I 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, I show that 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.