Year: 2026
Type: preprint
Abstract: We derive approximation rates for Sobolev functions defined on the complex unit sphere and complex projective space, representing quantum states, and on the special and projective unitary groups, representing quantum unitary operations. By using harmonic analysis on compact groups and compact homogeneous spaces, we characterize the corresponding Peter--Weyl decompositions and Sobolev spaces via irreducible representations and the Laplace--Beltrami operator. Combining spectral truncation with finite-depth quantum-circuit approximation, invoking the Solovay--Kitaev theorem, we establish quantitative rates that separate the spectral truncation error from the circuit approximation error.
Source: arXiv (Cornell University)
Author: Schmocker, Philipp
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221522758