  This note introduces "Q-marginals", which are quantum states encoding some
probability distribution in a manner suitable for use in Quantum Monte Carlo
Integration (QMCI), and shows that these can be prepared directly from a
classical circuit sampling for the probability distribution of interest. This
result is important as the quantum advantage in Monte Carlo integration is in
the form of a reduction in the number of uses of a quantum state encoding the
probability distribution (in QMCI) relative to the number of samples that would
be required in classical MCI -- hence it only translates into a computational
advantage if the number of operations required to prepare this quantum state
encoding the probability distribution is comparable to the number of operations
required to generate a classical sample (as the Q-marginal construction
achieves).
