Codes as fractals and noncommutative spaces
Matilde Marcolli, Christopher Perez
TL;DR
This paper explores the geometric and noncommutative space structures underlying classical and quantum codes, linking coding theory with noncommutative geometry and fractal analysis.
Contribution
It introduces a novel framework connecting classical and quantum codes to geometric spaces derived from noncommutative geometry and fractals.
Findings
Classical and quantum codes can be associated with geometric spaces from noncommutative tori.
The framework links coding theory with noncommutative geometry and fractal structures.
New insights into the geometric interpretation of quantum stabilizer codes.
Abstract
We consider the CSS algorithm relating self-orthogonal classical linear codes to q-ary quantum stabilizer codes and we show that to such a pair of a classical and a quantum code one can associate geometric spaces constructed using methods from noncommutative geometry, arising from rational noncommutative tori and finite abelian group actions on Cuntz algebras and fractals associated to the classical codes.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Quantum Computing Algorithms and Architecture · Computability, Logic, AI Algorithms