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Quantum analogues of Kolmogorov-Arnold theorem established for unitary maps

By PulseAugur Editorial · [1 sources] ·

Researchers have established two quantum analogues of the Kolmogorov-Arnold representation theorem, which deals with the decomposition of continuous multivariate functions. These new theorems apply to continuous unitary-valued maps, specifically addressing anti-Hermitian-valued maps and providing a factorized version for quantum operators due to their non-commutative nature. The findings demonstrate that these local representation theorems cannot be globally extended to the entire unitary group. AI

IMPACT Establishes theoretical foundations that could influence future quantum machine learning architectures.

RANK_REASON Academic paper detailing a new theoretical result in quantum mathematics. [lever_c_demoted from research: ic=1 ai=0.7]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

Quantum analogues of Kolmogorov-Arnold theorem established for unitary maps

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Academic paper detailing a new theoretical result in quantum mathematics. [lever_c_demoted from research: ic=1 ai=0.7]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Sviatoslav V. Dzhenzher ·

    Quantum Kolmogorov--Arnold representation theorem for continuous unitary-valued maps

    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…

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