A simpler Gaussian state-preparation

TL;DR

This paper introduces a simplified and resource-efficient method for preparing Gaussian quantum states, reducing complexity and improving practicality over previous algorithms, with potential extensions to complex functions.

Contribution

A new intuitive method for Gaussian state preparation using fewer rotations and optimized T-depth, improving practicality over existing algorithms.

Findings

Uses exactly n-1 rotations and fewer controlled rotations

Achieves linear T-depth through circuit optimization

Can be extended to prepare complex functions with polynomial phase

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.