Comment on “Multivariable quantum signal processing (M-QSP): prophecies of the two-headed oracle”

IF 5.1 2区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY Quantum Pub Date : 2024-10-29 DOI:10.22331/q-2024-10-29-1512
Hitomi Mori, Kaoru Mizuta, Keisuke Fujii
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Abstract

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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关于 "多变量量子信号处理(M-QSP):双头神谕的预言 "的评论
多变量量子信号处理(M-QSP)[1] 被认为是同时处理多变量多项式变换的有效方法。然而,我们发现主定理(其中提供了可实现多项式的必要条件和充分条件)与参考文献[1]中的证明存在若干不一致之处。[1].此外,参考文献[1]中的猜想有一个反例。[1] 中猜想的反例,并在此基础上构建了主定理。[2],这意味着猜想的要求应作为条件包含在定理中。在此,我们指出了我们的观察结果,并提出了修改后的 M-QSP 必要条件。我们还证明了这些必要条件不可能是充分条件,因此在这些修订的基础上还需要一些附加条件才能得到完整的 M-QSP 定理。
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来源期刊
Quantum
Quantum Physics and Astronomy-Physics and Astronomy (miscellaneous)
CiteScore
9.20
自引率
10.90%
发文量
241
审稿时长
16 weeks
期刊介绍: Quantum is an open-access peer-reviewed journal for quantum science and related fields. Quantum is non-profit and community-run: an effort by researchers and for researchers to make science more open and publishing more transparent and efficient.
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