Multivariable Quantum Signal Processing (M-QSP) [1] is expected to provide an efficient means to handle polynomial transformations of multiple variables simultaneously. However, we identified several inconsistencies in the main theorem, where necessary and sufficient conditions for achievable polynomials are provided, and its proof in Ref. [1]. Moreover, a counterexample to the conjecture in Ref. [1], based on which the main theorem is constructed, is presented in Ref. [2], meaning the requirement of the conjecture should be included as a condition in the theorem. Here we note our observations and propose the revised necessary conditions for M-QSP. We also show that these necessary conditions cannot be sufficient conditions, and thus some additional condition on top of these revisions is essentially required for the complete M-QSP theorem.

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评论 “多变量量子信号处理 （M-QSP）：双头预言”


多变量量子信号处理 （M-QSP） [1] 有望提供一种有效的方法来同时处理多个变量的多项式变换。然而，我们在主定理中发现了几个不一致的地方，其中提供了可实现多项式的必要和充分条件，其证明见参考文献 [1]。此外，参考文献 [2] 中给出了参考文献 [1] 中猜想的反例，主定理就是基于该猜想构建的，这意味着猜想的要求应该作为条件包含在定理中。在这里，我们记录了我们的观察结果，并提出了修订后的 M-QSP 必要条件。我们还表明，这些必要条件不能是充分条件，因此，在这些修订之上的一些附加条件对于完整的 M-QSP 定理来说基本上是必需的。