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This is the QCSE version of What should you do if you spotted a non-trivial error in a highly cited paper? (maybe replace "highly cited" with "moderately cited" and "a non-trivial" with "several minor").

While going through the pre-print v2 as well as the published version of the paper `Quantum Circuit Design for Solving Linear Systems of Equations' by Cao et al., I found several errors in the paper:

  1. In the published version the connections of the $e^{iAt/2^i}$ gates are connected to clock register in the wrong order (Figure 4).

  2. In the pre-print the gates $e^{-iAt/2^i}$ should actually have been $e^{iAt/2^i}$ (Figure 4).

  3. In the pre-print the gate decomposition of $e^{iAt/2^i}$ is wrong. The last $Z$ gate must have been a controlled $Z$.

  4. The $5$ coefficients of the gate decompositions are wrong in both the pre-print and published version. Only the coefficients given for $e^{iAt/16}$ are fine but the rest they have to be found by some method of multivariable optimization (this was implemented by @Nelimee in QISKit and I had verified it)

  5. No SWAP gate is required in the circuit, as explained by @DaftWullie here.

  6. They skipped most explanations of why they chose the specific form of matrix $A$ in the paper, and everything about the scaling required.

Anyhow, this paper was essentially what I worked on, through the summer and I need to write a report on what I did, which might be put up on arXiv (and maybe for publishing, probably in QIP, later on, if I can think of sufficiently original material).

Now, I'm not sure how the quantum computing academic community looks at these type of "correction papers". So, basically, is it ethical to write up a correction paper like this (which doesn't correct a "huge" mistake in a "highly cited" paper but rather several small mistakes in a "moderately cited" paper) or are they highly frowned upon? In case the latter is true, I'll probably avoid putting it up on arXiv and wait till I can come up with sufficiently original additions to the paper (like extending it to higher dimensions and making the circuit more general).

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When you believe there are errors in a paper, you have the opportunity to publish a "comment" on the paper, in the same journal that the paper was originally published. The paper to which you refer as published in Molecular Physics, and here is an example of a "comment" published in that very same journal in 2002, about a paper that was originally published in 1968.

However, be careful when publishing a comment. You are publicly saying that they have made errors in a piece of work on which they have spent a lot of time and energy. Before contacting the journal, you should notify the authors privately. Instead of telling them that you have found errors in their paper, ask them if your suggestions are correct. For example:

Dear Prof. Kais,
I found your paper "Quantum circuit design for solving linear systems of equations" very interesting and it was the subject of my summer project, for which I have to write a report now. While working through the paper I have found the following 6 points came up, which I would like to clarify with you: [here you can point out the 6 things you listed in your question, but I would recommend never to say they are "wrong" or they "skipped" something, but instead just say something like "I think the $Z$ should be a $cZ$, am I correct?"].

Colleagues have suggested that I publish a Comment on your article in Molecular Physics, but I would like to consult you on it first.

Most respectfully yours,
Blue

I have written an email like this before, and the author's response indicated to me that he agreed with me (on a much more profound error than the above 6 points: he had claimed something is in QMA but there was an error in his proof of that so it is still an open question whether or not it is in QMA), but it was clear from his response that he would be very angry at me if I published a Comment. I decided to swallow my pride and not publish the Comment. One day he might be the referee for one of my papers, or be the examiner for one of my grant proposals, and I do not want him to have bitterness towards me for publicly exposing that he made this mistake.

This author suggested that the two of us publish an "Erratum" instead of a "Comment", so he could be a co-author on the paper saying that there was an error in the original, but in the end we didn't even do that. Comment and Erratum papers, like the one you may be considering to write in this case, are not so helpful for your CV anyway. They are not regarded at nearly the same level as an "original" paper. I have never published a Comment, and I only know a small number of people who have. The important thing is that you now know the problems with the original paper and the corrections to those problems, and it's up to the original authors whether or not they want to publish an Erratum.


There is also a journal where you can publish a re-analysis of other people's papers, which most people don't know about. It's the "Analysis" section in the journal Nature. They allow you to publish a re-analysis of other people's already published work, but they do this very rarely. The only example I know is this paper. Nature is not likely to publish the 6 minor things that you point out, because the standards in Nature are very high and you would have to find a much more profound re-analysis of the original paper rather than just 6 minor errors.

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