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We provide explicit circuits implementing the Kitaev-Webb algorithm for thepreparation of multi-dimensional Gaussian states on quantum computers. Whileasymptotically efficient due to its polynomial scaling, we find that thecircuits implementing the preparation of one-dimensional Gaussian states andthose subsequently entangling them to reproduce the required covariance matrixdiffer substantially in terms of both the gates and ancillae required. Theoperations required for the preparation of one-dimensional Gaussians aresufficiently involved that generic exponentially-scaling state-preparationalgorithms are likely to be preferred in the near term for many states ofinterest. Conversely, polynomial-resource algorithms for implementingmulti-dimensional rotations quickly become more efficient for all but the verysmallest states, and their deployment will be a key part of any directmultidimensional state preparation method in the future.

Practical considerations for the preparation of multivariate Gaussian states on quantum computers