English(EN) Quantum Kolmogorov--Arnold representation theorem for continuous unitary-valued maps

Kolmogorov-Arnold定理的量子类似物已为酉映射建立

作者 PulseAugur 编辑部 · [1 个来源] · 2026-07-07 04:00

研究人员建立了Kolmogorov-Arnold表示定理的两个量子类似物，该定理处理连续多元函数的分解。这些新定理适用于连续酉值映射，特别是处理反厄米值映射，并由于量子算子的非交换性质为其提供了因子化版本。研究结果表明，这些局部表示定理不能全局扩展到整个酉群。 AI

影响建立了可能影响未来量子机器学习架构的理论基础。

排序理由详细介绍量子数学新理论成果的学术论文。[lever_c_demoted from research: ic=1 ai=0.7]

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arXiv cs.LG TIER_1 English(EN) · Sviatoslav V. Dzhenzher · 2026-07-07 04:00

连续酉值映射的量子Kolmogorov--Arnold表示定理

arXiv:2607.03187v1 Announce Type: cross Abstract: The classical Kolmogorov--Arnold representation theorem states that any continuous multivariate function can be exactly decomposed into a finite composition of univariate continuous functions and addition operations. This foundati…