorithms over deterministic (classical) algorithms, if the
smoothness is small; (2) there is a (roughly) quadratic speed-up of quantum
algorithms over randomized classical methods, if the smoothness is small.
