  We provide explicit circuits implementing the Kitaev-Webb algorithm for the
preparation of multi-dimensional Gaussian states on quantum computers. While
asymptotically efficient due to its polynomial scaling, we find that the
circuits implementing the preparation of one-dimensional Gaussian states and
those subsequently entangling them to reproduce the required covariance matrix
differ substantially in terms of both the gates and ancillae required. The
operations required for the preparation of one-dimensional Gaussians are
sufficiently involved that generic exponentially-scaling state-preparation
algorithms are likely to be preferred in the near term for many states of
interest. Conversely, polynomial-resource algorithms for implementing
multi-dimensional rotations quickly become more efficient for all but the very
smallest states, and their deployment will be a key part of any direct
multidimensional state preparation method in the future.
