A Note On One Realization of a Scalable Shor Algorithm

TL;DR

This paper critiques a recent demonstration of a scalable Shor algorithm on ion-trap quantum computers, highlighting flaws in the circuit design and lack of clear explanation of its principles, correctness, and complexity.

Contribution

It identifies critical flaws in a recent experimental implementation of a scalable Shor algorithm and clarifies the underlying principles and complexities involved.

Findings

The reported circuit diagram has three flaws.

The principles and correctness of the demonstration are not properly explained.

The complexity analysis of the algorithm is lacking.

Abstract

Very recently, Monz, et al. [arXiv:1507.08852] have reported the demonstration of factoring 15 using a scalable Shor algorithm with an ion-trap quantum computer. In this note, we remark that the report is somewhat misleading because there are three flaws in the proposed circuit diagram of Shor algorithm. We also remark that the principles behind the demonstration have not been explained properly, including its correctness and complexity.