Comment on arXiv:2307.08384 "Efficient Quantum State Preparation with Walsh Series"

TL;DR

This paper clarifies the implementation of the Walsh Series Loader algorithm, providing a complete quantum circuit including the zero-order term, and empirically evaluates its performance on highly entangled states.

Contribution

It offers a detailed implementation guide for WSL, including the zero-order term, and releases source code to facilitate practical use and validation.

Findings

Incorrect implementation leads to poor fidelity states

Including the zero-order term improves accuracy

WSL struggles with highly entangled states

Abstract

In this paper, we discuss the Walsh Series Loader (WSL) algorithm, proposed by. In particular, we observe that the paper does not describe how to implement the term of order zero of the operator WSL is based on. While this does not affect the theoretical validity of WSL, it poses obstacles for practitioners aiming to use WSL because, as we show in our experiments, an incorrect implementation leads to states with very poor fidelity. In this paper, we describe how to implement the full quantum circuit required by WSL, including the term of order zero, releasing our source code online, and show that the algorithm works correctly. Finally, we empirically show how, as was theoretically demonstrated in the original article, truncated WSL does not prepare well highly entangled states.