  To simulate bosons on a qubit- or qudit-based quantum computer, one has to
regularize the theory by truncating infinite-dimensional local Hilbert spaces
to finite dimensions. In the search for practical quantum applications, it is
important to know how big the truncation errors can be. In general, it is not
easy to estimate errors unless we have a good quantum computer. In this paper,
we show that traditional sampling methods on classical devices, specifically
Markov Chain Monte Carlo, can address this issue for a rather generic class of
bosonic systems with a reasonable amount of computational resources available
today. As a demonstration, we apply this idea to the scalar field theory on a
two-dimensional lattice, with a size that goes beyond what is achievable using
exact diagonalization methods. This method can be used to estimate the
resources needed for realistic quantum simulations of bosonic theories, and
also, to check the validity of the results of the corresponding quantum
simulations.
