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The Childs et al. (2017) algorithm can solve the quantum linear systems problem (QLSP) in $\operatorname{poly}(\log N, \log(1/\epsilon))$ time while the HHL algorithm solves it in $\operatorname{poly}(\log N, 1/\epsilon)$ time. So, if the Childs algorithm is superior, then why is the HHL more popular?

Additionally, are there any examples of the Childs algorithm being used to solve a system of equations on a real or simulated quantum computer?

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    $\begingroup$ I suppose only because HHL came earlier and is easier to understand? $\endgroup$
    – wdaochen
    Mar 26 at 17:05
  • $\begingroup$ Yea, that makes sense. I was just wondering if there is a technical reason for it. $\endgroup$ Mar 26 at 18:24

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