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

TL;DR

This paper discusses the implementation of quantum circuits for preparing multivariate Gaussian states, highlighting the efficiency and resource considerations for different approaches on quantum computers.

Contribution

It provides explicit quantum circuits for the Kitaev-Webb algorithm and compares their resource requirements for one-dimensional and multi-dimensional Gaussian state preparation.

Findings

One-dimensional Gaussian state preparation circuits are resource-intensive.

Multi-dimensional rotations can be more efficient for larger states.

Generic exponential algorithms may be preferable for small or specific states.

Abstract

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.