Parker Kuklinski, Benjamin Rempfer, Kevin Obenland, Justin Elenewski (Aug 07 2025).

Abstract: The ability to efficiently state-prepare Gaussian distributions is critical to the success of numerous quantum algorithms. The most popular algorithm for this subroutine (Kitaev-Webb) has favorable polynomial resource scaling, however it faces enormous resource overheads making it functionally impractical. In this paper, we present a new, more intuitive method which uses exactly $n-1$ rotations, $(n-1)(n-2)/2$ two-qubit controlled rotations, and $\lfloor(n-1)/2\rfloor$ ancilla to state-prepare an $n$-qubit Gaussian state. We then apply optimizations to the circuit to render it linear in T-depth. This method can be extended to state-preparations of complex functions with polynomial phase.

Arxiv: https://arxiv.org/abs/2508.03987