Quantum Kolmogorov--Arnold representation theorem for continuous unitary-valued maps
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 foundational result has recently inspired the development of Kolmogorov--Arnold Networks (KANs) in classical machine learning, as well as their extensions into the quantum domain (QKANs). In this paper, we establish two quantum analogues of the Kolmogorov--Arnold representation theorem for continuous unitary-valued maps of several variables within an open $1$-neighbourhood of the identity matrix \(O_1(\mathbf{I}) \subset \mathcal{U}(n)\). First, we prove a representation...
| Authors | Sviatoslav V. Dzhenzher |
|---|---|
| Primary category | quant-ph |
| Published | 3 July 2026 |
| Last updated at source | 4 September 2026 |
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