  A recently introduced classical simulation method for universal quantum
computation with magic states operates by repeated sampling from probability
functions [M. Zurel et al. PRL 260404 (2020)]. This method is closely related
to sampling algorithms based on Wigner functions, with the important
distinction that Wigner functions can take negative values obstructing the
sampling. Indeed, negativity in Wigner functions has been identified as a
precondition for a quantum speed-up. However, in the present method of
classical simulation, negativity of quasiprobability functions never arises.
This model remains probabilistic for all quantum computations. In this paper,
we analyze the amount of classical data that the simulation procedure must
track. We find that this amount is small. Specifically, for any number $n$ of
magic states, the number of bits that describe the quantum system at any given
time is $2n^2+O(n)$.
